Introduction and Motivation

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# Introduction and Motivation
## High Dimensional Data Analysis
### Anastasios Panagiotelis & Ruben Loaiza-Maya
### Lecture 1

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# A Data Story

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# High-Dimensional Data?

- First what do we mean by *High Dimensional*?
- The data we look at will have:
  + Observations
  + Variables
- Generally *High Dimensional* implies that the number of *variables* is large.
--

- The term, high-dimensional also relates thinking about and visualising data as points in space.

---

# US States

- Five indicators of the quality of life in the 50 States of the USA in 1977.
  - Income,
  - Illiteracy rate,  
  - High school graduation rate,
  - Life expectancy,
  - Murder rates.
- Let's explore!
---

# A dataset

<div style="border: 1px solid #ddd; padding: 0px; overflow-y: scroll; height:500px; "><table class="table table-striped table-hover table-condensed" style="margin-left: auto; margin-right: auto;">
 <thead>
  <tr>
   <th style="text-align:left;position: sticky; top:0; background-color: #FFFFFF;"> State </th>
   <th style="text-align:right;position: sticky; top:0; background-color: #FFFFFF;"> Income </th>
   <th style="text-align:right;position: sticky; top:0; background-color: #FFFFFF;"> Illiteracy </th>
   <th style="text-align:right;position: sticky; top:0; background-color: #FFFFFF;"> LifeExp </th>
   <th style="text-align:right;position: sticky; top:0; background-color: #FFFFFF;"> Murder </th>
   <th style="text-align:right;position: sticky; top:0; background-color: #FFFFFF;"> HSGrad </th>
   <th style="text-align:left;position: sticky; top:0; background-color: #FFFFFF;"> StateAbb </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> Alabama </td>
   <td style="text-align:right;"> 3624 </td>
   <td style="text-align:right;"> 2.1 </td>
   <td style="text-align:right;"> 69.05 </td>
   <td style="text-align:right;"> 15.1 </td>
   <td style="text-align:right;"> 41.3 </td>
   <td style="text-align:left;"> AL </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Alaska </td>
   <td style="text-align:right;"> 6315 </td>
   <td style="text-align:right;"> 1.5 </td>
   <td style="text-align:right;"> 69.31 </td>
   <td style="text-align:right;"> 11.3 </td>
   <td style="text-align:right;"> 66.7 </td>
   <td style="text-align:left;"> AK </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Arizona </td>
   <td style="text-align:right;"> 4530 </td>
   <td style="text-align:right;"> 1.8 </td>
   <td style="text-align:right;"> 70.55 </td>
   <td style="text-align:right;"> 7.8 </td>
   <td style="text-align:right;"> 58.1 </td>
   <td style="text-align:left;"> AZ </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Arkansas </td>
   <td style="text-align:right;"> 3378 </td>
   <td style="text-align:right;"> 1.9 </td>
   <td style="text-align:right;"> 70.66 </td>
   <td style="text-align:right;"> 10.1 </td>
   <td style="text-align:right;"> 39.9 </td>
   <td style="text-align:left;"> AR </td>
  </tr>
  <tr>
   <td style="text-align:left;"> California </td>
   <td style="text-align:right;"> 5114 </td>
   <td style="text-align:right;"> 1.1 </td>
   <td style="text-align:right;"> 71.71 </td>
   <td style="text-align:right;"> 10.3 </td>
   <td style="text-align:right;"> 62.6 </td>
   <td style="text-align:left;"> CA </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Colorado </td>
   <td style="text-align:right;"> 4884 </td>
   <td style="text-align:right;"> 0.7 </td>
   <td style="text-align:right;"> 72.06 </td>
   <td style="text-align:right;"> 6.8 </td>
   <td style="text-align:right;"> 63.9 </td>
   <td style="text-align:left;"> CO </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Connecticut </td>
   <td style="text-align:right;"> 5348 </td>
   <td style="text-align:right;"> 1.1 </td>
   <td style="text-align:right;"> 72.48 </td>
   <td style="text-align:right;"> 3.1 </td>
   <td style="text-align:right;"> 56.0 </td>
   <td style="text-align:left;"> CT </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Delaware </td>
   <td style="text-align:right;"> 4809 </td>
   <td style="text-align:right;"> 0.9 </td>
   <td style="text-align:right;"> 70.06 </td>
   <td style="text-align:right;"> 6.2 </td>
   <td style="text-align:right;"> 54.6 </td>
   <td style="text-align:left;"> DE </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Florida </td>
   <td style="text-align:right;"> 4815 </td>
   <td style="text-align:right;"> 1.3 </td>
   <td style="text-align:right;"> 70.66 </td>
   <td style="text-align:right;"> 10.7 </td>
   <td style="text-align:right;"> 52.6 </td>
   <td style="text-align:left;"> FL </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Georgia </td>
   <td style="text-align:right;"> 4091 </td>
   <td style="text-align:right;"> 2.0 </td>
   <td style="text-align:right;"> 68.54 </td>
   <td style="text-align:right;"> 13.9 </td>
   <td style="text-align:right;"> 40.6 </td>
   <td style="text-align:left;"> GA </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Hawaii </td>
   <td style="text-align:right;"> 4963 </td>
   <td style="text-align:right;"> 1.9 </td>
   <td style="text-align:right;"> 73.60 </td>
   <td style="text-align:right;"> 6.2 </td>
   <td style="text-align:right;"> 61.9 </td>
   <td style="text-align:left;"> HI </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Idaho </td>
   <td style="text-align:right;"> 4119 </td>
   <td style="text-align:right;"> 0.6 </td>
   <td style="text-align:right;"> 71.87 </td>
   <td style="text-align:right;"> 5.3 </td>
   <td style="text-align:right;"> 59.5 </td>
   <td style="text-align:left;"> ID </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Illinois </td>
   <td style="text-align:right;"> 5107 </td>
   <td style="text-align:right;"> 0.9 </td>
   <td style="text-align:right;"> 70.14 </td>
   <td style="text-align:right;"> 10.3 </td>
   <td style="text-align:right;"> 52.6 </td>
   <td style="text-align:left;"> IL </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Indiana </td>
   <td style="text-align:right;"> 4458 </td>
   <td style="text-align:right;"> 0.7 </td>
   <td style="text-align:right;"> 70.88 </td>
   <td style="text-align:right;"> 7.1 </td>
   <td style="text-align:right;"> 52.9 </td>
   <td style="text-align:left;"> IN </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Iowa </td>
   <td style="text-align:right;"> 4628 </td>
   <td style="text-align:right;"> 0.5 </td>
   <td style="text-align:right;"> 72.56 </td>
   <td style="text-align:right;"> 2.3 </td>
   <td style="text-align:right;"> 59.0 </td>
   <td style="text-align:left;"> IA </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Kansas </td>
   <td style="text-align:right;"> 4669 </td>
   <td style="text-align:right;"> 0.6 </td>
   <td style="text-align:right;"> 72.58 </td>
   <td style="text-align:right;"> 4.5 </td>
   <td style="text-align:right;"> 59.9 </td>
   <td style="text-align:left;"> KS </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Kentucky </td>
   <td style="text-align:right;"> 3712 </td>
   <td style="text-align:right;"> 1.6 </td>
   <td style="text-align:right;"> 70.10 </td>
   <td style="text-align:right;"> 10.6 </td>
   <td style="text-align:right;"> 38.5 </td>
   <td style="text-align:left;"> KY </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Louisiana </td>
   <td style="text-align:right;"> 3545 </td>
   <td style="text-align:right;"> 2.8 </td>
   <td style="text-align:right;"> 68.76 </td>
   <td style="text-align:right;"> 13.2 </td>
   <td style="text-align:right;"> 42.2 </td>
   <td style="text-align:left;"> LA </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Maine </td>
   <td style="text-align:right;"> 3694 </td>
   <td style="text-align:right;"> 0.7 </td>
   <td style="text-align:right;"> 70.39 </td>
   <td style="text-align:right;"> 2.7 </td>
   <td style="text-align:right;"> 54.7 </td>
   <td style="text-align:left;"> ME </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Maryland </td>
   <td style="text-align:right;"> 5299 </td>
   <td style="text-align:right;"> 0.9 </td>
   <td style="text-align:right;"> 70.22 </td>
   <td style="text-align:right;"> 8.5 </td>
   <td style="text-align:right;"> 52.3 </td>
   <td style="text-align:left;"> MD </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Massachusetts </td>
   <td style="text-align:right;"> 4755 </td>
   <td style="text-align:right;"> 1.1 </td>
   <td style="text-align:right;"> 71.83 </td>
   <td style="text-align:right;"> 3.3 </td>
   <td style="text-align:right;"> 58.5 </td>
   <td style="text-align:left;"> MA </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Michigan </td>
   <td style="text-align:right;"> 4751 </td>
   <td style="text-align:right;"> 0.9 </td>
   <td style="text-align:right;"> 70.63 </td>
   <td style="text-align:right;"> 11.1 </td>
   <td style="text-align:right;"> 52.8 </td>
   <td style="text-align:left;"> MI </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Minnesota </td>
   <td style="text-align:right;"> 4675 </td>
   <td style="text-align:right;"> 0.6 </td>
   <td style="text-align:right;"> 72.96 </td>
   <td style="text-align:right;"> 2.3 </td>
   <td style="text-align:right;"> 57.6 </td>
   <td style="text-align:left;"> MN </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Mississippi </td>
   <td style="text-align:right;"> 3098 </td>
   <td style="text-align:right;"> 2.4 </td>
   <td style="text-align:right;"> 68.09 </td>
   <td style="text-align:right;"> 12.5 </td>
   <td style="text-align:right;"> 41.0 </td>
   <td style="text-align:left;"> MS </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Missouri </td>
   <td style="text-align:right;"> 4254 </td>
   <td style="text-align:right;"> 0.8 </td>
   <td style="text-align:right;"> 70.69 </td>
   <td style="text-align:right;"> 9.3 </td>
   <td style="text-align:right;"> 48.8 </td>
   <td style="text-align:left;"> MO </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Montana </td>
   <td style="text-align:right;"> 4347 </td>
   <td style="text-align:right;"> 0.6 </td>
   <td style="text-align:right;"> 70.56 </td>
   <td style="text-align:right;"> 5.0 </td>
   <td style="text-align:right;"> 59.2 </td>
   <td style="text-align:left;"> MT </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Nebraska </td>
   <td style="text-align:right;"> 4508 </td>
   <td style="text-align:right;"> 0.6 </td>
   <td style="text-align:right;"> 72.60 </td>
   <td style="text-align:right;"> 2.9 </td>
   <td style="text-align:right;"> 59.3 </td>
   <td style="text-align:left;"> NE </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Nevada </td>
   <td style="text-align:right;"> 5149 </td>
   <td style="text-align:right;"> 0.5 </td>
   <td style="text-align:right;"> 69.03 </td>
   <td style="text-align:right;"> 11.5 </td>
   <td style="text-align:right;"> 65.2 </td>
   <td style="text-align:left;"> NV </td>
  </tr>
  <tr>
   <td style="text-align:left;"> New Hampshire </td>
   <td style="text-align:right;"> 4281 </td>
   <td style="text-align:right;"> 0.7 </td>
   <td style="text-align:right;"> 71.23 </td>
   <td style="text-align:right;"> 3.3 </td>
   <td style="text-align:right;"> 57.6 </td>
   <td style="text-align:left;"> NH </td>
  </tr>
  <tr>
   <td style="text-align:left;"> New Jersey </td>
   <td style="text-align:right;"> 5237 </td>
   <td style="text-align:right;"> 1.1 </td>
   <td style="text-align:right;"> 70.93 </td>
   <td style="text-align:right;"> 5.2 </td>
   <td style="text-align:right;"> 52.5 </td>
   <td style="text-align:left;"> NJ </td>
  </tr>
  <tr>
   <td style="text-align:left;"> New Mexico </td>
   <td style="text-align:right;"> 3601 </td>
   <td style="text-align:right;"> 2.2 </td>
   <td style="text-align:right;"> 70.32 </td>
   <td style="text-align:right;"> 9.7 </td>
   <td style="text-align:right;"> 55.2 </td>
   <td style="text-align:left;"> NM </td>
  </tr>
  <tr>
   <td style="text-align:left;"> New York </td>
   <td style="text-align:right;"> 4903 </td>
   <td style="text-align:right;"> 1.4 </td>
   <td style="text-align:right;"> 70.55 </td>
   <td style="text-align:right;"> 10.9 </td>
   <td style="text-align:right;"> 52.7 </td>
   <td style="text-align:left;"> NY </td>
  </tr>
  <tr>
   <td style="text-align:left;"> North Carolina </td>
   <td style="text-align:right;"> 3875 </td>
   <td style="text-align:right;"> 1.8 </td>
   <td style="text-align:right;"> 69.21 </td>
   <td style="text-align:right;"> 11.1 </td>
   <td style="text-align:right;"> 38.5 </td>
   <td style="text-align:left;"> NC </td>
  </tr>
  <tr>
   <td style="text-align:left;"> North Dakota </td>
   <td style="text-align:right;"> 5087 </td>
   <td style="text-align:right;"> 0.8 </td>
   <td style="text-align:right;"> 72.78 </td>
   <td style="text-align:right;"> 1.4 </td>
   <td style="text-align:right;"> 50.3 </td>
   <td style="text-align:left;"> ND </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Ohio </td>
   <td style="text-align:right;"> 4561 </td>
   <td style="text-align:right;"> 0.8 </td>
   <td style="text-align:right;"> 70.82 </td>
   <td style="text-align:right;"> 7.4 </td>
   <td style="text-align:right;"> 53.2 </td>
   <td style="text-align:left;"> OH </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Oklahoma </td>
   <td style="text-align:right;"> 3983 </td>
   <td style="text-align:right;"> 1.1 </td>
   <td style="text-align:right;"> 71.42 </td>
   <td style="text-align:right;"> 6.4 </td>
   <td style="text-align:right;"> 51.6 </td>
   <td style="text-align:left;"> OK </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Oregon </td>
   <td style="text-align:right;"> 4660 </td>
   <td style="text-align:right;"> 0.6 </td>
   <td style="text-align:right;"> 72.13 </td>
   <td style="text-align:right;"> 4.2 </td>
   <td style="text-align:right;"> 60.0 </td>
   <td style="text-align:left;"> OR </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Pennsylvania </td>
   <td style="text-align:right;"> 4449 </td>
   <td style="text-align:right;"> 1.0 </td>
   <td style="text-align:right;"> 70.43 </td>
   <td style="text-align:right;"> 6.1 </td>
   <td style="text-align:right;"> 50.2 </td>
   <td style="text-align:left;"> PA </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Rhode Island </td>
   <td style="text-align:right;"> 4558 </td>
   <td style="text-align:right;"> 1.3 </td>
   <td style="text-align:right;"> 71.90 </td>
   <td style="text-align:right;"> 2.4 </td>
   <td style="text-align:right;"> 46.4 </td>
   <td style="text-align:left;"> RI </td>
  </tr>
  <tr>
   <td style="text-align:left;"> South Carolina </td>
   <td style="text-align:right;"> 3635 </td>
   <td style="text-align:right;"> 2.3 </td>
   <td style="text-align:right;"> 67.96 </td>
   <td style="text-align:right;"> 11.6 </td>
   <td style="text-align:right;"> 37.8 </td>
   <td style="text-align:left;"> SC </td>
  </tr>
  <tr>
   <td style="text-align:left;"> South Dakota </td>
   <td style="text-align:right;"> 4167 </td>
   <td style="text-align:right;"> 0.5 </td>
   <td style="text-align:right;"> 72.08 </td>
   <td style="text-align:right;"> 1.7 </td>
   <td style="text-align:right;"> 53.3 </td>
   <td style="text-align:left;"> SD </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Tennessee </td>
   <td style="text-align:right;"> 3821 </td>
   <td style="text-align:right;"> 1.7 </td>
   <td style="text-align:right;"> 70.11 </td>
   <td style="text-align:right;"> 11.0 </td>
   <td style="text-align:right;"> 41.8 </td>
   <td style="text-align:left;"> TN </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Texas </td>
   <td style="text-align:right;"> 4188 </td>
   <td style="text-align:right;"> 2.2 </td>
   <td style="text-align:right;"> 70.90 </td>
   <td style="text-align:right;"> 12.2 </td>
   <td style="text-align:right;"> 47.4 </td>
   <td style="text-align:left;"> TX </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Utah </td>
   <td style="text-align:right;"> 4022 </td>
   <td style="text-align:right;"> 0.6 </td>
   <td style="text-align:right;"> 72.90 </td>
   <td style="text-align:right;"> 4.5 </td>
   <td style="text-align:right;"> 67.3 </td>
   <td style="text-align:left;"> UT </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Vermont </td>
   <td style="text-align:right;"> 3907 </td>
   <td style="text-align:right;"> 0.6 </td>
   <td style="text-align:right;"> 71.64 </td>
   <td style="text-align:right;"> 5.5 </td>
   <td style="text-align:right;"> 57.1 </td>
   <td style="text-align:left;"> VT </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Virginia </td>
   <td style="text-align:right;"> 4701 </td>
   <td style="text-align:right;"> 1.4 </td>
   <td style="text-align:right;"> 70.08 </td>
   <td style="text-align:right;"> 9.5 </td>
   <td style="text-align:right;"> 47.8 </td>
   <td style="text-align:left;"> VA </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Washington </td>
   <td style="text-align:right;"> 4864 </td>
   <td style="text-align:right;"> 0.6 </td>
   <td style="text-align:right;"> 71.72 </td>
   <td style="text-align:right;"> 4.3 </td>
   <td style="text-align:right;"> 63.5 </td>
   <td style="text-align:left;"> WA </td>
  </tr>
  <tr>
   <td style="text-align:left;"> West Virginia </td>
   <td style="text-align:right;"> 3617 </td>
   <td style="text-align:right;"> 1.4 </td>
   <td style="text-align:right;"> 69.48 </td>
   <td style="text-align:right;"> 6.7 </td>
   <td style="text-align:right;"> 41.6 </td>
   <td style="text-align:left;"> WV </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Wisconsin </td>
   <td style="text-align:right;"> 4468 </td>
   <td style="text-align:right;"> 0.7 </td>
   <td style="text-align:right;"> 72.48 </td>
   <td style="text-align:right;"> 3.0 </td>
   <td style="text-align:right;"> 54.5 </td>
   <td style="text-align:left;"> WI </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Wyoming </td>
   <td style="text-align:right;"> 4566 </td>
   <td style="text-align:right;"> 0.6 </td>
   <td style="text-align:right;"> 70.29 </td>
   <td style="text-align:right;"> 6.9 </td>
   <td style="text-align:right;"> 62.9 </td>
   <td style="text-align:left;"> WY </td>
  </tr>
</tbody>
</table></div>

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# Observations and Variables

On the previous slide and in general:

- Each row corresponds to an *observation*
  - In this example that is a State.
- Each column corresponds to a *variable* 
  - In this example that is an attribute of each State.

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# Histogram: Income

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# Scatter-plot: Income v Mortality

<div id="htmlwidget-cc6518da8d3cba40e0a2" style="width:100%;height:50%;" class="widgetframe html-widget"></div>
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# 3D Scatter-plot

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# 3D Scatter-plot

Click and drag to rotate

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* Copyright (C) 2009 Apple Inc. All Rights Reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the above copyright
*    notice, this list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
*    notice, this list of conditions and the following disclaimer in the
*    documentation and/or other materials provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY APPLE INC. ``AS IS'' AND ANY
* EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
* PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL APPLE INC. OR
* CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
* EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
* PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
* PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
* OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
* Copyright (2016) Duncan Murdoch - fixed CanvasMatrix4.ortho,
* cleaned up.
*/
/*
CanvasMatrix4 class
This class implements a 4x4 matrix. It has functions which
duplicate the functionality of the OpenGL matrix stack and
glut functions.
IDL:
[
Constructor(in CanvasMatrix4 matrix),           // copy passed matrix into new CanvasMatrix4
Constructor(in sequence<float> array)           // create new CanvasMatrix4 with 16 floats (row major)
Constructor()                                   // create new CanvasMatrix4 with identity matrix
]
interface CanvasMatrix4 {
attribute float m11;
attribute float m12;
attribute float m13;
attribute float m14;
attribute float m21;
attribute float m22;
attribute float m23;
attribute float m24;
attribute float m31;
attribute float m32;
attribute float m33;
attribute float m34;
attribute float m41;
attribute float m42;
attribute float m43;
attribute float m44;
void load(in CanvasMatrix4 matrix);                 // copy the values from the passed matrix
void load(in sequence<float> array);                // copy 16 floats into the matrix
sequence<float> getAsArray();                       // return the matrix as an array of 16 floats
WebGLFloatArray getAsCanvasFloatArray();           // return the matrix as a WebGLFloatArray with 16 values
void makeIdentity();                                // replace the matrix with identity
void transpose();                                   // replace the matrix with its transpose
void invert();                                      // replace the matrix with its inverse
void translate(in float x, in float y, in float z); // multiply the matrix by passed translation values on the right
void scale(in float x, in float y, in float z);     // multiply the matrix by passed scale values on the right
void rotate(in float angle,                         // multiply the matrix by passed rotation values on the right
in float x, in float y, in float z);    // (angle is in degrees)
void multRight(in CanvasMatrix matrix);             // multiply the matrix by the passed matrix on the right
void multLeft(in CanvasMatrix matrix);              // multiply the matrix by the passed matrix on the left
void ortho(in float left, in float right,           // multiply the matrix by the passed ortho values on the right
in float bottom, in float top,
in float near, in float far);
void frustum(in float left, in float right,         // multiply the matrix by the passed frustum values on the right
in float bottom, in float top,
in float near, in float far);
void perspective(in float fovy, in float aspect,    // multiply the matrix by the passed perspective values on the right
in float zNear, in float zFar);
void lookat(in float eyex, in float eyey, in float eyez,    // multiply the matrix by the passed lookat
in float ctrx, in float ctry, in float ctrz,    // values on the right
in float upx, in float upy, in float upz);
}
*/
CanvasMatrix4 = function(m)
{
if (typeof m == 'object') {
if ("length" in m && m.length >= 16) {
this.load(m[0], m[1], m[2], m[3], m[4], m[5], m[6], m[7], m[8], m[9], m[10], m[11], m[12], m[13], m[14], m[15]);
return;
}
else if (m instanceof CanvasMatrix4) {
this.load(m);
return;
}
}
this.makeIdentity();
};
CanvasMatrix4.prototype.load = function()
{
if (arguments.length == 1 && typeof arguments[0] == 'object') {
var matrix = arguments[0];
if ("length" in matrix && matrix.length == 16) {
this.m11 = matrix[0];
this.m12 = matrix[1];
this.m13 = matrix[2];
this.m14 = matrix[3];
this.m21 = matrix[4];
this.m22 = matrix[5];
this.m23 = matrix[6];
this.m24 = matrix[7];
this.m31 = matrix[8];
this.m32 = matrix[9];
this.m33 = matrix[10];
this.m34 = matrix[11];
this.m41 = matrix[12];
this.m42 = matrix[13];
this.m43 = matrix[14];
this.m44 = matrix[15];
return;
}
if (arguments[0] instanceof CanvasMatrix4) {
this.m11 = matrix.m11;
this.m12 = matrix.m12;
this.m13 = matrix.m13;
this.m14 = matrix.m14;
this.m21 = matrix.m21;
this.m22 = matrix.m22;
this.m23 = matrix.m23;
this.m24 = matrix.m24;
this.m31 = matrix.m31;
this.m32 = matrix.m32;
this.m33 = matrix.m33;
this.m34 = matrix.m34;
this.m41 = matrix.m41;
this.m42 = matrix.m42;
this.m43 = matrix.m43;
this.m44 = matrix.m44;
return;
}
}
this.makeIdentity();
};
CanvasMatrix4.prototype.getAsArray = function()
{
return [
this.m11, this.m12, this.m13, this.m14,
this.m21, this.m22, this.m23, this.m24,
this.m31, this.m32, this.m33, this.m34,
this.m41, this.m42, this.m43, this.m44
];
};
CanvasMatrix4.prototype.getAsWebGLFloatArray = function()
{
return new WebGLFloatArray(this.getAsArray());
};
CanvasMatrix4.prototype.makeIdentity = function()
{
this.m11 = 1;
this.m12 = 0;
this.m13 = 0;
this.m14 = 0;
this.m21 = 0;
this.m22 = 1;
this.m23 = 0;
this.m24 = 0;
this.m31 = 0;
this.m32 = 0;
this.m33 = 1;
this.m34 = 0;
this.m41 = 0;
this.m42 = 0;
this.m43 = 0;
this.m44 = 1;
};
CanvasMatrix4.prototype.transpose = function()
{
var tmp = this.m12;
this.m12 = this.m21;
this.m21 = tmp;
tmp = this.m13;
this.m13 = this.m31;
this.m31 = tmp;
tmp = this.m14;
this.m14 = this.m41;
this.m41 = tmp;
tmp = this.m23;
this.m23 = this.m32;
this.m32 = tmp;
tmp = this.m24;
this.m24 = this.m42;
this.m42 = tmp;
tmp = this.m34;
this.m34 = this.m43;
this.m43 = tmp;
};
CanvasMatrix4.prototype.invert = function()
{
// Calculate the 4x4 determinant
// If the determinant is zero,
// then the inverse matrix is not unique.
var det = this._determinant4x4();
if (Math.abs(det) < 1e-8)
return null;
this._makeAdjoint();
// Scale the adjoint matrix to get the inverse
this.m11 /= det;
this.m12 /= det;
this.m13 /= det;
this.m14 /= det;
this.m21 /= det;
this.m22 /= det;
this.m23 /= det;
this.m24 /= det;
this.m31 /= det;
this.m32 /= det;
this.m33 /= det;
this.m34 /= det;
this.m41 /= det;
this.m42 /= det;
this.m43 /= det;
this.m44 /= det;
};
CanvasMatrix4.prototype.translate = function(x,y,z)
{
if (x === undefined)
x = 0;
if (y === undefined)
y = 0;
if (z === undefined)
z = 0;
var matrix = new CanvasMatrix4();
matrix.m41 = x;
matrix.m42 = y;
matrix.m43 = z;
this.multRight(matrix);
};
CanvasMatrix4.prototype.scale = function(x,y,z)
{
if (x === undefined)
x = 1;
if (z === undefined) {
if (y === undefined) {
y = x;
z = x;
}
else
z = 1;
}
else if (y === undefined)
y = x;
var matrix = new CanvasMatrix4();
matrix.m11 = x;
matrix.m22 = y;
matrix.m33 = z;
this.multRight(matrix);
};
CanvasMatrix4.prototype.rotate = function(angle,x,y,z)
{
// angles are in degrees. Switch to radians
angle = angle / 180 * Math.PI;
angle /= 2;
var sinA = Math.sin(angle);
var cosA = Math.cos(angle);
var sinA2 = sinA * sinA;
// normalize
var length = Math.sqrt(x * x + y * y + z * z);
if (length === 0) {
// bad vector, just use something reasonable
x = 0;
y = 0;
z = 1;
} else if (length != 1) {
x /= length;
y /= length;
z /= length;
}
var mat = new CanvasMatrix4();
// optimize case where axis is along major axis
if (x == 1 && y === 0 && z === 0) {
mat.m11 = 1;
mat.m12 = 0;
mat.m13 = 0;
mat.m21 = 0;
mat.m22 = 1 - 2 * sinA2;
mat.m23 = 2 * sinA * cosA;
mat.m31 = 0;
mat.m32 = -2 * sinA * cosA;
mat.m33 = 1 - 2 * sinA2;
mat.m14 = mat.m24 = mat.m34 = 0;
mat.m41 = mat.m42 = mat.m43 = 0;
mat.m44 = 1;
} else if (x === 0 && y == 1 && z === 0) {
mat.m11 = 1 - 2 * sinA2;
mat.m12 = 0;
mat.m13 = -2 * sinA * cosA;
mat.m21 = 0;
mat.m22 = 1;
mat.m23 = 0;
mat.m31 = 2 * sinA * cosA;
mat.m32 = 0;
mat.m33 = 1 - 2 * sinA2;
mat.m14 = mat.m24 = mat.m34 = 0;
mat.m41 = mat.m42 = mat.m43 = 0;
mat.m44 = 1;
} else if (x === 0 && y === 0 && z == 1) {
mat.m11 = 1 - 2 * sinA2;
mat.m12 = 2 * sinA * cosA;
mat.m13 = 0;
mat.m21 = -2 * sinA * cosA;
mat.m22 = 1 - 2 * sinA2;
mat.m23 = 0;
mat.m31 = 0;
mat.m32 = 0;
mat.m33 = 1;
mat.m14 = mat.m24 = mat.m34 = 0;
mat.m41 = mat.m42 = mat.m43 = 0;
mat.m44 = 1;
} else {
var x2 = x*x;
var y2 = y*y;
var z2 = z*z;
mat.m11 = 1 - 2 * (y2 + z2) * sinA2;
mat.m12 = 2 * (x * y * sinA2 + z * sinA * cosA);
mat.m13 = 2 * (x * z * sinA2 - y * sinA * cosA);
mat.m21 = 2 * (y * x * sinA2 - z * sinA * cosA);
mat.m22 = 1 - 2 * (z2 + x2) * sinA2;
mat.m23 = 2 * (y * z * sinA2 + x * sinA * cosA);
mat.m31 = 2 * (z * x * sinA2 + y * sinA * cosA);
mat.m32 = 2 * (z * y * sinA2 - x * sinA * cosA);
mat.m33 = 1 - 2 * (x2 + y2) * sinA2;
mat.m14 = mat.m24 = mat.m34 = 0;
mat.m41 = mat.m42 = mat.m43 = 0;
mat.m44 = 1;
}
this.multRight(mat);
};
CanvasMatrix4.prototype.multRight = function(mat)
{
var m11 = (this.m11 * mat.m11 + this.m12 * mat.m21 +
this.m13 * mat.m31 + this.m14 * mat.m41);
var m12 = (this.m11 * mat.m12 + this.m12 * mat.m22 +
this.m13 * mat.m32 + this.m14 * mat.m42);
var m13 = (this.m11 * mat.m13 + this.m12 * mat.m23 +
this.m13 * mat.m33 + this.m14 * mat.m43);
var m14 = (this.m11 * mat.m14 + this.m12 * mat.m24 +
this.m13 * mat.m34 + this.m14 * mat.m44);
var m21 = (this.m21 * mat.m11 + this.m22 * mat.m21 +
this.m23 * mat.m31 + this.m24 * mat.m41);
var m22 = (this.m21 * mat.m12 + this.m22 * mat.m22 +
this.m23 * mat.m32 + this.m24 * mat.m42);
var m23 = (this.m21 * mat.m13 + this.m22 * mat.m23 +
this.m23 * mat.m33 + this.m24 * mat.m43);
var m24 = (this.m21 * mat.m14 + this.m22 * mat.m24 +
this.m23 * mat.m34 + this.m24 * mat.m44);
var m31 = (this.m31 * mat.m11 + this.m32 * mat.m21 +
this.m33 * mat.m31 + this.m34 * mat.m41);
var m32 = (this.m31 * mat.m12 + this.m32 * mat.m22 +
this.m33 * mat.m32 + this.m34 * mat.m42);
var m33 = (this.m31 * mat.m13 + this.m32 * mat.m23 +
this.m33 * mat.m33 + this.m34 * mat.m43);
var m34 = (this.m31 * mat.m14 + this.m32 * mat.m24 +
this.m33 * mat.m34 + this.m34 * mat.m44);
var m41 = (this.m41 * mat.m11 + this.m42 * mat.m21 +
this.m43 * mat.m31 + this.m44 * mat.m41);
var m42 = (this.m41 * mat.m12 + this.m42 * mat.m22 +
this.m43 * mat.m32 + this.m44 * mat.m42);
var m43 = (this.m41 * mat.m13 + this.m42 * mat.m23 +
this.m43 * mat.m33 + this.m44 * mat.m43);
var m44 = (this.m41 * mat.m14 + this.m42 * mat.m24 +
this.m43 * mat.m34 + this.m44 * mat.m44);
this.m11 = m11;
this.m12 = m12;
this.m13 = m13;
this.m14 = m14;
this.m21 = m21;
this.m22 = m22;
this.m23 = m23;
this.m24 = m24;
this.m31 = m31;
this.m32 = m32;
this.m33 = m33;
this.m34 = m34;
this.m41 = m41;
this.m42 = m42;
this.m43 = m43;
this.m44 = m44;
};
CanvasMatrix4.prototype.multLeft = function(mat)
{
var m11 = (mat.m11 * this.m11 + mat.m12 * this.m21 +
mat.m13 * this.m31 + mat.m14 * this.m41);
var m12 = (mat.m11 * this.m12 + mat.m12 * this.m22 +
mat.m13 * this.m32 + mat.m14 * this.m42);
var m13 = (mat.m11 * this.m13 + mat.m12 * this.m23 +
mat.m13 * this.m33 + mat.m14 * this.m43);
var m14 = (mat.m11 * this.m14 + mat.m12 * this.m24 +
mat.m13 * this.m34 + mat.m14 * this.m44);
var m21 = (mat.m21 * this.m11 + mat.m22 * this.m21 +
mat.m23 * this.m31 + mat.m24 * this.m41);
var m22 = (mat.m21 * this.m12 + mat.m22 * this.m22 +
mat.m23 * this.m32 + mat.m24 * this.m42);
var m23 = (mat.m21 * this.m13 + mat.m22 * this.m23 +
mat.m23 * this.m33 + mat.m24 * this.m43);
var m24 = (mat.m21 * this.m14 + mat.m22 * this.m24 +
mat.m23 * this.m34 + mat.m24 * this.m44);
var m31 = (mat.m31 * this.m11 + mat.m32 * this.m21 +
mat.m33 * this.m31 + mat.m34 * this.m41);
var m32 = (mat.m31 * this.m12 + mat.m32 * this.m22 +
mat.m33 * this.m32 + mat.m34 * this.m42);
var m33 = (mat.m31 * this.m13 + mat.m32 * this.m23 +
mat.m33 * this.m33 + mat.m34 * this.m43);
var m34 = (mat.m31 * this.m14 + mat.m32 * this.m24 +
mat.m33 * this.m34 + mat.m34 * this.m44);
var m41 = (mat.m41 * this.m11 + mat.m42 * this.m21 +
mat.m43 * this.m31 + mat.m44 * this.m41);
var m42 = (mat.m41 * this.m12 + mat.m42 * this.m22 +
mat.m43 * this.m32 + mat.m44 * this.m42);
var m43 = (mat.m41 * this.m13 + mat.m42 * this.m23 +
mat.m43 * this.m33 + mat.m44 * this.m43);
var m44 = (mat.m41 * this.m14 + mat.m42 * this.m24 +
mat.m43 * this.m34 + mat.m44 * this.m44);
this.m11 = m11;
this.m12 = m12;
this.m13 = m13;
this.m14 = m14;
this.m21 = m21;
this.m22 = m22;
this.m23 = m23;
this.m24 = m24;
this.m31 = m31;
this.m32 = m32;
this.m33 = m33;
this.m34 = m34;
this.m41 = m41;
this.m42 = m42;
this.m43 = m43;
this.m44 = m44;
};
CanvasMatrix4.prototype.ortho = function(left, right, bottom, top, near, far)
{
var tx = (left + right) / (left - right);
var ty = (top + bottom) / (bottom - top);
var tz = (far + near) / (near - far);
var matrix = new CanvasMatrix4();
matrix.m11 = 2 / (right - left);
matrix.m12 = 0;
matrix.m13 = 0;
matrix.m14 = 0;
matrix.m21 = 0;
matrix.m22 = 2 / (top - bottom);
matrix.m23 = 0;
matrix.m24 = 0;
matrix.m31 = 0;
matrix.m32 = 0;
matrix.m33 = -2 / (far - near);
matrix.m34 = 0;
matrix.m41 = tx;
matrix.m42 = ty;
matrix.m43 = tz;
matrix.m44 = 1;
this.multRight(matrix);
};
CanvasMatrix4.prototype.frustum = function(left, right, bottom, top, near, far)
{
var matrix = new CanvasMatrix4();
var A = (right + left) / (right - left);
var B = (top + bottom) / (top - bottom);
var C = -(far + near) / (far - near);
var D = -(2 * far * near) / (far - near);
matrix.m11 = (2 * near) / (right - left);
matrix.m12 = 0;
matrix.m13 = 0;
matrix.m14 = 0;
matrix.m21 = 0;
matrix.m22 = 2 * near / (top - bottom);
matrix.m23 = 0;
matrix.m24 = 0;
matrix.m31 = A;
matrix.m32 = B;
matrix.m33 = C;
matrix.m34 = -1;
matrix.m41 = 0;
matrix.m42 = 0;
matrix.m43 = D;
matrix.m44 = 0;
this.multRight(matrix);
};
CanvasMatrix4.prototype.perspective = function(fovy, aspect, zNear, zFar)
{
var top = Math.tan(fovy * Math.PI / 360) * zNear;
var bottom = -top;
var left = aspect * bottom;
var right = aspect * top;
this.frustum(left, right, bottom, top, zNear, zFar);
};
CanvasMatrix4.prototype.lookat = function(eyex, eyey, eyez, centerx, centery, centerz, upx, upy, upz)
{
var matrix = new CanvasMatrix4();
// Make rotation matrix
// Z vector
var zx = eyex - centerx;
var zy = eyey - centery;
var zz = eyez - centerz;
var mag = Math.sqrt(zx * zx + zy * zy + zz * zz);
if (mag) {
zx /= mag;
zy /= mag;
zz /= mag;
}
// Y vector
var yx = upx;
var yy = upy;
var yz = upz;
// X vector = Y cross Z
xx =  yy * zz - yz * zy;
xy = -yx * zz + yz * zx;
xz =  yx * zy - yy * zx;
// Recompute Y = Z cross X
yx = zy * xz - zz * xy;
yy = -zx * xz + zz * xx;
yx = zx * xy - zy * xx;
// cross product gives area of parallelogram, which is < 1.0 for
// non-perpendicular unit-length vectors; so normalize x, y here
mag = Math.sqrt(xx * xx + xy * xy + xz * xz);
if (mag) {
xx /= mag;
xy /= mag;
xz /= mag;
}
mag = Math.sqrt(yx * yx + yy * yy + yz * yz);
if (mag) {
yx /= mag;
yy /= mag;
yz /= mag;
}
matrix.m11 = xx;
matrix.m12 = xy;
matrix.m13 = xz;
matrix.m14 = 0;
matrix.m21 = yx;
matrix.m22 = yy;
matrix.m23 = yz;
matrix.m24 = 0;
matrix.m31 = zx;
matrix.m32 = zy;
matrix.m33 = zz;
matrix.m34 = 0;
matrix.m41 = 0;
matrix.m42 = 0;
matrix.m43 = 0;
matrix.m44 = 1;
matrix.translate(-eyex, -eyey, -eyez);
this.multRight(matrix);
};
// Support functions
CanvasMatrix4.prototype._determinant2x2 = function(a, b, c, d)
{
return a * d - b * c;
};
CanvasMatrix4.prototype._determinant3x3 = function(a1, a2, a3, b1, b2, b3, c1, c2, c3)
{
return a1 * this._determinant2x2(b2, b3, c2, c3) -
b1 * this._determinant2x2(a2, a3, c2, c3) +
c1 * this._determinant2x2(a2, a3, b2, b3);
};
CanvasMatrix4.prototype._determinant4x4 = function()
{
var a1 = this.m11;
var b1 = this.m12;
var c1 = this.m13;
var d1 = this.m14;
var a2 = this.m21;
var b2 = this.m22;
var c2 = this.m23;
var d2 = this.m24;
var a3 = this.m31;
var b3 = this.m32;
var c3 = this.m33;
var d3 = this.m34;
var a4 = this.m41;
var b4 = this.m42;
var c4 = this.m43;
var d4 = this.m44;
return a1 * this._determinant3x3(b2, b3, b4, c2, c3, c4, d2, d3, d4) -
b1 * this._determinant3x3(a2, a3, a4, c2, c3, c4, d2, d3, d4) +
c1 * this._determinant3x3(a2, a3, a4, b2, b3, b4, d2, d3, d4) -
d1 * this._determinant3x3(a2, a3, a4, b2, b3, b4, c2, c3, c4);
};
CanvasMatrix4.prototype._makeAdjoint = function()
{
var a1 = this.m11;
var b1 = this.m12;
var c1 = this.m13;
var d1 = this.m14;
var a2 = this.m21;
var b2 = this.m22;
var c2 = this.m23;
var d2 = this.m24;
var a3 = this.m31;
var b3 = this.m32;
var c3 = this.m33;
var d3 = this.m34;
var a4 = this.m41;
var b4 = this.m42;
var c4 = this.m43;
var d4 = this.m44;
// Row column labeling reversed since we transpose rows & columns
this.m11  =   this._determinant3x3(b2, b3, b4, c2, c3, c4, d2, d3, d4);
this.m21  = - this._determinant3x3(a2, a3, a4, c2, c3, c4, d2, d3, d4);
this.m31  =   this._determinant3x3(a2, a3, a4, b2, b3, b4, d2, d3, d4);
this.m41  = - this._determinant3x3(a2, a3, a4, b2, b3, b4, c2, c3, c4);
this.m12  = - this._determinant3x3(b1, b3, b4, c1, c3, c4, d1, d3, d4);
this.m22  =   this._determinant3x3(a1, a3, a4, c1, c3, c4, d1, d3, d4);
this.m32  = - this._determinant3x3(a1, a3, a4, b1, b3, b4, d1, d3, d4);
this.m42  =   this._determinant3x3(a1, a3, a4, b1, b3, b4, c1, c3, c4);
this.m13  =   this._determinant3x3(b1, b2, b4, c1, c2, c4, d1, d2, d4);
this.m23  = - this._determinant3x3(a1, a2, a4, c1, c2, c4, d1, d2, d4);
this.m33  =   this._determinant3x3(a1, a2, a4, b1, b2, b4, d1, d2, d4);
this.m43  = - this._determinant3x3(a1, a2, a4, b1, b2, b4, c1, c2, c4);
this.m14  = - this._determinant3x3(b1, b2, b3, c1, c2, c3, d1, d2, d3);
this.m24  =   this._determinant3x3(a1, a2, a3, c1, c2, c3, d1, d2, d3);
this.m34  = - this._determinant3x3(a1, a2, a3, b1, b2, b3, d1, d2, d3);
this.m44  =   this._determinant3x3(a1, a2, a3, b1, b2, b3, c1, c2, c3);
};</script>
<script>// To generate the help pages for this library, use
// jsdoc --destination ../../../doc/rglwidgetClass --template ~/node_modules/jsdoc-baseline rglClass.src.js
// To validate, use
// setwd(".../inst/htmlwidgets/lib/rglClass")
// hints <- js::jshint(readLines("rglClass.src.js"))
// hints[, c("line", "reason")]
/**
* The class of an rgl widget
* @class
*/
rglwidgetClass = function() {
this.canvas = null;
this.userMatrix = new CanvasMatrix4();
this.types = [];
this.prMatrix = new CanvasMatrix4();
this.mvMatrix = new CanvasMatrix4();
this.vp = null;
this.prmvMatrix = null;
this.origs = null;
this.gl = null;
this.scene = null;
this.select = {state: "inactive", subscene: null, region: {p1: {x:0, y:0}, p2: {x:0, y:0}}};
this.drawing = false;
};
/**
* Multiply matrix by vector
* @returns {number[]}
* @param M {number[][]} Left operand
* @param v {number[]} Right operand
*/
rglwidgetClass.prototype.multMV = function(M, v) {
return [ M.m11 * v[0] + M.m12 * v[1] + M.m13 * v[2] + M.m14 * v[3],
M.m21 * v[0] + M.m22 * v[1] + M.m23 * v[2] + M.m24 * v[3],
M.m31 * v[0] + M.m32 * v[1] + M.m33 * v[2] + M.m34 * v[3],
M.m41 * v[0] + M.m42 * v[1] + M.m43 * v[2] + M.m44 * v[3]
];
};
/**
* Multiply row vector by Matrix
* @returns {number[]}
* @param v {number[]} left operand
* @param M {number[][]} right operand
*/
rglwidgetClass.prototype.multVM = function(v, M) {
return [ M.m11 * v[0] + M.m21 * v[1] + M.m31 * v[2] + M.m41 * v[3],
M.m12 * v[0] + M.m22 * v[1] + M.m32 * v[2] + M.m42 * v[3],
M.m13 * v[0] + M.m23 * v[1] + M.m33 * v[2] + M.m43 * v[3],
M.m14 * v[0] + M.m24 * v[1] + M.m34 * v[2] + M.m44 * v[3]
];
};
/**
* Euclidean length of a vector
* @returns {number}
* @param v {number[]}
*/
rglwidgetClass.prototype.vlen = function(v) {
return Math.sqrt(this.dotprod(v, v));
};
/**
* Dot product of two vectors
* @instance rglwidgetClass
* @returns {number}
* @param a {number[]}
* @param b {number[]}
*/
rglwidgetClass.prototype.dotprod = function(a, b) {
return a[0]*b[0] + a[1]*b[1] + a[2]*b[2];
};
/**
* Cross product of two vectors
* @returns {number[]}
* @param a {number[]}
* @param b {number[]}
*/
rglwidgetClass.prototype.xprod = function(a, b) {
return [a[1]*b[2] - a[2]*b[1],
a[2]*b[0] - a[0]*b[2],
a[0]*b[1] - a[1]*b[0]];
};
/**
* Bind vectors or matrices by columns
* @returns {number[][]}
* @param a {number[]|number[][]}
* @param b {number[]|number[][]}
*/
rglwidgetClass.prototype.cbind = function(a, b) {
if (b.length < a.length)
b = this.repeatToLen(b, a.length);
else if (a.length < b.length)
a = this.repeatToLen(a, b.length);
return a.map(function(currentValue, index, array) {
return currentValue.concat(b[index]);
});
};
/**
* Swap elements
* @returns {any[]}
* @param a {any[]}
* @param i {number} Element to swap
* @param j {number} Other element to swap
*/
rglwidgetClass.prototype.swap = function(a, i, j) {
var temp = a[i];
a[i] = a[j];
a[j] = temp;
};
/**
* Flatten a matrix into a vector
* @returns {any[]}
* @param a {any[][]}
*/
rglwidgetClass.prototype.flatten = function(arr, result) {
var value;
if (typeof result === "undefined") result = [];
for (var i = 0, length = arr.length; i < length; i++) {
value = arr[i];
if (Array.isArray(value)) {
this.flatten(value, result);
} else {
result.push(value);
}
}
return result;
};
/**
* set element of 1d or 2d array as if it was flattened.
* Column major, zero based!
* @returns {any[]|any[][]}
* @param {any[]|any[][]} a - array
* @param {number} i - element
* @param {any} value
*/
rglwidgetClass.prototype.setElement = function(a, i, value) {
if (Array.isArray(a[0])) {
var dim = a.length,
col = Math.floor(i/dim),
row = i % dim;
a[row][col] = value;
} else {
a[i] = value;
}
};
/**
* Transpose an array
* @returns {any[][]}
* @param {any[][]} a
*/
rglwidgetClass.prototype.transpose = function(a) {
var newArray = [],
n = a.length,
m = a[0].length,
i;
for(i = 0; i < m; i++){
newArray.push([]);
}
for(i = 0; i < n; i++){
for(var j = 0; j < m; j++){
newArray[j].push(a[i][j]);
}
}
return newArray;
};
/**
* Calculate sum of squares of a numeric vector
* @returns {number}
* @param {number[]} x
*/
rglwidgetClass.prototype.sumsq = function(x) {
var result = 0, i;
for (i=0; i < x.length; i++)
result += x[i]*x[i];
return result;
};
/**
* Convert a matrix to a CanvasMatrix4
* @returns {CanvasMatrix4}
* @param {number[][]|number[]} mat
*/
rglwidgetClass.prototype.toCanvasMatrix4 = function(mat) {
if (mat instanceof CanvasMatrix4)
return mat;
var result = new CanvasMatrix4();
mat = this.flatten(this.transpose(mat));
result.load(mat);
return result;
};
/**
* Convert an R-style numeric colour string to an rgb vector
* @returns {number[]}
* @param {string} s
*/
rglwidgetClass.prototype.stringToRgb = function(s) {
s = s.replace("#", "");
var bigint = parseInt(s, 16);
return [((bigint >> 16) & 255)/255,
((bigint >> 8) & 255)/255,
(bigint & 255)/255];
};
/**
* Take a component-by-component product of two 3 vectors
* @returns {number[]}
* @param {number[]} x
* @param {number[]} y
*/
rglwidgetClass.prototype.componentProduct = function(x, y) {
if (typeof y === "undefined") {
this.alertOnce("Bad arg to componentProduct");
}
var result = new Float32Array(3), i;
for (i = 0; i<3; i++)
result[i] = x[i]*y[i];
return result;
};
/**
* Get next higher power of two
* @returns { number }
* @param { number } value - input value
*/
rglwidgetClass.prototype.getPowerOfTwo = function(value) {
var pow = 1;
while(pow<value) {
pow *= 2;
}
return pow;
};
/**
* Unique entries
* @returns { any[] }
* @param { any[] } arr - An array
*/
rglwidgetClass.prototype.unique = function(arr) {
arr = [].concat(arr);
return arr.filter(function(value, index, self) {
return self.indexOf(value) === index;
});
};
/**
* Shallow compare of arrays
* @returns { boolean }
* @param { any[] } a - An array
* @param { any[] } b - Another array
*/
rglwidgetClass.prototype.equalArrays = function(a, b) {
return a === b || (a && b &&
a.length === b.length &&
a.every(function(v, i) {return v === b[i];}));
};
/**
* Repeat an array to a desired length
* @returns {any[]}
* @param {any | any[]} arr The input array
* @param {number} len The desired output length
*/
rglwidgetClass.prototype.repeatToLen = function(arr, len) {
arr = [].concat(arr);
while (arr.length < len/2)
arr = arr.concat(arr);
return arr.concat(arr.slice(0, len - arr.length));
};
/**
* Give a single alert message, not to be repeated.
* @param {string} msg  The message to give.
*/
rglwidgetClass.prototype.alertOnce = function(msg) {
if (typeof this.alerted !== "undefined")
return;
this.alerted = true;
alert(msg);
};
rglwidgetClass.prototype.f_is_lit = 1;
rglwidgetClass.prototype.f_is_smooth = 2;
rglwidgetClass.prototype.f_has_texture = 4;
rglwidgetClass.prototype.f_depth_sort = 8;
rglwidgetClass.prototype.f_fixed_quads = 16;
rglwidgetClass.prototype.f_is_transparent = 32;
rglwidgetClass.prototype.f_is_lines = 64;
rglwidgetClass.prototype.f_sprites_3d = 128;
rglwidgetClass.prototype.f_sprite_3d = 256;
rglwidgetClass.prototype.f_is_subscene = 512;
rglwidgetClass.prototype.f_is_clipplanes = 1024;
rglwidgetClass.prototype.f_fixed_size = 2048;
rglwidgetClass.prototype.f_is_points = 4096;
rglwidgetClass.prototype.f_is_twosided = 8192;
rglwidgetClass.prototype.f_fat_lines = 16384;
rglwidgetClass.prototype.f_is_brush = 32768;
/**
* Which list does a particular id come from?
* @returns { string }
* @param {number} id The id to look up.
*/
rglwidgetClass.prototype.whichList = function(id) {
var obj = this.getObj(id),
flags = obj.flags;
if (obj.type === "light")
return "lights";
if (flags & this.f_is_subscene)
return "subscenes";
if (flags & this.f_is_clipplanes)
return "clipplanes";
if (flags & this.f_is_transparent)
return "transparent";
return "opaque";
};
/**
* Get an object by id number.
* @returns { Object }
* @param {number} id
*/
rglwidgetClass.prototype.getObj = function(id) {
if (typeof id !== "number") {
this.alertOnce("getObj id is "+typeof id);
}
return this.scene.objects[id];
};
/**
* Get ids of a particular type from a subscene or the whole scene
* @returns { number[] }
* @param {string} type What type of object?
* @param {number} subscene  Which subscene?  If not given, find in the whole scene
*/
rglwidgetClass.prototype.getIdsByType = function(type, subscene) {
var
result = [], i, self = this;
if (typeof subscene === "undefined") {
Object.keys(this.scene.objects).forEach(
function(key) {
key = parseInt(key, 10);
if (self.getObj(key).type === type)
result.push(key);
});
} else {
ids = this.getObj(subscene).objects;
for (i=0; i < ids.length; i++) {
if (this.getObj(ids[i]).type === type) {
result.push(ids[i]);
}
}
}
return result;
};
/**
* Get a particular material property for an id
* @returns { any }
* @param {number} id  Which object?
* @param {string} property Which material property?
*/
rglwidgetClass.prototype.getMaterial = function(id, property) {
var obj = this.getObj(id), mat;
if (typeof obj.material === "undefined")
console.error("material undefined");
mat = obj.material[property];
if (typeof mat === "undefined")
mat = this.scene.material[property];
return mat;
};
/**
* Is a particular id in a subscene?
* @returns { boolean }
* @param {number} id Which id?
* @param {number} subscene Which subscene id?
*/
rglwidgetClass.prototype.inSubscene = function(id, subscene) {
return this.getObj(subscene).objects.indexOf(id) > -1;
};
/**
* Add an id to a subscene.
* @param {number} id Which id?
* @param {number} subscene Which subscene id?
*/
rglwidgetClass.prototype.addToSubscene = function(id, subscene) {
var thelist,
thesub = this.getObj(subscene),
ids = [id],
obj = this.getObj(id), i;
if (typeof obj != "undefined" && typeof (obj.newIds) !== "undefined") {
ids = ids.concat(obj.newIds);
}
thesub.objects = [].concat(thesub.objects);
for (i = 0; i < ids.length; i++) {
id = ids[i];
if (thesub.objects.indexOf(id) == -1) {
thelist = this.whichList(id);
thesub.objects.push(id);
thesub[thelist].push(id);
}
}
};
/**
* Delete an id from a subscene
* @param { number } id - the id to add
* @param { number } subscene - the id of the subscene
*/
rglwidgetClass.prototype.delFromSubscene = function(id, subscene) {
var thelist,
thesub = this.getObj(subscene),
obj = this.getObj(id),
ids = [id], i;
if (typeof obj !== "undefined" && typeof (obj.newIds) !== "undefined")
ids = ids.concat(obj.newIds);
thesub.objects = [].concat(thesub.objects); // It might be a scalar
for (j=0; j<ids.length;j++) {
id = ids[j];
i = thesub.objects.indexOf(id);
if (i > -1) {
thesub.objects.splice(i, 1);
thelist = this.whichList(id);
i = thesub[thelist].indexOf(id);
thesub[thelist].splice(i, 1);
}
}
};
/**
* Set the ids in a subscene
* @param { number[] } ids - the ids to set
* @param { number } subsceneid - the id of the subscene
*/
rglwidgetClass.prototype.setSubsceneEntries = function(ids, subsceneid) {
var sub = this.getObj(subsceneid);
sub.objects = ids;
this.initSubscene(subsceneid);
};
/**
* Get the ids in a subscene
* @returns {number[]}
* @param { number } subscene - the id of the subscene
*/
rglwidgetClass.prototype.getSubsceneEntries = function(subscene) {
return this.getObj(subscene).objects;
};
/**
* Get the ids of the subscenes within a subscene
* @returns { number[] }
* @param { number } subscene - the id of the subscene
*/
rglwidgetClass.prototype.getChildSubscenes = function(subscene) {
return this.getObj(subscene).subscenes;
};
/**
* Start drawing
* @returns { boolean } Previous state
*/
rglwidgetClass.prototype.startDrawing = function() {
var value = this.drawing;
this.drawing = true;
return value;
};
/**
* Stop drawing and check for context loss
* @param { boolean } saved - Previous state
*/
rglwidgetClass.prototype.stopDrawing = function(saved) {
this.drawing = saved;
if (!saved && this.gl && this.gl.isContextLost())
this.restartCanvas();
};
/**
* Generate the vertex shader for an object
* @returns {string}
* @param { number } id - Id of object
*/
rglwidgetClass.prototype.getVertexShader = function(id) {
var obj = this.getObj(id),
userShader = obj.userVertexShader,
flags = obj.flags,
type = obj.type,
is_lit = flags & this.f_is_lit,
has_texture = flags & this.f_has_texture,
fixed_quads = flags & this.f_fixed_quads,
sprites_3d = flags & this.f_sprites_3d,
sprite_3d = flags & this.f_sprite_3d,
nclipplanes = this.countClipplanes(),
fixed_size = flags & this.f_fixed_size,
is_points = flags & this.f_is_points,
is_twosided = flags & this.f_is_twosided,
fat_lines = flags & this.f_fat_lines,
is_brush = flags & this.f_is_brush,
result;
if (type === "clipplanes" || sprites_3d) return;
if (typeof userShader !== "undefined") return userShader;
result = "  /* ****** "+type+" object "+id+" vertex shader ****** */\n"+
"  attribute vec3 aPos;\n"+
"  attribute vec4 aCol;\n"+
" uniform mat4 mvMatrix;\n"+
" uniform mat4 prMatrix;\n"+
" varying vec4 vCol;\n"+
" varying vec4 vPosition;\n";
if ((is_lit && !fixed_quads && !is_brush) || sprite_3d)
result = result + "  attribute vec3 aNorm;\n"+
" uniform mat4 normMatrix;\n"+
" varying vec3 vNormal;\n";
if (has_texture || type === "text")
result = result + " attribute vec2 aTexcoord;\n"+
" varying vec2 vTexcoord;\n";
if (fixed_size)
result = result + "  uniform vec2 textScale;\n";
if (fixed_quads)
result = result + "  attribute vec2 aOfs;\n";
else if (sprite_3d)
result = result + "  uniform vec3 uOrig;\n"+
"  uniform float uSize;\n"+
"  uniform mat4 usermat;\n";
if (is_twosided)
result = result + "  attribute vec3 aPos1;\n"+
"  attribute vec3 aPos2;\n"+
"  varying float normz;\n";
if (fat_lines) {
result = result +   "  attribute vec3 aNext;\n"+
"  attribute vec2 aPoint;\n"+
"  varying vec2 vPoint;\n"+
"  varying float vLength;\n"+
"  uniform float uAspect;\n"+
"  uniform float uLwd;\n";
}
result = result + "  void main(void) {\n";
if ((nclipplanes || (!fixed_quads && !sprite_3d)) && !is_brush)
result = result + "    vPosition = mvMatrix * vec4(aPos, 1.);\n";
if (!fixed_quads && !sprite_3d && !is_brush)
result = result + "    gl_Position = prMatrix * vPosition;\n";
if (is_points) {
var size = this.getMaterial(id, "size");
result = result + "    gl_PointSize = "+size.toFixed(1)+";\n";
}
result = result + "    vCol = aCol;\n";
if (is_lit && !fixed_quads && !sprite_3d && !is_brush)
result = result + "    vNormal = normalize((normMatrix * vec4(aNorm, 1.)).xyz);\n";
if (has_texture || type == "text")
result = result + "    vTexcoord = aTexcoord;\n";
if (fixed_size)
result = result + "    vec4 pos = prMatrix * mvMatrix * vec4(aPos, 1.);\n"+
"   pos = pos/pos.w;\n"+
"   gl_Position = pos + vec4(aOfs*textScale, 0.,0.);\n";
if (type == "sprites" && !fixed_size)
result = result + "    vec4 pos = mvMatrix * vec4(aPos, 1.);\n"+
"   pos = pos/pos.w + vec4(aOfs, 0., 0.);\n"+
"   gl_Position = prMatrix*pos;\n";
if (sprite_3d)
result = result + "   vNormal = normalize((normMatrix * vec4(aNorm, 1.)).xyz);\n"+
"   vec4 pos = mvMatrix * vec4(uOrig, 1.);\n"+
"   vPosition = pos/pos.w + vec4(uSize*(vec4(aPos, 1.)*usermat).xyz,0.);\n"+
"   gl_Position = prMatrix * vPosition;\n";
if (is_twosided)
result = result + "   vec4 pos1 = prMatrix*(mvMatrix*vec4(aPos1, 1.));\n"+
"   pos1 = pos1/pos1.w - gl_Position/gl_Position.w;\n"+
"   vec4 pos2 = prMatrix*(mvMatrix*vec4(aPos2, 1.));\n"+
"   pos2 = pos2/pos2.w - gl_Position/gl_Position.w;\n"+
"   normz = pos1.x*pos2.y - pos1.y*pos2.x;\n";
if (fat_lines) 
/* This code was inspired by Matt Deslauriers' code in https://mattdesl.svbtle.com/drawing-lines-is-hard */
result = result + "   vec2 aspectVec = vec2(uAspect, 1.0);\n"+
"   mat4 projViewModel = prMatrix * mvMatrix;\n"+
"   vec4 currentProjected = projViewModel * vec4(aPos, 1.0);\n"+
"   currentProjected = currentProjected/currentProjected.w;\n"+
"   vec4 nextProjected = projViewModel * vec4(aNext, 1.0);\n"+
"   vec2 currentScreen = currentProjected.xy * aspectVec;\n"+
"   vec2 nextScreen = (nextProjected.xy / nextProjected.w) * aspectVec;\n"+
"   float len = uLwd;\n"+
"   vec2 dir = vec2(1.0, 0.0);\n"+
"   vPoint = aPoint;\n"+
"   vLength = length(nextScreen - currentScreen)/2.0;\n"+
"   vLength = vLength/(vLength + len);\n"+
"   if (vLength > 0.0) {\n"+
"     dir = normalize(nextScreen - currentScreen);\n"+
"   }\n"+
"   vec2 normal = vec2(-dir.y, dir.x);\n"+
"   dir.x /= uAspect;\n"+
"   normal.x /= uAspect;\n"+
"   vec4 offset = vec4(len*(normal*aPoint.x*aPoint.y - dir), 0.0, 0.0);\n"+
"   gl_Position = currentProjected + offset;\n";
if (is_brush)
result = result + "   gl_Position = vec4(aPos, 1.);\n";
result = result + "  }\n";
// console.log(result);
return result;
};
/**
* Generate the fragment shader for an object
* @returns {string}
* @param { number } id - Id of object
*/
rglwidgetClass.prototype.getFragmentShader = function(id) {
var obj = this.getObj(id),
userShader = obj.userFragmentShader,
flags = obj.flags,
type = obj.type,
is_lit = flags & this.f_is_lit,
has_texture = flags & this.f_has_texture,
fixed_quads = flags & this.f_fixed_quads,
sprites_3d = flags & this.f_sprites_3d,
is_twosided = (flags & this.f_is_twosided) > 0,
fat_lines = flags & this.f_fat_lines,
is_transparent = flags & this.f_is_transparent,
nclipplanes = this.countClipplanes(), i,
texture_format, nlights,
result;
if (type === "clipplanes" || sprites_3d) return;
if (typeof userShader !== "undefined") return userShader;
if (has_texture)
texture_format = this.getMaterial(id, "textype");
result = "/* ****** "+type+" object "+id+" fragment shader ****** */\n"+
"#ifdef GL_ES\n"+
"#ifdef GL_FRAGMENT_PRECISION_HIGH\n"+
"  precision highp float;\n"+
"#else\n"+
"  precision mediump float;\n"+
"#endif\n"+
"#endif\n"+
"  varying vec4 vCol; // carries alpha\n"+
"  varying vec4 vPosition;\n";
if (has_texture || type === "text")
result = result + "  varying vec2 vTexcoord;\n"+
" uniform sampler2D uSampler;\n";
if (is_lit && !fixed_quads)
result = result + "  varying vec3 vNormal;\n";
for (i = 0; i < nclipplanes; i++)
result = result + "  uniform vec4 vClipplane"+i+";\n";
if (is_lit) {
nlights = this.countLights();
if (nlights)
result = result + "  uniform mat4 mvMatrix;\n";
else
is_lit = false;
}
if (is_lit) {
result = result + "   uniform vec3 emission;\n"+
"   uniform float shininess;\n";
for (i=0; i < nlights; i++) {
result = result + "   uniform vec3 ambient" + i + ";\n"+
"   uniform vec3 specular" + i +"; // light*material\n"+
"   uniform vec3 diffuse" + i + ";\n"+
"   uniform vec3 lightDir" + i + ";\n"+
"   uniform bool viewpoint" + i + ";\n"+
"   uniform bool finite" + i + ";\n";
}
}
if (is_twosided)
result = result + "   uniform bool front;\n"+
"   varying float normz;\n";
if (fat_lines)
result = result + "   varying vec2 vPoint;\n"+
"   varying float vLength;\n";
result = result + "  void main(void) {\n";
if (fat_lines) {
result = result + "    vec2 point = vPoint;\n"+
"    bool neg = point.y < 0.0;\n"+
"    point.y = neg ? "+
"      (point.y + vLength)/(1.0 - vLength) :\n"+
"     -(point.y - vLength)/(1.0 - vLength);\n";
if (is_transparent && type == "linestrip")
result = result+"    if (neg && length(point) <= 1.0) discard;\n";
result = result + "    point.y = min(point.y, 0.0);\n"+
"    if (length(point) > 1.0) discard;\n";
}
for (i=0; i < nclipplanes;i++)
result = result + "    if (dot(vPosition, vClipplane"+i+") < 0.0) discard;\n";
if (fixed_quads) {
result = result +   "    vec3 n = vec3(0., 0., 1.);\n";
} else if (is_lit) {
result = result +   "    vec3 n = normalize(vNormal);\n";
}
if (is_twosided) {
result = result +   "    if ((normz <= 0.) != front) discard;\n";
}
if (is_lit) {
result = result + "    vec3 eye = normalize(-vPosition.xyz);\n"+
"   vec3 lightdir;\n"+
"   vec4 colDiff;\n"+
"   vec3 halfVec;\n"+
"   vec4 lighteffect = vec4(emission, 0.);\n"+
"   vec3 col;\n"+
"   float nDotL;\n";
if (!fixed_quads) {
result = result +   "   n = -faceforward(n, n, eye);\n";
}
for (i=0; i < nlights; i++) {
result = result + "   colDiff = vec4(vCol.rgb * diffuse" + i + ", vCol.a);\n"+
"   lightdir = lightDir" + i + ";\n"+
"   if (!viewpoint" + i +")\n"+
"     lightdir = (mvMatrix * vec4(lightdir, 1.)).xyz;\n"+
"   if (!finite" + i + ") {\n"+
"     halfVec = normalize(lightdir + eye);\n"+
"   } else {\n"+
"     lightdir = normalize(lightdir - vPosition.xyz);\n"+
"     halfVec = normalize(lightdir + eye);\n"+
"   }\n"+
"    col = ambient" + i + ";\n"+
"   nDotL = dot(n, lightdir);\n"+
"   col = col + max(nDotL, 0.) * colDiff.rgb;\n"+
"   col = col + pow(max(dot(halfVec, n), 0.), shininess) * specular" + i + ";\n"+
"   lighteffect = lighteffect + vec4(col, colDiff.a);\n";
}
} else {
result = result +   "   vec4 colDiff = vCol;\n"+
"    vec4 lighteffect = colDiff;\n";
}
if (type === "text")
result = result +   "    vec4 textureColor = lighteffect*texture2D(uSampler, vTexcoord);\n";
if (has_texture) {
result = result + {
rgb:            "   vec4 textureColor = lighteffect*vec4(texture2D(uSampler, vTexcoord).rgb, 1.);\n",
rgba:           "   vec4 textureColor = lighteffect*texture2D(uSampler, vTexcoord);\n",
alpha:          "   vec4 textureColor = texture2D(uSampler, vTexcoord);\n"+
"   float luminance = dot(vec3(1.,1.,1.), textureColor.rgb)/3.;\n"+
"   textureColor =  vec4(lighteffect.rgb, lighteffect.a*luminance);\n",
luminance:      "   vec4 textureColor = vec4(lighteffect.rgb*dot(texture2D(uSampler, vTexcoord).rgb, vec3(1.,1.,1.))/3., lighteffect.a);\n",
"luminance.alpha":"    vec4 textureColor = texture2D(uSampler, vTexcoord);\n"+
"   float luminance = dot(vec3(1.,1.,1.),textureColor.rgb)/3.;\n"+
"   textureColor = vec4(lighteffect.rgb*luminance, lighteffect.a*textureColor.a);\n"
}[texture_format]+
"   gl_FragColor = textureColor;\n";
} else if (type === "text") {
result = result +   "    if (textureColor.a < 0.1)\n"+
"     discard;\n"+
"   else\n"+
"     gl_FragColor = textureColor;\n";
} else
result = result +   "   gl_FragColor = lighteffect;\n";
//if (fat_lines)
//  result = result +   "   gl_FragColor = vec4(0.0, abs(point.x), abs(point.y), 1.0);"
result = result + "  }\n";
// console.log(result);
return result;
};
/**
* Call gl functions to create and compile shader
* @returns {Object}
* @param { number } shaderType - gl code for shader type
* @param { string } code - code for the shader
*/
rglwidgetClass.prototype.getShader = function(shaderType, code) {
var gl = this.gl, shader;
shader = gl.createShader(shaderType);
gl.shaderSource(shader, code);
gl.compileShader(shader);
if (!gl.getShaderParameter(shader, gl.COMPILE_STATUS) && !gl.isContextLost())
alert(gl.getShaderInfoLog(shader));
return shader;
};
/**
* Handle a texture after its image has been loaded
* @param { Object } texture - the gl texture object
* @param { Object } textureCanvas - the canvas holding the image
*/
rglwidgetClass.prototype.handleLoadedTexture = function(texture, textureCanvas) {
var gl = this.gl || this.initGL();
gl.pixelStorei(gl.UNPACK_FLIP_Y_WEBGL, true);
gl.bindTexture(gl.TEXTURE_2D, texture);
gl.texImage2D(gl.TEXTURE_2D, 0, gl.RGBA, gl.RGBA, gl.UNSIGNED_BYTE, textureCanvas);
gl.texParameteri(gl.TEXTURE_2D, gl.TEXTURE_MAG_FILTER, gl.LINEAR);
gl.texParameteri(gl.TEXTURE_2D, gl.TEXTURE_MIN_FILTER, gl.LINEAR_MIPMAP_NEAREST);
gl.generateMipmap(gl.TEXTURE_2D);
gl.bindTexture(gl.TEXTURE_2D, null);
};
/**
* Get maximum dimension of texture in current browser.
* @returns {number}
*/
rglwidgetClass.prototype.getMaxTexSize = function() {
var gl = this.gl || this.initGL();	
return Math.min(4096, gl.getParameter(gl.MAX_TEXTURE_SIZE));
};
/**
* Load an image to a texture
* @param { string } uri - The image location
* @param { Object } texture - the gl texture object
*/
rglwidgetClass.prototype.loadImageToTexture = function(uri, texture) {
var canvas = this.textureCanvas,
ctx = canvas.getContext("2d"),
image = new Image(),
self = this;
image.onload = function() {
var w = image.width,
h = image.height,
canvasX = self.getPowerOfTwo(w),
canvasY = self.getPowerOfTwo(h),
gl = self.gl || self.initGL(),
maxTexSize = self.getMaxTexSize();
while (canvasX > 1 && canvasY > 1 && (canvasX > maxTexSize || canvasY > maxTexSize)) {
canvasX /= 2;
canvasY /= 2;
}
canvas.width = canvasX;
canvas.height = canvasY;
ctx.imageSmoothingEnabled = true;
ctx.drawImage(image, 0, 0, canvasX, canvasY);
self.handleLoadedTexture(texture, canvas);
self.drawScene();
};
image.src = uri;
};
/**
* Draw text to the texture canvas
* @returns { Object } object with text measurements
* @param { string } text - the text
* @param { number } cex - expansion
* @param { string } family - font family
* @param { number } font - font number
*/
rglwidgetClass.prototype.drawTextToCanvas = function(text, cex, family, font) {
var canvasX, canvasY,
textY,
scaling = 20,
textColour = "white",
backgroundColour = "rgba(0,0,0,0)",
canvas = this.textureCanvas,
ctx = canvas.getContext("2d"),
i, textHeight = 0, textHeights = [], width, widths = [], 
offsetx, offsety = 0, line, lines = [], offsetsx = [],
offsetsy = [], lineoffsetsy = [], fontStrings = [],
maxTexSize = this.getMaxTexSize(),
getFontString = function(i) {
textHeights[i] = scaling*cex[i];
var fontString = textHeights[i] + "px",
family0 = family[i],
font0 = font[i];
if (family0 === "sans")
family0 = "sans-serif";
else if (family0 === "mono")
family0 = "monospace";
fontString = fontString + " " + family0;
if (font0 === 2 || font0 === 4)
fontString = "bold " + fontString;
if (font0 === 3 || font0 === 4)
fontString = "italic " + fontString;
return fontString;
};
cex = this.repeatToLen(cex, text.length);
family = this.repeatToLen(family, text.length);
font = this.repeatToLen(font, text.length);
canvasX = 1;
line = -1;
offsetx = maxTexSize;
for (i = 0; i < text.length; i++)  {
ctx.font = fontStrings[i] = getFontString(i);
width = widths[i] = ctx.measureText(text[i]).width;
if (offsetx + width > maxTexSize) {
line += 1;
offsety = lineoffsetsy[line] = offsety + 2*textHeight;
if (offsety > maxTexSize)
console.error("Too many strings for texture.");
textHeight = 0;
offsetx = 0;
}
textHeight = Math.max(textHeight, textHeights[i]);
offsetsx[i] = offsetx;
offsetx += width;
canvasX = Math.max(canvasX, offsetx);
lines[i] = line;
}
offsety = lineoffsetsy[line] = offsety + 2*textHeight;
for (i = 0; i < text.length; i++) {
offsetsy[i] = lineoffsetsy[lines[i]];
}
canvasX = this.getPowerOfTwo(canvasX);
canvasY = this.getPowerOfTwo(offsety);
canvas.width = canvasX;
canvas.height = canvasY;
ctx.fillStyle = backgroundColour;
ctx.fillRect(0, 0, ctx.canvas.width, ctx.canvas.height);
ctx.textBaseline = "alphabetic";
for(i = 0; i < text.length; i++) {
ctx.font = fontStrings[i];
ctx.fillStyle = textColour;
ctx.textAlign = "left";
ctx.fillText(text[i], offsetsx[i],  offsetsy[i]);
}
return {canvasX:canvasX, canvasY:canvasY,
widths:widths, textHeights:textHeights,
offsetsx:offsetsx, offsetsy:offsetsy};
};
/**
* Set the gl viewport and scissor test
* @param { number } id - id of subscene
*/
rglwidgetClass.prototype.setViewport = function(id) {
var gl = this.gl || this.initGL(),
vp = this.getObj(id).par3d.viewport,
x = vp.x*this.canvas.width,
y = vp.y*this.canvas.height,
width = vp.width*this.canvas.width,
height = vp.height*this.canvas.height;
this.vp = {x:x, y:y, width:width, height:height};
gl.viewport(x, y, width, height);
gl.scissor(x, y, width, height);
gl.enable(gl.SCISSOR_TEST);
};
/**
* Set the projection matrix for a subscene
* @param { number } id - id of subscene
*/
rglwidgetClass.prototype.setprMatrix = function(id) {
var subscene = this.getObj(id),
embedding = subscene.embeddings.projection;
if (embedding === "replace")
this.prMatrix.makeIdentity();
else
this.setprMatrix(subscene.parent);
if (embedding === "inherit")
return;
// This is based on the Frustum::enclose code from geom.cpp
var bbox = subscene.par3d.bbox,
scale = subscene.par3d.scale,
ranges = [(bbox[1]-bbox[0])*scale[0]/2,
(bbox[3]-bbox[2])*scale[1]/2,
(bbox[5]-bbox[4])*scale[2]/2],
radius = Math.sqrt(this.sumsq(ranges))*1.1; // A bit bigger to handle labels
if (radius <= 0) radius = 1;
var observer = subscene.par3d.observer,
distance = observer[2],
FOV = subscene.par3d.FOV, ortho = FOV === 0,
t = ortho ? 1 : Math.tan(FOV*Math.PI/360),
near = distance - radius,
far = distance + radius,
hlen,
aspect = this.vp.width/this.vp.height,
z = subscene.par3d.zoom,
userProjection = subscene.par3d.userProjection;
if (far < 0.0)
far = 1.0;
if (near < far/100.0)
near = far/100.0;
hlen = t*near;
if (ortho) {
if (aspect > 1)
this.prMatrix.ortho(-hlen*aspect*z, hlen*aspect*z,
-hlen*z, hlen*z, near, far);
else
this.prMatrix.ortho(-hlen*z, hlen*z,
-hlen*z/aspect, hlen*z/aspect,
near, far);
} else {
if (aspect > 1)
this.prMatrix.frustum(-hlen*aspect*z, hlen*aspect*z,
-hlen*z, hlen*z, near, far);
else
this.prMatrix.frustum(-hlen*z, hlen*z,
-hlen*z/aspect, hlen*z/aspect,
near, far);
}
this.prMatrix.multRight(userProjection);
};
/**
* Set the model-view matrix for a subscene
* @param { number } id - id of the subscene
*/
rglwidgetClass.prototype.setmvMatrix = function(id) {
var observer = this.getObj(id).par3d.observer;
this.mvMatrix.makeIdentity();
this.setmodelMatrix(id);
this.mvMatrix.translate(-observer[0], -observer[1], -observer[2]);
};
/**
* Set the model matrix for a subscene
* @param { number } id - id of the subscene
*/
rglwidgetClass.prototype.setmodelMatrix = function(id) {
var subscene = this.getObj(id),
embedding = subscene.embeddings.model;
if (embedding !== "inherit") {
var scale = subscene.par3d.scale,
bbox = subscene.par3d.bbox,
center = [(bbox[0]+bbox[1])/2,
(bbox[2]+bbox[3])/2,
(bbox[4]+bbox[5])/2];
this.mvMatrix.translate(-center[0], -center[1], -center[2]);
this.mvMatrix.scale(scale[0], scale[1], scale[2]);
this.mvMatrix.multRight( subscene.par3d.userMatrix );
}
if (embedding !== "replace")
this.setmodelMatrix(subscene.parent);
};
/**
* Set the normals matrix for a subscene
* @param { number } subsceneid - id of the subscene
*/
rglwidgetClass.prototype.setnormMatrix = function(subsceneid) {
var self = this,
recurse = function(id) {
var sub = self.getObj(id),
embedding = sub.embeddings.model;
if (embedding !== "inherit") {
var scale = sub.par3d.scale;
self.normMatrix.scale(1/scale[0], 1/scale[1], 1/scale[2]);
self.normMatrix.multRight(sub.par3d.userMatrix);
}
if (embedding !== "replace")
recurse(sub.parent);
};
self.normMatrix.makeIdentity();
recurse(subsceneid);
};
/**
* Set the combined projection-model-view matrix
*/
rglwidgetClass.prototype.setprmvMatrix = function() {
this.prmvMatrix = new CanvasMatrix4( this.mvMatrix );
this.prmvMatrix.multRight( this.prMatrix );
};
/**
* Count clipping planes in a scene
* @returns {number}
*/
rglwidgetClass.prototype.countClipplanes = function() {
return this.countObjs("clipplanes");
};
/**
* Count lights in a scene
* @returns { number }
*/
rglwidgetClass.prototype.countLights = function() {
return this.countObjs("light");
};
/**
* Count objects of specific type in a scene
* @returns { number }
* @param { string } type - Type of object to count
*/
rglwidgetClass.prototype.countObjs = function(type) {
var self = this,
bound = 0;
Object.keys(this.scene.objects).forEach(
function(key) {
if (self.getObj(parseInt(key, 10)).type === type)
bound = bound + 1;
});
return bound;
};
/**
* Initialize a subscene
* @param { number } id - id of subscene.
*/
rglwidgetClass.prototype.initSubscene = function(id) {
var sub = this.getObj(id),
i, obj;
if (sub.type !== "subscene")
return;
sub.par3d.userMatrix = this.toCanvasMatrix4(sub.par3d.userMatrix);
sub.par3d.userProjection = this.toCanvasMatrix4(sub.par3d.userProjection);
sub.par3d.userProjection.transpose();
sub.par3d.listeners = [].concat(sub.par3d.listeners);
sub.backgroundId = undefined;
sub.subscenes = [];
sub.clipplanes = [];
sub.transparent = [];
sub.opaque = [];
sub.lights = [];
for (i=0; i < sub.objects.length; i++) {
obj = this.getObj(sub.objects[i]);
if (typeof obj === "undefined") {
sub.objects.splice(i, 1);
i--;
} else if (obj.type === "background")
sub.backgroundId = obj.id;
else
sub[this.whichList(obj.id)].push(obj.id);
}
};
/**
* Copy object
* @param { number } id - id of object to copy
* @param { string } reuse - Document id of scene to reuse
*/
rglwidgetClass.prototype.copyObj = function(id, reuse) {
var obj = this.getObj(id),
prev = document.getElementById(reuse);
if (prev !== null) {
prev = prev.rglinstance;
var
prevobj = prev.getObj(id),
fields = ["flags", "type",
"colors", "vertices", "centers",
"normals", "offsets",
"texts", "cex", "family", "font", "adj",
"material",
"radii",
"texcoords",
"userMatrix", "ids",
"dim",
"par3d", "userMatrix",
"viewpoint", "finite",
"pos"],
i;
for (i = 0; i < fields.length; i++) {
if (typeof prevobj[fields[i]] !== "undefined")
obj[fields[i]] = prevobj[fields[i]];
}
} else
console.warn("copyObj failed");
};
/**
* Update the triangles used to display a plane
* @param { number } id - id of the plane
* @param { Object } bbox - bounding box in which to display the plane
*/
rglwidgetClass.prototype.planeUpdateTriangles = function(id, bbox) {
var perms = [[0,0,1], [1,2,2], [2,1,0]],
x, xrow, elem, A, d, nhits, i, j, k, u, v, w, intersect, which, v0, v2, vx, reverse,
face1 = [], face2 = [], normals = [],
obj = this.getObj(id),
nPlanes = obj.normals.length;
obj.bbox = bbox;
obj.vertices = [];
obj.initialized = false;
for (elem = 0; elem < nPlanes; elem++) {
//    Vertex Av = normal.getRecycled(elem);
x = [];
A = obj.normals[elem];
d = obj.offsets[elem][0];
nhits = 0;
for (i=0; i<3; i++)
for (j=0; j<2; j++)
for (k=0; k<2; k++) {
u = perms[0][i];
v = perms[1][i];
w = perms[2][i];
if (A[w] !== 0.0) {
intersect = -(d + A[u]*bbox[j+2*u] + A[v]*bbox[k+2*v])/A[w];
if (bbox[2*w] < intersect && intersect < bbox[1+2*w]) {
xrow = [];
xrow[u] = bbox[j+2*u];
xrow[v] = bbox[k+2*v];
xrow[w] = intersect;
x.push(xrow);
face1[nhits] = j + 2*u;
face2[nhits] = k + 2*v;
nhits++;
}
}
}
if (nhits > 3) {
/* Re-order the intersections so the triangles work */
for (i=0; i<nhits-2; i++) {
which = 0; /* initialize to suppress warning */
for (j=i+1; j<nhits; j++) {
if (face1[i] == face1[j] || face1[i] == face2[j] ||
face2[i] == face1[j] || face2[i] == face2[j] ) {
which = j;
break;
}
}
if (which > i+1) {
this.swap(x, i+1, which);
this.swap(face1, i+1, which);
this.swap(face2, i+1, which);
}
}
}
if (nhits >= 3) {
/* Put in order so that the normal points out the FRONT of the faces */
v0 = [x[0][0] - x[1][0] , x[0][1] - x[1][1], x[0][2] - x[1][2]];
v2 = [x[2][0] - x[1][0] , x[2][1] - x[1][1], x[2][2] - x[1][2]];
/* cross-product */
vx = this.xprod(v0, v2);
reverse = this.dotprod(vx, A) > 0;
for (i=0; i<nhits-2; i++) {
obj.vertices.push(x[0]);
normals.push(A);
for (j=1; j<3; j++) {
obj.vertices.push(x[i + (reverse ? 3-j : j)]);
normals.push(A);
}
}
}
}
obj.pnormals = normals;
};
rglwidgetClass.prototype.getAdj = function (pos, offset, text) {
switch(pos) {
case 1: return [0.5, 1 + offset];
case 2: return [1 + offset/text.length, 0.5];
case 3: return [0.5, -offset];
case 4: return [-offset/text.length, 0.5];
}
}
/**
* Initialize object for display
* @param { number } id - id of object to initialize
*/
rglwidgetClass.prototype.initObj = function(id) {
var obj = this.getObj(id),
flags = obj.flags,
type = obj.type,
is_lit = flags & this.f_is_lit,
is_lines = flags & this.f_is_lines,
fat_lines = flags & this.f_fat_lines,
has_texture = flags & this.f_has_texture,
fixed_quads = flags & this.f_fixed_quads,
is_transparent = obj.is_transparent,
depth_sort = flags & this.f_depth_sort,
sprites_3d = flags & this.f_sprites_3d,
sprite_3d = flags & this.f_sprite_3d,
fixed_size = flags & this.f_fixed_size,
is_twosided = (flags & this.f_is_twosided) > 0,
is_brush = flags & this.f_is_brush,
gl = this.gl || this.initGL(),
polygon_offset,
texinfo, drawtype, nclipplanes, f, nrows, oldrows,
i,j,v,v1,v2, mat, uri, matobj, pass, passes, pmode,
dim, nx, nz, attr;
if (typeof id !== "number") {
this.alertOnce("initObj id is "+typeof id);
}
obj.initialized = true;
if (type === "bboxdeco" || type === "subscene")
return;
if (type === "light") {
obj.ambient = new Float32Array(obj.colors[0].slice(0,3));
obj.diffuse = new Float32Array(obj.colors[1].slice(0,3));
obj.specular = new Float32Array(obj.colors[2].slice(0,3));
obj.lightDir = new Float32Array(obj.vertices[0]);
return;
}
if (type === "clipplanes") {
obj.vClipplane = this.flatten(this.cbind(obj.normals, obj.offsets));
return;
}
if (type === "background" && typeof obj.ids !== "undefined") {
obj.quad = this.flatten([].concat(obj.ids));
return;
}
polygon_offset = this.getMaterial(id, "polygon_offset");
if (polygon_offset[0] != 0 || polygon_offset[1] != 0)
obj.polygon_offset = polygon_offset;
if (is_transparent) {
depth_sort = ["triangles", "quads", "surface",
"spheres", "sprites", "text"].indexOf(type) >= 0;
}
if (is_brush)
this.initSelection(id);
if (typeof obj.vertices === "undefined")
obj.vertices = [];
v = obj.vertices;
obj.vertexCount = v.length;
if (!obj.vertexCount) return;
if (is_twosided) {
if (typeof obj.userAttributes === "undefined")
obj.userAttributes = {};
v1 = Array(v.length);
v2 = Array(v.length);
if (obj.type == "triangles" || obj.type == "quads") {
if (obj.type == "triangles")
nrow = 3;
else
nrow = 4;
for (i=0; i<Math.floor(v.length/nrow); i++)
for (j=0; j<nrow; j++) {
v1[nrow*i + j] = v[nrow*i + ((j+1) % nrow)];
v2[nrow*i + j] = v[nrow*i + ((j+2) % nrow)];
}
} else if (obj.type == "surface") {
dim = obj.dim[0];
nx = dim[0];
nz = dim[1];
for (j=0; j<nx; j++) {
for (i=0; i<nz; i++) {
if (i+1 < nz && j+1 < nx) {
v2[j + nx*i] = v[j + nx*(i+1)];
v1[j + nx*i] = v[j+1 + nx*(i+1)];
} else if (i+1 < nz) {
v2[j + nx*i] = v[j-1 + nx*i];
v1[j + nx*i] = v[j + nx*(i+1)];
} else {
v2[j + nx*i] = v[j + nx*(i-1)];
v1[j + nx*i] = v[j-1 + nx*(i-1)];
}
}
}
}
obj.userAttributes.aPos1 = v1;
obj.userAttributes.aPos2 = v2;
}
if (!sprites_3d) {
if (gl.isContextLost()) return;
obj.prog = gl.createProgram();
gl.attachShader(obj.prog, this.getShader( gl.VERTEX_SHADER,
this.getVertexShader(id) ));
gl.attachShader(obj.prog, this.getShader( gl.FRAGMENT_SHADER,
this.getFragmentShader(id) ));
//  Force aPos to location 0, aCol to location 1
gl.bindAttribLocation(obj.prog, 0, "aPos");
gl.bindAttribLocation(obj.prog, 1, "aCol");
gl.linkProgram(obj.prog);
var linked = gl.getProgramParameter(obj.prog, gl.LINK_STATUS);
if (!linked) {
// An error occurred while linking
var lastError = gl.getProgramInfoLog(obj.prog);
console.warn("Error in program linking:" + lastError);
gl.deleteProgram(obj.prog);
return;
}
}
if (type === "text") {
texinfo = this.drawTextToCanvas(obj.texts,
this.flatten(obj.cex),
this.flatten(obj.family),
this.flatten(obj.family));
}
if (fixed_quads && !sprites_3d) {
obj.ofsLoc = gl.getAttribLocation(obj.prog, "aOfs");
}
if (sprite_3d) {
obj.origLoc = gl.getUniformLocation(obj.prog, "uOrig");
obj.sizeLoc = gl.getUniformLocation(obj.prog, "uSize");
obj.usermatLoc = gl.getUniformLocation(obj.prog, "usermat");
}
if (has_texture || type == "text") {
if (!obj.texture)
obj.texture = gl.createTexture();
obj.texLoc = gl.getAttribLocation(obj.prog, "aTexcoord");
obj.sampler = gl.getUniformLocation(obj.prog, "uSampler");
}
if (has_texture) {
mat = obj.material;
if (typeof mat.uri !== "undefined")
uri = mat.uri;
else if (typeof mat.uriElementId === "undefined") {
matobj = this.getObj(mat.uriId);
if (typeof matobj !== "undefined") {
uri = matobj.material.uri;
} else {
uri = "";
}
} else
uri = document.getElementById(mat.uriElementId).rglinstance.getObj(mat.uriId).material.uri;
this.loadImageToTexture(uri, obj.texture);
}
if (type === "text") {
this.handleLoadedTexture(obj.texture, this.textureCanvas);
}
var stride = 3, nc, cofs, nofs, radofs, oofs, tofs, vnew, fnew,
nextofs = -1, pointofs = -1, alias, colors, key, selection, filter, adj, pos, offset;
obj.alias = undefined;
colors = obj.colors;
j = this.scene.crosstalk.id.indexOf(id);
if (j >= 0) {
key = this.scene.crosstalk.key[j];
options = this.scene.crosstalk.options[j];
colors = colors.slice(0); 
for (i = 0; i < v.length; i++)
colors[i] = obj.colors[i % obj.colors.length].slice(0);
if ( (selection = this.scene.crosstalk.selection) &&
(selection.length || !options.selectedIgnoreNone) )
for (i = 0; i < v.length; i++) {
if (!selection.includes(key[i])) {
if (options.deselectedColor)
colors[i] = options.deselectedColor.slice(0);
colors[i][3] = colors[i][3]*options.deselectedFade;   /* default: mostly transparent if not selected */
} else if (options.selectedColor)
colors[i] = options.selectedColor.slice(0);
}
if ( (filter = this.scene.crosstalk.filter) )
for (i = 0; i < v.length; i++) 
if (!filter.includes(key[i])) {
if (options.filteredColor)
colors[i] = options.filteredColor.slice(0);
colors[i][3] = colors[i][3]*options.filteredFade;   /* default: completely hidden if filtered */
}
}  
nc = obj.colorCount = colors.length;
if (nc > 1) {
cofs = stride;
stride = stride + 4;
v = this.cbind(v, colors);
} else {
cofs = -1;
obj.onecolor = this.flatten(colors);
}
if (typeof obj.normals !== "undefined") {
nofs = stride;
stride = stride + 3;
v = this.cbind(v, typeof obj.pnormals !== "undefined" ? obj.pnormals : obj.normals);
} else
nofs = -1;
if (typeof obj.radii !== "undefined") {
radofs = stride;
stride = stride + 1;
// FIXME:  always concat the radii?
if (obj.radii.length === v.length) {
v = this.cbind(v, obj.radii);
} else if (obj.radii.length === 1) {
v = v.map(function(row, i, arr) { return row.concat(obj.radii[0]);});
}
} else
radofs = -1;
// Add default indices
f = Array(v.length);
for (i = 0; i < v.length; i++)
f[i] = i;
obj.f = [f,f];
if (type == "sprites" && !sprites_3d) {
tofs = stride;
stride += 2;
oofs = stride;
stride += 2;
vnew = new Array(4*v.length);
fnew = new Array(4*v.length);
alias = new Array(v.length);
var rescale = fixed_size ? 72 : 1,
size = obj.radii, s = rescale*size[0]/2;
last = v.length;
f = obj.f[0];
for (i=0; i < v.length; i++) {
if (size.length > 1)
s = rescale*size[i]/2;
vnew[i]  = v[i].concat([0,0,-s,-s]);
fnew[4*i] = f[i];
vnew[last]= v[i].concat([1,0, s,-s]);
fnew[4*i+1] = last++;
vnew[last]= v[i].concat([1,1, s, s]);
fnew[4*i+2] = last++;
vnew[last]= v[i].concat([0,1,-s, s]);
fnew[4*i+3] = last++;
alias[i] = [last-3, last-2, last-1];
}
v = vnew;
obj.vertexCount = v.length;
obj.f = [fnew, fnew];
} else if (type === "text") {
tofs = stride;
stride += 2;
oofs = stride;
stride += 2;
vnew = new Array(4*v.length);
f = obj.f[0];
fnew = new Array(4*f.length);
alias = new Array(v.length);
last = v.length;
adj = this.flatten(obj.adj);
if (typeof obj.pos !== "undefined") {
pos = this.flatten(obj.pos);
offset = adj[0];
}
for (i=0; i < v.length; i++) {
if (typeof pos !== "undefined")
adj = this.getAdj(pos[i % pos.length], offset, obj.texts[i]);
vnew[i]  = v[i].concat([0,-0.5]).concat(adj);
fnew[4*i] = f[i];
vnew[last] = v[i].concat([1,-0.5]).concat(adj);
fnew[4*i+1] = last++;
vnew[last] = v[i].concat([1, 1.5]).concat(adj);
fnew[4*i+2] = last++;
vnew[last] = v[i].concat([0, 1.5]).concat(adj);
fnew[4*i+3] = last++;
alias[i] = [last-3, last-2, last-1];
for (j=0; j < 4; j++) {
v1 = vnew[fnew[4*i+j]];
v1[tofs+2] = 2*(v1[tofs]-v1[tofs+2])*texinfo.widths[i];
v1[tofs+3] = 2*(v1[tofs+1]-v1[tofs+3])*texinfo.textHeights[i];
v1[tofs] = (texinfo.offsetsx[i] + v1[tofs]*texinfo.widths[i])/texinfo.canvasX;
v1[tofs+1] = 1.0-(texinfo.offsetsy[i] -
v1[tofs+1]*texinfo.textHeights[i])/texinfo.canvasY;
vnew[fnew[4*i+j]] = v1;
}
}
v = vnew;
obj.vertexCount = v.length;
obj.f = [fnew, fnew];
} else if (typeof obj.texcoords !== "undefined") {
tofs = stride;
stride += 2;
oofs = -1;
v = this.cbind(v, obj.texcoords);
} else {
tofs = -1;
oofs = -1;
}
obj.alias = alias;
if (typeof obj.userAttributes !== "undefined") {
obj.userAttribOffsets = {};
obj.userAttribLocations = {};
obj.userAttribSizes = {};
for (attr in obj.userAttributes) {
obj.userAttribLocations[attr] = gl.getAttribLocation(obj.prog, attr);
if (obj.userAttribLocations[attr] >= 0) { // Attribute may not have been used
obj.userAttribOffsets[attr] = stride;
v = this.cbind(v, obj.userAttributes[attr]);
stride = v[0].length;
obj.userAttribSizes[attr] = stride - obj.userAttribOffsets[attr];
}
}
}
if (typeof obj.userUniforms !== "undefined") {
obj.userUniformLocations = {};
for (attr in obj.userUniforms)
obj.userUniformLocations[attr] = gl.getUniformLocation(obj.prog, attr);
}
if (sprites_3d) {
obj.userMatrix = new CanvasMatrix4(obj.userMatrix);
obj.objects = this.flatten([].concat(obj.ids));
is_lit = false;
for (i=0; i < obj.objects.length; i++)
this.initObj(obj.objects[i]);
}
if (is_lit && !fixed_quads) {
obj.normLoc = gl.getAttribLocation(obj.prog, "aNorm");
}
nclipplanes = this.countClipplanes();
if (nclipplanes && !sprites_3d) {
obj.clipLoc = [];
for (i=0; i < nclipplanes; i++)
obj.clipLoc[i] = gl.getUniformLocation(obj.prog,"vClipplane" + i);
}
if (is_lit) {
obj.emissionLoc = gl.getUniformLocation(obj.prog, "emission");
obj.emission = new Float32Array(this.stringToRgb(this.getMaterial(id, "emission")));
obj.shininessLoc = gl.getUniformLocation(obj.prog, "shininess");
obj.shininess = this.getMaterial(id, "shininess");
obj.nlights = this.countLights();
obj.ambientLoc = [];
obj.ambient = new Float32Array(this.stringToRgb(this.getMaterial(id, "ambient")));
obj.specularLoc = [];
obj.specular = new Float32Array(this.stringToRgb(this.getMaterial(id, "specular")));
obj.diffuseLoc = [];
obj.lightDirLoc = [];
obj.viewpointLoc = [];
obj.finiteLoc = [];
for (i=0; i < obj.nlights; i++) {
obj.ambientLoc[i] = gl.getUniformLocation(obj.prog, "ambient" + i);
obj.specularLoc[i] = gl.getUniformLocation(obj.prog, "specular" + i);
obj.diffuseLoc[i] = gl.getUniformLocation(obj.prog, "diffuse" + i);
obj.lightDirLoc[i] = gl.getUniformLocation(obj.prog, "lightDir" + i);
obj.viewpointLoc[i] = gl.getUniformLocation(obj.prog, "viewpoint" + i);
obj.finiteLoc[i] = gl.getUniformLocation(obj.prog, "finite" + i);
}
}
obj.passes = is_twosided + 1;
obj.pmode = new Array(obj.passes);
for (pass = 0; pass < obj.passes; pass++) {
if (type === "triangles" || type === "quads" || type === "surface")
pmode = this.getMaterial(id, (pass === 0) ? "front" : "back");
else pmode = "filled";
obj.pmode[pass] = pmode;
}
obj.f.length = obj.passes;
for (pass = 0; pass < obj.passes; pass++) {
f = fnew = obj.f[pass];
pmode = obj.pmode[pass];
if (pmode === "culled")
f = [];
else if (pmode === "points") {
// stay with default
} else if ((type === "quads" || type === "text" ||
type === "sprites") && !sprites_3d) {
nrows = Math.floor(obj.vertexCount/4);
if (pmode === "filled") {
fnew = Array(6*nrows);
for (i=0; i < nrows; i++) {
fnew[6*i] = f[4*i];
fnew[6*i+1] = f[4*i + 1];
fnew[6*i+2] = f[4*i + 2];
fnew[6*i+3] = f[4*i];
fnew[6*i+4] = f[4*i + 2];
fnew[6*i+5] = f[4*i + 3];
}
} else {
fnew = Array(8*nrows);
for (i=0; i < nrows; i++) {
fnew[8*i] = f[4*i];
fnew[8*i+1] = f[4*i + 1];
fnew[8*i+2] = f[4*i + 1];
fnew[8*i+3] = f[4*i + 2];
fnew[8*i+4] = f[4*i + 2];
fnew[8*i+5] = f[4*i + 3];
fnew[8*i+6] = f[4*i + 3];
fnew[8*i+7] = f[4*i];
}
}
} else if (type === "triangles") {
nrows = Math.floor(obj.vertexCount/3);
if (pmode === "filled") {
fnew = Array(3*nrows);
for (i=0; i < fnew.length; i++) {
fnew[i] = f[i];
}
} else if (pmode === "lines") {
fnew = Array(6*nrows);
for (i=0; i < nrows; i++) {
fnew[6*i] = f[3*i];
fnew[6*i + 1] = f[3*i + 1];
fnew[6*i + 2] = f[3*i + 1];
fnew[6*i + 3] = f[3*i + 2];
fnew[6*i + 4] = f[3*i + 2];
fnew[6*i + 5] = f[3*i];
}
}
} else if (type === "spheres") {
// default
} else if (type === "surface") {
dim = obj.dim[0];
nx = dim[0];
nz = dim[1];
if (pmode === "filled") {
fnew = [];
for (j=0; j<nx-1; j++) {
for (i=0; i<nz-1; i++) {
fnew.push(f[j + nx*i],
f[j + nx*(i+1)],
f[j + 1 + nx*(i+1)],
f[j + nx*i],
f[j + 1 + nx*(i+1)],
f[j + 1 + nx*i]);
}
}
} else if (pmode === "lines") {
fnew = [];
for (j=0; j<nx; j++) {
for (i=0; i<nz; i++) {
if (i+1 < nz)
fnew.push(f[j + nx*i],
f[j + nx*(i+1)]);
if (j+1 < nx)
fnew.push(f[j + nx*i],
f[j+1 + nx*i]);
}
}
}
}
obj.f[pass] = fnew;
if (depth_sort) {
drawtype = "DYNAMIC_DRAW";
} else {
drawtype = "STATIC_DRAW";
}
}
if (fat_lines) {
alias = undefined;
obj.nextLoc = gl.getAttribLocation(obj.prog, "aNext");
obj.pointLoc = gl.getAttribLocation(obj.prog, "aPoint");
obj.aspectLoc = gl.getUniformLocation(obj.prog, "uAspect");
obj.lwdLoc = gl.getUniformLocation(obj.prog, "uLwd");
// Expand vertices to turn each segment into a pair of triangles
for (pass = 0; pass < obj.passes; pass++) {
f = obj.f[pass];	
oldrows = f.length;
if (obj.pmode[pass] === "lines") 
break;
}
if (type === "linestrip") 
nrows = 4*(oldrows - 1); 
else
nrows = 2*oldrows;
vnew = new Array(nrows);
fnew = new Array(1.5*nrows);
var fnext = new Array(nrows),
fpt = new Array(nrows), 
pt, start, gap = type === "linestrip" ? 3 : 1;
// We're going to turn each pair of vertices into 4 new ones, with the "next" and "pt" attributes
// added.
// We do this by copying the originals in the first pass, adding the new attributes, then in a 
// second pass add new vertices at the end.
for (i = 0; i < v.length; i++) {
vnew[i] = v[i].concat([0,0,0,0,0]); 
}
nextofs = stride;
pointofs = stride + 3;
stride = stride + 5;
// Now add the extras
last = v.length - 1;
ind = 0;
alias = new Array(f.length);
for (i = 0; i < f.length; i++)
alias[i] = [];
for (i = 0; i < f.length - 1; i++) {
if (type !== "linestrip" && i % 2 == 1)
continue;
k = ++last;
vnew[k] = vnew[f[i]].slice();
for (j=0; j<3; j++)
vnew[k][nextofs + j] = vnew[f[i+1]][j];
vnew[k][pointofs] = -1;
vnew[k][pointofs+1] = -1;
fnew[ind] = k;
last++;
vnew[last] = vnew[k].slice();
vnew[last][pointofs] = 1;
fnew[ind+1] = last;
alias[f[i]].push(last-1, last);
last++;
k = last;
vnew[k] = vnew[f[i+1]].slice();
for (j=0; j<3; j++)
vnew[k][nextofs + j] = vnew[f[i]][j];
vnew[k][pointofs] = -1;
vnew[k][pointofs+1] = 1;
fnew[ind+2] = k;
fnew[ind+3] = fnew[ind+1];
last++;
vnew[last] = vnew[k].slice();
vnew[last][pointofs] = 1;
fnew[ind+4] = last;
fnew[ind+5] = fnew[ind+2];
ind += 6;
alias[f[i+1]].push(last-1, last);
}
vnew.length = last+1;
v = vnew;
obj.vertexCount = v.length;
if (typeof alias !== "undefined" && typeof obj.alias !== "undefined") {  // Already have aliases from previous section?
var oldalias = obj.alias, newalias = Array(obj.alias.length);
for (i = 0; i < newalias.length; i++) {
newalias[i] = oldalias[i].slice();
for (j = 0; j < oldalias[i].length; j++)
Array.prototype.push.apply(newalias[i], alias[oldalias[j]]); // pushes each element 
}
obj.alias = newalias;
} else
obj.alias = alias;
for (pass = 0; pass < obj.passes; pass++)
if (type === "lines" || type === "linestrip" || obj.pmode[pass] == "lines") {
obj.f[pass] = fnew;
}
if (depth_sort) 
drawtype = "DYNAMIC_DRAW";
else
drawtype = "STATIC_DRAW";
}
for (pass = 0; pass < obj.passes; pass++) {
if (obj.vertexCount > 65535) {
if (this.index_uint) {
obj.f[pass] = new Uint32Array(obj.f[pass]);
obj.index_uint = true;
} else
this.alertOnce("Object has "+obj.vertexCount+" vertices, not supported in this browser.");
} else {
obj.f[pass] = new Uint16Array(obj.f[pass]);
obj.index_uint = false;
}
}
if (stride !== v[0].length) {
this.alertOnce("problem in stride calculation");
}
obj.vOffsets = {vofs:0, cofs:cofs, nofs:nofs, radofs:radofs, oofs:oofs, tofs:tofs,
nextofs:nextofs, pointofs:pointofs, stride:stride};
obj.values = new Float32Array(this.flatten(v));
if (type !== "spheres" && !sprites_3d) {
obj.buf = gl.createBuffer();
gl.bindBuffer(gl.ARRAY_BUFFER, obj.buf);
gl.bufferData(gl.ARRAY_BUFFER, obj.values, gl.STATIC_DRAW); //
obj.ibuf = Array(obj.passes);
obj.ibuf[0] = gl.createBuffer();
gl.bindBuffer(gl.ELEMENT_ARRAY_BUFFER, obj.ibuf[0]);
gl.bufferData(gl.ELEMENT_ARRAY_BUFFER, obj.f[0], gl[drawtype]);
if (is_twosided) {
obj.ibuf[1] = gl.createBuffer();
gl.bindBuffer(gl.ELEMENT_ARRAY_BUFFER, obj.ibuf[1]);
gl.bufferData(gl.ELEMENT_ARRAY_BUFFER, obj.f[1], gl[drawtype]);
}
}
if (!sprites_3d) {
obj.mvMatLoc = gl.getUniformLocation(obj.prog, "mvMatrix");
obj.prMatLoc = gl.getUniformLocation(obj.prog, "prMatrix");
}
if (fixed_size) {
obj.textScaleLoc = gl.getUniformLocation(obj.prog, "textScale");
}
if (is_lit && !sprites_3d) {
obj.normMatLoc = gl.getUniformLocation(obj.prog, "normMatrix");
}
if (is_twosided) {
obj.frontLoc = gl.getUniformLocation(obj.prog, "front");
}
};
/**
* Set gl depth test based on object's material
* @param { number } id - object to use
*/
rglwidgetClass.prototype.setDepthTest = function(id) {
var gl = this.gl || this.initGL(),
tests = {never: gl.NEVER,
less:  gl.LESS,
equal: gl.EQUAL,
lequal:gl.LEQUAL,
greater: gl.GREATER,
notequal: gl.NOTEQUAL,
gequal: gl.GEQUAL,
always: gl.ALWAYS},
test = tests[this.getMaterial(id, "depth_test")];
gl.depthFunc(test);
};
rglwidgetClass.prototype.mode4type = {points : "POINTS",
linestrip : "LINE_STRIP",
abclines : "LINES",
lines : "LINES",
sprites : "TRIANGLES",
planes : "TRIANGLES",
text : "TRIANGLES",
quads : "TRIANGLES",
surface : "TRIANGLES",
triangles : "TRIANGLES"};
/**
* Sort objects from back to front
* @returns { number[] }
* @param { Object } obj - object to sort
*/
rglwidgetClass.prototype.depthSort = function(obj) {
var n = obj.centers.length,
depths = new Float32Array(n),
result = new Array(n),
compare = function(i,j) { return depths[j] - depths[i]; },
z, w;
for(i=0; i<n; i++) {
z = this.prmvMatrix.m13*obj.centers[i][0] +
this.prmvMatrix.m23*obj.centers[i][1] +
this.prmvMatrix.m33*obj.centers[i][2] +
this.prmvMatrix.m43;
w = this.prmvMatrix.m14*obj.centers[i][0] +
this.prmvMatrix.m24*obj.centers[i][1] +
this.prmvMatrix.m34*obj.centers[i][2] +
this.prmvMatrix.m44;
depths[i] = z/w;
result[i] = i;
}
result.sort(compare);
return result;
};
rglwidgetClass.prototype.disableArrays = function(obj, enabled) {
var gl = this.gl || this.initGL(),
objLocs = ["normLoc", "texLoc", "ofsLoc", "pointLoc", "nextLoc"],
thisLocs = ["posLoc", "colLoc"], i, attr;
for (i = 0; i < objLocs.length; i++) 
if (enabled[objLocs[i]]) gl.disableVertexAttribArray(obj[objLocs[i]]);
for (i = 0; i < thisLocs.length; i++)
if (enabled[thisLocs[i]]) gl.disableVertexAttribArray(this[objLocs[i]]);
if (typeof obj.userAttributes !== "undefined") {
for (attr in obj.userAttribSizes) {  // Not all attributes may have been used
gl.disableVertexAttribArray( obj.userAttribLocations[attr] );
}
}
}
/**
* Draw an object in a subscene
* @param { number } id - object to draw
* @param { number } subsceneid - id of subscene
*/
rglwidgetClass.prototype.drawObj = function(id, subsceneid) {
var obj = this.getObj(id),
subscene = this.getObj(subsceneid),
flags = obj.flags,
type = obj.type,
is_lit = flags & this.f_is_lit,
has_texture = flags & this.f_has_texture,
fixed_quads = flags & this.f_fixed_quads,
is_transparent = flags & this.f_is_transparent,
depth_sort = flags & this.f_depth_sort,
sprites_3d = flags & this.f_sprites_3d,
sprite_3d = flags & this.f_sprite_3d,
is_lines = flags & this.f_is_lines,
fat_lines = flags & this.f_fat_lines,
is_points = flags & this.f_is_points,
fixed_size = flags & this.f_fixed_size,
is_twosided = (flags & this.f_is_twosided) > 0,
gl = this.gl || this.initGL(),
mat,
sphereMV, baseofs, ofs, sscale, i, count, light,
pass, mode, pmode, attr,
enabled = {};
if (typeof id !== "number") {
this.alertOnce("drawObj id is "+typeof id);
}
if (type === "planes") {
if (obj.bbox !== subscene.par3d.bbox || !obj.initialized) {
this.planeUpdateTriangles(id, subscene.par3d.bbox);
}
}
if (!obj.initialized)
this.initObj(id);
if (type === "clipplanes") {
count = obj.offsets.length;
var IMVClip = [];
for (i=0; i < count; i++) {
IMVClip[i] = this.multMV(this.invMatrix, obj.vClipplane.slice(4*i, 4*(i+1)));
}
obj.IMVClip = IMVClip;
return;
}
if (type === "light" || type === "bboxdeco" || !obj.vertexCount)
return;
if (!is_transparent &&
obj.someHidden) {
is_transparent = true;
depth_sort = ["triangles", "quads", "surface",
"spheres", "sprites", "text"].indexOf(type) >= 0;
}        
this.setDepthTest(id);
if (sprites_3d) {
var norigs = obj.vertices.length,
savenorm = new CanvasMatrix4(this.normMatrix);
this.origs = obj.vertices;
this.usermat = new Float32Array(obj.userMatrix.getAsArray());
this.radii = obj.radii;
this.normMatrix = subscene.spriteNormmat;
for (this.iOrig=0; this.iOrig < norigs; this.iOrig++) {
for (i=0; i < obj.objects.length; i++) {
this.drawObj(obj.objects[i], subsceneid);
}
}
this.normMatrix = savenorm;
return;
} else {
gl.useProgram(obj.prog);
}
if (typeof obj.polygon_offset !== "undefined") {
gl.polygonOffset(obj.polygon_offset[0],
obj.polygon_offset[1]);
gl.enable(gl.POLYGON_OFFSET_FILL);
}
if (sprite_3d) {
gl.uniform3fv(obj.origLoc, new Float32Array(this.origs[this.iOrig]));
if (this.radii.length > 1) {
gl.uniform1f(obj.sizeLoc, this.radii[this.iOrig][0]);
} else {
gl.uniform1f(obj.sizeLoc, this.radii[0][0]);
}
gl.uniformMatrix4fv(obj.usermatLoc, false, this.usermat);
}
if (type === "spheres") {
gl.bindBuffer(gl.ARRAY_BUFFER, this.sphere.buf);
} else {
gl.bindBuffer(gl.ARRAY_BUFFER, obj.buf);
}
gl.uniformMatrix4fv( obj.prMatLoc, false, new Float32Array(this.prMatrix.getAsArray()) );
gl.uniformMatrix4fv( obj.mvMatLoc, false, new Float32Array(this.mvMatrix.getAsArray()) );
var clipcheck = 0,
clipplaneids = subscene.clipplanes,
clip, j;
for (i=0; i < clipplaneids.length; i++) {
clip = this.getObj(clipplaneids[i]);
for (j=0; j < clip.offsets.length; j++) {
gl.uniform4fv(obj.clipLoc[clipcheck + j], clip.IMVClip[j]);
}
clipcheck += clip.offsets.length;
}
if (typeof obj.clipLoc !== "undefined")
for (i=clipcheck; i < obj.clipLoc.length; i++)
gl.uniform4f(obj.clipLoc[i], 0,0,0,0);
if (is_lit) {
gl.uniformMatrix4fv( obj.normMatLoc, false, new Float32Array(this.normMatrix.getAsArray()) );
gl.uniform3fv( obj.emissionLoc, obj.emission);
gl.uniform1f( obj.shininessLoc, obj.shininess);
for (i=0; i < subscene.lights.length; i++) {
light = this.getObj(subscene.lights[i]);
if (!light.initialized) this.initObj(subscene.lights[i]);
gl.uniform3fv( obj.ambientLoc[i], this.componentProduct(light.ambient, obj.ambient));
gl.uniform3fv( obj.specularLoc[i], this.componentProduct(light.specular, obj.specular));
gl.uniform3fv( obj.diffuseLoc[i], light.diffuse);
gl.uniform3fv( obj.lightDirLoc[i], light.lightDir);
gl.uniform1i( obj.viewpointLoc[i], light.viewpoint);
gl.uniform1i( obj.finiteLoc[i], light.finite);
}
for (i=subscene.lights.length; i < obj.nlights; i++) {
gl.uniform3f( obj.ambientLoc[i], 0,0,0);
gl.uniform3f( obj.specularLoc[i], 0,0,0);
gl.uniform3f( obj.diffuseLoc[i], 0,0,0);
}
}
if (fixed_size) {
gl.uniform2f( obj.textScaleLoc, 0.75/this.vp.width, 0.75/this.vp.height);
}
gl.enableVertexAttribArray( this.posLoc );
enabled.posLoc = true;
var nc = obj.colorCount;
count = obj.vertexCount;
if (type === "spheres") {
subscene = this.getObj(subsceneid);
var scale = subscene.par3d.scale,
scount = count, indices;
gl.vertexAttribPointer(this.posLoc,  3, gl.FLOAT, false, 4*this.sphere.vOffsets.stride,  0);
gl.enableVertexAttribArray(obj.normLoc );
enabled.normLoc = true;
gl.vertexAttribPointer(obj.normLoc,  3, gl.FLOAT, false, 4*this.sphere.vOffsets.stride,  0);
gl.disableVertexAttribArray( this.colLoc );
var sphereNorm = new CanvasMatrix4();
sphereNorm.scale(scale[0], scale[1], scale[2]);
sphereNorm.multRight(this.normMatrix);
gl.uniformMatrix4fv( obj.normMatLoc, false, new Float32Array(sphereNorm.getAsArray()) );
if (nc == 1) {
gl.vertexAttrib4fv( this.colLoc, new Float32Array(obj.onecolor));
}
if (has_texture) {
gl.enableVertexAttribArray( obj.texLoc );
enabled.texLoc = true;
gl.vertexAttribPointer(obj.texLoc, 2, gl.FLOAT, false, 4*this.sphere.vOffsets.stride,
4*this.sphere.vOffsets.tofs);
gl.activeTexture(gl.TEXTURE0);
gl.bindTexture(gl.TEXTURE_2D, obj.texture);
gl.uniform1i( obj.sampler, 0);
}
if (depth_sort)
indices = this.depthSort(obj);
for (i = 0; i < scount; i++) {
sphereMV = new CanvasMatrix4();
if (depth_sort) {
baseofs = indices[i]*obj.vOffsets.stride;
} else {
baseofs = i*obj.vOffsets.stride;
}
ofs = baseofs + obj.vOffsets.radofs;
sscale = obj.values[ofs];
sphereMV.scale(sscale/scale[0], sscale/scale[1], sscale/scale[2]);
sphereMV.translate(obj.values[baseofs],
obj.values[baseofs+1],
obj.values[baseofs+2]);
sphereMV.multRight(this.mvMatrix);
gl.uniformMatrix4fv( obj.mvMatLoc, false, new Float32Array(sphereMV.getAsArray()) );
if (nc > 1) {
ofs = baseofs + obj.vOffsets.cofs;
gl.vertexAttrib4f( this.colLoc, obj.values[ofs],
obj.values[ofs+1],
obj.values[ofs+2],
obj.values[ofs+3] );
}
gl.bindBuffer(gl.ELEMENT_ARRAY_BUFFER, this.sphere.ibuf);
gl.drawElements(gl.TRIANGLES, this.sphere.sphereCount, gl.UNSIGNED_SHORT, 0);
}
this.disableArrays(obj, enabled);
if (typeof obj.polygon_offset !== "undefined") 
gl.disable(gl.POLYGON_OFFSET_FILL);
return;
} else {
if (obj.colorCount === 1) {
gl.disableVertexAttribArray( this.colLoc );
gl.vertexAttrib4fv( this.colLoc, new Float32Array(obj.onecolor));
} else {
gl.enableVertexAttribArray( this.colLoc );
enabled.colLoc = true;
gl.vertexAttribPointer(this.colLoc, 4, gl.FLOAT, false, 4*obj.vOffsets.stride, 4*obj.vOffsets.cofs);
}
}
if (is_lit && obj.vOffsets.nofs > 0) {
gl.enableVertexAttribArray( obj.normLoc );
enabled.normLoc = true;
gl.vertexAttribPointer(obj.normLoc, 3, gl.FLOAT, false, 4*obj.vOffsets.stride, 4*obj.vOffsets.nofs);
}
if (has_texture || type === "text") {
gl.enableVertexAttribArray( obj.texLoc );
enabled.texLoc = true;
gl.vertexAttribPointer(obj.texLoc, 2, gl.FLOAT, false, 4*obj.vOffsets.stride, 4*obj.vOffsets.tofs);
gl.activeTexture(gl.TEXTURE0);
gl.bindTexture(gl.TEXTURE_2D, obj.texture);
gl.uniform1i( obj.sampler, 0);
}
if (fixed_quads) {
gl.enableVertexAttribArray( obj.ofsLoc );
enabled.ofsLoc = true;
gl.vertexAttribPointer(obj.ofsLoc, 2, gl.FLOAT, false, 4*obj.vOffsets.stride, 4*obj.vOffsets.oofs);
}
if (typeof obj.userAttributes !== "undefined") {
for (attr in obj.userAttribSizes) {  // Not all attributes may have been used
gl.enableVertexAttribArray( obj.userAttribLocations[attr] );
gl.vertexAttribPointer( obj.userAttribLocations[attr], obj.userAttribSizes[attr],
gl.FLOAT, false, 4*obj.vOffsets.stride, 4*obj.userAttribOffsets[attr]);
}
}
if (typeof obj.userUniforms !== "undefined") {
for (attr in obj.userUniformLocations) {
var loc = obj.userUniformLocations[attr];
if (loc !== null) {
var uniform = obj.userUniforms[attr];
if (typeof uniform.length === "undefined")
gl.uniform1f(loc, uniform);
else if (typeof uniform[0].length === "undefined") {
uniform = new Float32Array(uniform);
switch(uniform.length) {
case 2: gl.uniform2fv(loc, uniform); break;
case 3: gl.uniform3fv(loc, uniform); break;
case 4: gl.uniform4fv(loc, uniform); break;
default: console.warn("bad uniform length");
}
} else if (uniform.length == 4 && uniform[0].length == 4)
gl.uniformMatrix4fv(loc, false, new Float32Array(uniform.getAsArray()));
else
console.warn("unsupported uniform matrix");
}
}
}
for (pass = 0; pass < obj.passes; pass++) {
pmode = obj.pmode[pass];
if (pmode === "culled")
continue;
mode = fat_lines && (is_lines || pmode == "lines") ? "TRIANGLES" : this.mode4type[type];
if (depth_sort && pmode == "filled") {// Don't try depthsorting on wireframe or points
var faces = this.depthSort(obj),
nfaces = faces.length,
frowsize = Math.floor(obj.f[pass].length/nfaces);
if (type !== "spheres") {
var f = obj.index_uint ? new Uint32Array(obj.f[pass].length) : new Uint16Array(obj.f[pass].length);
for (i=0; i<nfaces; i++) {
for (j=0; j<frowsize; j++) {
f[frowsize*i + j] = obj.f[pass][frowsize*faces[i] + j];
}
}
gl.bindBuffer(gl.ELEMENT_ARRAY_BUFFER, obj.ibuf[pass]);
gl.bufferData(gl.ELEMENT_ARRAY_BUFFER, f, gl.DYNAMIC_DRAW);
}
}
if (is_twosided)
gl.uniform1i(obj.frontLoc, pass !== 0);
if (type !== "spheres") 
gl.bindBuffer(gl.ELEMENT_ARRAY_BUFFER, obj.ibuf[pass]);
if (type === "sprites" || type === "text" || type === "quads") {
count = count * 6/4;
} else if (type === "surface") {
count = obj.f[pass].length;
}
count = obj.f[pass].length;
if (!is_lines && pmode === "lines" && !fat_lines) {
mode = "LINES";
} else if (pmode === "points") {
mode = "POINTS";
}
if ((is_lines || pmode === "lines") && fat_lines) {
gl.enableVertexAttribArray(obj.pointLoc);
enabled.pointLoc = true;
gl.vertexAttribPointer(obj.pointLoc, 2, gl.FLOAT, false, 4*obj.vOffsets.stride, 4*obj.vOffsets.pointofs);
gl.enableVertexAttribArray(obj.nextLoc );
enabled.nextLoc = true;
gl.vertexAttribPointer(obj.nextLoc, 3, gl.FLOAT, false, 4*obj.vOffsets.stride, 4*obj.vOffsets.nextofs);
gl.uniform1f(obj.aspectLoc, this.vp.width/this.vp.height);
gl.uniform1f(obj.lwdLoc, this.getMaterial(id, "lwd")/this.vp.height);
}
gl.vertexAttribPointer(this.posLoc,  3, gl.FLOAT, false, 4*obj.vOffsets.stride,  4*obj.vOffsets.vofs);
gl.drawElements(gl[mode], count, obj.index_uint ? gl.UNSIGNED_INT : gl.UNSIGNED_SHORT, 0);
this.disableArrays(obj, enabled);
}
if (typeof obj.polygon_offset !== "undefined") 
gl.disable(gl.POLYGON_OFFSET_FILL);
};
/**
* Draw the background for a subscene
* @param { number } id - id of background object
* @param { number } subsceneid - id of subscene
*/
rglwidgetClass.prototype.drawBackground = function(id, subsceneid) {
var gl = this.gl || this.initGL(),
obj = this.getObj(id),
bg, i;
if (!obj.initialized)
this.initObj(id);
if (obj.colors.length) {
bg = obj.colors[0];
gl.clearColor(bg[0], bg[1], bg[2], bg[3]);
gl.depthMask(true);
gl.clear(gl.COLOR_BUFFER_BIT | gl.DEPTH_BUFFER_BIT);
}
if (typeof obj.quad !== "undefined") {
this.prMatrix.makeIdentity();
this.mvMatrix.makeIdentity();
gl.disable(gl.BLEND);
gl.disable(gl.DEPTH_TEST);
gl.depthMask(false);
for (i=0; i < obj.quad.length; i++)
this.drawObj(obj.quad[i], subsceneid);
}
};
/**
* Draw a subscene
* @param { number } subsceneid - id of subscene
* @param { boolean } opaquePass - is this the opaque drawing pass?
*/
rglwidgetClass.prototype.drawSubscene = function(subsceneid, opaquePass) {
var gl = this.gl || this.initGL(),
sub = this.getObj(subsceneid),
objects = this.scene.objects,
subids = sub.objects,
subscene_has_faces = false,
subscene_needs_sorting = false,
flags, i, obj;
if (sub.par3d.skipRedraw)
return;
for (i=0; i < subids.length; i++) {
obj = objects[subids[i]];
flags = obj.flags;
if (typeof flags !== "undefined") {
subscene_has_faces |= (flags & this.f_is_lit)
& !(flags & this.f_fixed_quads);
obj.is_transparent = (flags & this.f_is_transparent) || obj.someHidden;
subscene_needs_sorting |= (flags & this.f_depth_sort) || obj.is_transparent;
}
}
this.setViewport(subsceneid);
if (typeof sub.backgroundId !== "undefined" && opaquePass)
this.drawBackground(sub.backgroundId, subsceneid);
if (subids.length) {
this.setprMatrix(subsceneid);
this.setmvMatrix(subsceneid);
if (subscene_has_faces) {
this.setnormMatrix(subsceneid);
if ((sub.flags & this.f_sprites_3d) &&
typeof sub.spriteNormmat === "undefined") {
sub.spriteNormmat = new CanvasMatrix4(this.normMatrix);
}
}
if (subscene_needs_sorting)
this.setprmvMatrix();
var clipids = sub.clipplanes;
if (typeof clipids === "undefined") {
console.warn("bad clipids");
}
if (clipids.length > 0) {
this.invMatrix = new CanvasMatrix4(this.mvMatrix);
this.invMatrix.invert();
for (i = 0; i < clipids.length; i++)
this.drawObj(clipids[i], subsceneid);
}
subids = sub.opaque.concat(sub.transparent);
if (opaquePass) {
gl.enable(gl.DEPTH_TEST);
gl.depthMask(true);
gl.disable(gl.BLEND);
for (i = 0; i < subids.length; i++) {
if (!this.getObj(subids[i]).is_transparent)	
this.drawObj(subids[i], subsceneid);
}
} else {
gl.depthMask(false);
gl.blendFuncSeparate(gl.SRC_ALPHA, gl.ONE_MINUS_SRC_ALPHA,
gl.ONE, gl.ONE);
gl.enable(gl.BLEND);
for (i = 0; i < subids.length; i++) {
if (this.getObj(subids[i]).is_transparent)
this.drawObj(subids[i], subsceneid);
}
}
subids = sub.subscenes;
for (i = 0; i < subids.length; i++) {
this.drawSubscene(subids[i], opaquePass);
}
}
};
/**
* Respond to brush change
*/
rglwidgetClass.prototype.selectionChanged = function() {
var i, j, k, id, subid = this.select.subscene, subscene,
objids, obj,
p1 = this.select.region.p1, p2 = this.select.region.p2,
filter, selection = [], handle, keys, xmin, x, xmax, ymin, y, ymax, z, v,
someHidden;
if (!subid)
return;
subscene = this.getObj(subid);
objids = subscene.objects;
filter = this.scene.crosstalk.filter;
this.setmvMatrix(subid);
this.setprMatrix(subid);
this.setprmvMatrix();
xmin = Math.min(p1.x, p2.x);
xmax = Math.max(p1.x, p2.x);
ymin = Math.min(p1.y, p2.y);
ymax = Math.max(p1.y, p2.y);
for (i = 0; i < objids.length; i++) {
id = objids[i];
j = this.scene.crosstalk.id.indexOf(id);
if (j >= 0) {
keys = this.scene.crosstalk.key[j];
obj = this.getObj(id);
someHidden = false;
for (k = 0; k < keys.length; k++) {
if (filter && filter.indexOf(keys[k]) < 0) {
someHidden = true;
continue;
}
v = [].concat(obj.vertices[k]).concat(1.0);
v = this.multVM(v, this.prmvMatrix);
x = v[0]/v[3];
y = v[1]/v[3];
z = v[2]/v[3];
if (xmin <= x && x <= xmax && ymin <= y && y <= ymax && -1.0 <= z && z <= 1.0) {
selection.push(keys[k]);
} else
someHidden = true;
}
obj.someHidden = someHidden && (filter || selection.length);
obj.initialized = false;
/* Who should we notify?  Only shared data in the current subscene, or everyone? */
if (!this.equalArrays(selection, this.scene.crosstalk.selection)) {
handle = this.scene.crosstalk.sel_handle[j];
handle.set(selection, {rglSubsceneId: this.select.subscene});
}
}
}
};
/**
* Respond to selection or filter change from crosstalk
* @param { Object } event - crosstalk event
* @param { boolean } filter - filter or selection?
*/
rglwidgetClass.prototype.selection = function(event, filter) {
var i, j, ids, obj, keys, crosstalk = this.scene.crosstalk,
selection, someHidden;
// Record the message and find out if this event makes some objects have mixed values:
crosstalk = this.scene.crosstalk;
if (filter) {
filter = crosstalk.filter = event.value;
selection = crosstalk.selection;
} else {  
selection = crosstalk.selection = event.value;
filter = crosstalk.filter;
}
ids = crosstalk.id;
for (i = 0; i < ids.length ; i++) {
obj = this.getObj(ids[i]);
obj.initialized = false;
keys = crosstalk.key[i];
someHidden = false;
for (j = 0; j < keys.length && !someHidden; j++) {
if ((filter && filter.indexOf(keys[j]) < 0) ||
(selection.length && selection.indexOf(keys[j]) < 0))
someHidden = true;
}
obj.someHidden = someHidden;
}
this.drawScene();
};
/**
* Clear the selection brush
* @param { number } except - Subscene that should ignore this request
*/
rglwidgetClass.prototype.clearBrush = function(except) {
if (this.select.subscene != except) {
this.select.state = "inactive";
this.delFromSubscene(this.scene.brushId, this.select.subscene);
}
this.drawScene();
};
/**
* Compute mouse coordinates relative to current canvas
* @returns { Object }
* @param { Object } event - event object from mouse click
*/
rglwidgetClass.prototype.relMouseCoords = function(event) {
var totalOffsetX = 0,
totalOffsetY = 0,
currentElement = this.canvas;
do {
totalOffsetX += currentElement.offsetLeft;
totalOffsetY += currentElement.offsetTop;
currentElement = currentElement.offsetParent;
}
while(currentElement);
var canvasX = event.pageX - totalOffsetX,
canvasY = event.pageY - totalOffsetY;
return {x:canvasX, y:canvasY};
};
/**
* Set mouse handlers for the scene
*/
rglwidgetClass.prototype.setMouseHandlers = function() {
var self = this, activeSubscene, handler,
handlers = {}, drag = 0;
handlers.rotBase = 0;
this.screenToVector = function(x, y) {
var viewport = this.getObj(activeSubscene).par3d.viewport,
width = viewport.width*this.canvas.width,
height = viewport.height*this.canvas.height,
radius = Math.max(width, height)/2.0,
cx = width/2.0,
cy = height/2.0,
px = (x-cx)/radius,
py = (y-cy)/radius,
plen = Math.sqrt(px*px+py*py);
if (plen > 1.e-6) {
px = px/plen;
py = py/plen;
}
var angle = (Math.SQRT2 - plen)/Math.SQRT2*Math.PI/2,
z = Math.sin(angle),
zlen = Math.sqrt(1.0 - z*z);
px = px * zlen;
py = py * zlen;
return [px, py, z];
};
handlers.trackballdown = function(x,y) {
var activeSub = this.getObj(activeSubscene),
activeModel = this.getObj(this.useid(activeSub.id, "model")),
i, l = activeModel.par3d.listeners;
handlers.rotBase = this.screenToVector(x, y);
this.saveMat = [];
for (i = 0; i < l.length; i++) {
activeSub = this.getObj(l[i]);
activeSub.saveMat = new CanvasMatrix4(activeSub.par3d.userMatrix);
}
};
handlers.trackballmove = function(x,y) {
var rotCurrent = this.screenToVector(x,y),
rotBase = handlers.rotBase,
dot = rotBase[0]*rotCurrent[0] +
rotBase[1]*rotCurrent[1] +
rotBase[2]*rotCurrent[2],
angle = Math.acos( dot/this.vlen(rotBase)/this.vlen(rotCurrent) )*180.0/Math.PI,
axis = this.xprod(rotBase, rotCurrent),
objects = this.scene.objects,
activeSub = this.getObj(activeSubscene),
activeModel = this.getObj(this.useid(activeSub.id, "model")),
l = activeModel.par3d.listeners,
i;
for (i = 0; i < l.length; i++) {
activeSub = this.getObj(l[i]);
activeSub.par3d.userMatrix.load(objects[l[i]].saveMat);
activeSub.par3d.userMatrix.rotate(angle, axis[0], axis[1], axis[2]);
}
this.drawScene();
};
handlers.trackballend = 0;
this.clamp = function(x, lo, hi) {
return Math.max(lo, Math.min(x, hi));
};
this.screenToPolar = function(x,y) {
var viewport = this.getObj(activeSubscene).par3d.viewport,
width = viewport.width*this.canvas.width,
height = viewport.height*this.canvas.height,
r = Math.min(width, height)/2,
dx = this.clamp(x - width/2, -r, r),
dy = this.clamp(y - height/2, -r, r);
return [Math.asin(dx/r), Math.asin(-dy/r)];
};
handlers.polardown = function(x,y) {
var activeSub = this.getObj(activeSubscene),
activeModel = this.getObj(this.useid(activeSub.id, "model")),
i, l = activeModel.par3d.listeners;
handlers.dragBase = this.screenToPolar(x, y);
this.saveMat = [];
for (i = 0; i < l.length; i++) {
activeSub = this.getObj(l[i]);
activeSub.saveMat = new CanvasMatrix4(activeSub.par3d.userMatrix);
activeSub.camBase = [-Math.atan2(activeSub.saveMat.m13, activeSub.saveMat.m11),
Math.atan2(activeSub.saveMat.m32, activeSub.saveMat.m22)];
}
};
handlers.polarmove = function(x,y) {
var dragCurrent = this.screenToPolar(x,y),
activeSub = this.getObj(activeSubscene),
activeModel = this.getObj(this.useid(activeSub.id, "model")),
objects = this.scene.objects,
l = activeModel.par3d.listeners,
i, changepos = [];
for (i = 0; i < l.length; i++) {
activeSub = this.getObj(l[i]);
for (j=0; j<2; j++)
changepos[j] = -(dragCurrent[j] - handlers.dragBase[j]);
activeSub.par3d.userMatrix.makeIdentity();
activeSub.par3d.userMatrix.rotate(changepos[0]*180/Math.PI, 0,-1,0);
activeSub.par3d.userMatrix.multRight(objects[l[i]].saveMat);
activeSub.par3d.userMatrix.rotate(changepos[1]*180/Math.PI, -1,0,0);
}
this.drawScene();
};
handlers.polarend = 0;
handlers.axisdown = function(x,y) {
handlers.rotBase = this.screenToVector(x, this.canvas.height/2);
var activeSub = this.getObj(activeSubscene),
activeModel = this.getObj(this.useid(activeSub.id, "model")),
i, l = activeModel.par3d.listeners;
for (i = 0; i < l.length; i++) {
activeSub = this.getObj(l[i]);
activeSub.saveMat = new CanvasMatrix4(activeSub.par3d.userMatrix);
}
};
handlers.axismove = function(x,y) {
var rotCurrent = this.screenToVector(x, this.canvas.height/2),
rotBase = handlers.rotBase,
angle = (rotCurrent[0] - rotBase[0])*180/Math.PI,
rotMat = new CanvasMatrix4();
rotMat.rotate(angle, handlers.axis[0], handlers.axis[1], handlers.axis[2]);
var activeSub = this.getObj(activeSubscene),
activeModel = this.getObj(this.useid(activeSub.id, "model")),
i, l = activeModel.par3d.listeners;
for (i = 0; i < l.length; i++) {
activeSub = this.getObj(l[i]);
activeSub.par3d.userMatrix.load(activeSub.saveMat);
activeSub.par3d.userMatrix.multLeft(rotMat);
}
this.drawScene();
};
handlers.axisend = 0;
handlers.y0zoom = 0;
handlers.zoom0 = 0;
handlers.zoomdown = function(x, y) {
var activeSub = this.getObj(activeSubscene),
activeProjection = this.getObj(this.useid(activeSub.id, "projection")),
i, l = activeProjection.par3d.listeners;
handlers.y0zoom = y;
for (i = 0; i < l.length; i++) {
activeSub = this.getObj(l[i]);
activeSub.zoom0 = Math.log(activeSub.par3d.zoom);
}
};
handlers.zoommove = function(x, y) {
var activeSub = this.getObj(activeSubscene),
activeProjection = this.getObj(this.useid(activeSub.id, "projection")),
i, l = activeProjection.par3d.listeners;
for (i = 0; i < l.length; i++) {
activeSub = this.getObj(l[i]);
activeSub.par3d.zoom = Math.exp(activeSub.zoom0 + (y-handlers.y0zoom)/this.canvas.height);
}
this.drawScene();
};
handlers.zoomend = 0;
handlers.y0fov = 0;
handlers.fovdown = function(x, y) {
handlers.y0fov = y;
var activeSub = this.getObj(activeSubscene),
activeProjection = this.getObj(this.useid(activeSub.id, "projection")),
i, l = activeProjection.par3d.listeners;
for (i = 0; i < l.length; i++) {
activeSub = this.getObj(l[i]);
activeSub.fov0 = activeSub.par3d.FOV;
}
};
handlers.fovmove = function(x, y) {
var activeSub = this.getObj(activeSubscene),
activeProjection = this.getObj(this.useid(activeSub.id, "projection")),
i, l = activeProjection.par3d.listeners;
for (i = 0; i < l.length; i++) {
activeSub = this.getObj(l[i]);
activeSub.par3d.FOV = Math.max(1, Math.min(179, activeSub.fov0 +
180*(y-handlers.y0fov)/this.canvas.height));
}
this.drawScene();
};
handlers.fovend = 0;
handlers.selectingdown = function(x, y) {
var viewport = this.getObj(activeSubscene).par3d.viewport,
width = viewport.width*this.canvas.width,
height = viewport.height*this.canvas.height, 
p = {x: 2.0*x/width - 1.0, y: 2.0*y/height - 1.0};
this.select.region = {p1: p, p2: p};
if (this.select.subscene && this.select.subscene != activeSubscene)
this.delFromSubscene(this.scene.brushId, this.select.subscene);
this.select.subscene = activeSubscene;
this.addToSubscene(this.scene.brushId, activeSubscene);
this.select.state = "changing";
if (typeof this.scene.brushId !== "undefined")
this.getObj(this.scene.brushId).initialized = false;
this.drawScene();
};
handlers.selectingmove = function(x, y) {
var viewport = this.getObj(activeSubscene).par3d.viewport,
width = viewport.width*this.canvas.width,
height = viewport.height*this.canvas.height;
if (this.select.state === "inactive") 
return;
this.select.region.p2 = {x: 2.0*x/width - 1.0, y: 2.0*y/height - 1.0};
if (typeof this.scene.brushId !== "undefined")
this.getObj(this.scene.brushId).initialized = false;
this.drawScene();
};
handlers.selectingend = 0;
this.canvas.onmousedown = function ( ev ){
if (!ev.which) // Use w3c defns in preference to MS
switch (ev.button) {
case 0: ev.which = 1; break;
case 1:
case 4: ev.which = 2; break;
case 2: ev.which = 3;
}
drag = ["left", "middle", "right"][ev.which-1];
var coords = self.relMouseCoords(ev);
coords.y = self.canvas.height-coords.y;
activeSubscene = self.whichSubscene(coords);
var sub = self.getObj(activeSubscene), f;
handler = sub.par3d.mouseMode[drag];
switch (handler) {
case "xAxis":
handler = "axis";
handlers.axis = [1.0, 0.0, 0.0];
break;
case "yAxis":
handler = "axis";
handlers.axis = [0.0, 1.0, 0.0];
break;
case "zAxis":
handler = "axis";
handlers.axis = [0.0, 0.0, 1.0];
break;
}
f = handlers[handler + "down"];
if (f) {
coords = self.translateCoords(activeSubscene, coords);
f.call(self, coords.x, coords.y);
ev.preventDefault();
} else
console.warn("Mouse handler '" + handler + "' is not implemented.");
};
this.canvas.onmouseup = function ( ev ){
if ( drag === 0 ) return;
var f = handlers[handler + "end"];
if (f) {
f.call(self);
ev.preventDefault();
}
drag = 0;
};
this.canvas.onmouseout = this.canvas.onmouseup;
this.canvas.onmousemove = function ( ev ) {
if ( drag === 0 ) return;
var f = handlers[handler + "move"];
if (f) {
var coords = self.relMouseCoords(ev);
coords.y = self.canvas.height - coords.y;
coords = self.translateCoords(activeSubscene, coords);
f.call(self, coords.x, coords.y);
}
};
handlers.wheelHandler = function(ev) {
var del = 1.02, i;
if (ev.shiftKey) del = 1.002;
var ds = ((ev.detail || ev.wheelDelta) > 0) ? del : (1 / del);
if (typeof activeSubscene === "undefined")
activeSubscene = self.scene.rootSubscene;
var activeSub = self.getObj(activeSubscene),
activeProjection = self.getObj(self.useid(activeSub.id, "projection")),
l = activeProjection.par3d.listeners;
for (i = 0; i < l.length; i++) {
activeSub = self.getObj(l[i]);
activeSub.par3d.zoom *= ds;
}
self.drawScene();
ev.preventDefault();
};
this.canvas.addEventListener("DOMMouseScroll", handlers.wheelHandler, false);
this.canvas.addEventListener("mousewheel", handlers.wheelHandler, false);
};
/**
* Find a particular subscene by inheritance
* @returns { number } id of subscene to use
* @param { number } subsceneid - child subscene
* @param { string } type - type of inheritance:  "projection" or "model"
*/
rglwidgetClass.prototype.useid = function(subsceneid, type) {
var sub = this.getObj(subsceneid);
if (sub.embeddings[type] === "inherit")
return(this.useid(sub.parent, type));
else
return subsceneid;
};
/**
* Check whether point is in viewport of subscene
* @returns {boolean}
* @param { Object } coords - screen coordinates of point
* @param { number } subsceneid - subscene to check
*/
rglwidgetClass.prototype.inViewport = function(coords, subsceneid) {
var viewport = this.getObj(subsceneid).par3d.viewport,
x0 = coords.x - viewport.x*this.canvas.width,
y0 = coords.y - viewport.y*this.canvas.height;
return 0 <= x0 && x0 <= viewport.width*this.canvas.width &&
0 <= y0 && y0 <= viewport.height*this.canvas.height;
};
/**
* Find which subscene contains a point
* @returns { number } subscene id
* @param { Object } coords - coordinates of point
*/
rglwidgetClass.prototype.whichSubscene = function(coords) {
var self = this,
recurse = function(subsceneid) {
var subscenes = self.getChildSubscenes(subsceneid), i, id;
for (i=0; i < subscenes.length; i++) {
id = recurse(subscenes[i]);
if (typeof(id) !== "undefined")
return(id);
}
if (self.inViewport(coords, subsceneid))
return(subsceneid);
else
return undefined;
},
rootid = this.scene.rootSubscene,
result = recurse(rootid);
if (typeof(result) === "undefined")
result = rootid;
return result;
};
/**
* Translate from window coordinates to viewport coordinates
* @returns { Object } translated coordinates
* @param { number } subsceneid - which subscene to use?
* @param { Object } coords - point to translate
*/
rglwidgetClass.prototype.translateCoords = function(subsceneid, coords) {
var viewport = this.getObj(subsceneid).par3d.viewport;
return {x: coords.x - viewport.x*this.canvas.width,
y: coords.y - viewport.y*this.canvas.height};
};
/**
* Initialize the sphere object
*/
rglwidgetClass.prototype.initSphere = function() {
var verts = this.scene.sphereVerts,
reuse = verts.reuse, result;
if (typeof reuse !== "undefined") {
var prev = document.getElementById(reuse).rglinstance.sphere;
result = {values: prev.values, vOffsets: prev.vOffsets, it: prev.it};
} else
result = {values: new Float32Array(this.flatten(this.cbind(this.transpose(verts.vb),
this.transpose(verts.texcoords)))),
it: new Uint16Array(this.flatten(this.transpose(verts.it))),
vOffsets: {vofs:0, cofs:-1, nofs:-1, radofs:-1, oofs:-1,
tofs:3, nextofs:-1, pointofs:-1, stride:5}};
result.sphereCount = result.it.length;
this.sphere = result;
};
/**
* Set the vertices in the selection box object
*/
rglwidgetClass.prototype.initSelection = function(id) {
if (typeof this.select.region === "undefined")
return;
var obj = this.getObj(id),
width = this.canvas.width,
height = this.canvas.height, 
p1 = this.select.region.p1,
p2 = this.select.region.p2;
obj.vertices = [[p1.x, p1.y, 0.0],
[p2.x, p1.y, 0.0],
[p2.x, p2.y, 0.0],
[p1.x, p2.y, 0.0],
[p1.x, p1.y, 0.0]];
};
/**
* Do the gl part of initializing the sphere
*/
rglwidgetClass.prototype.initSphereGL = function() {
var gl = this.gl || this.initGL(), sphere = this.sphere;
if (gl.isContextLost()) return;
sphere.buf = gl.createBuffer();
gl.bindBuffer(gl.ARRAY_BUFFER, sphere.buf);
gl.bufferData(gl.ARRAY_BUFFER, sphere.values, gl.STATIC_DRAW);
sphere.ibuf = gl.createBuffer();
gl.bindBuffer(gl.ELEMENT_ARRAY_BUFFER, sphere.ibuf);
gl.bufferData(gl.ELEMENT_ARRAY_BUFFER, sphere.it, gl.STATIC_DRAW);
return;
};
/**
* Initialize the DOM object
* @param { Object } el - the DOM object
* @param { Object } x - the scene data sent by JSON from R
*/
rglwidgetClass.prototype.initialize = function(el, x) {
this.textureCanvas = document.createElement("canvas");
this.textureCanvas.style.display = "block";
this.scene = x;
this.normMatrix = new CanvasMatrix4();
this.saveMat = {};
this.distance = null;
this.posLoc = 0;
this.colLoc = 1;
if (el) {
el.rglinstance = this;
this.el = el;
this.webGLoptions = el.rglinstance.scene.webGLoptions;
this.initCanvas();
}
if (typeof Shiny !== "undefined") {
var self = this;
Shiny.addCustomMessageHandler("shinyGetPar3d",
function(message) {
var i, param, 
subscene = self.getObj(message.subscene),
parameters = [].concat(message.parameters),
result = {tag: message.tag, subscene: message.subscene};
if (typeof subscene !== "undefined") {
for (i = 0; i < parameters.length; i++) {
param = parameters[i];
result[param] = subscene.par3d[param];
};
} else {
console.log("subscene "+message.subscene+" undefined.")
}
Shiny.setInputValue("par3d:shinyPar3d", result, {priority: "event"});
});
Shiny.addCustomMessageHandler("shinySetPar3d",
function(message) {
var param = message.parameter, 
subscene = self.getObj(message.subscene);
if (typeof subscene !== "undefined") {
subscene.par3d[param] = message.value;
subscene.initialized = false;
self.drawScene();
} else {
console.log("subscene "+message.subscene+" undefined.")
}
})
}
};
/**
* Restart the WebGL canvas
*/
rglwidgetClass.prototype.restartCanvas = function() {
var newcanvas = document.createElement("canvas"),
self = this;
newcanvas.width = this.el.width;
newcanvas.height = this.el.height;
newcanvas.addEventListener("webglcontextrestored",
this.onContextRestored, false);
newcanvas.addEventListener("webglcontextlost",
this.onContextLost, false);
while (this.el.firstChild) {
this.el.removeChild(this.el.firstChild);
}
this.el.appendChild(newcanvas);
this.canvas = newcanvas;
this.setMouseHandlers();
if (this.gl) 
Object.keys(this.scene.objects).forEach(function(key){
self.getObj(parseInt(key, 10)).texture = undefined; 
});
this.gl = null;
};
/**
* Initialize the WebGL canvas
*/
rglwidgetClass.prototype.initCanvas = function() {
this.restartCanvas();
var objs = this.scene.objects,
self = this;
Object.keys(objs).forEach(function(key){
var id = parseInt(key, 10),
obj = self.getObj(id);
if (typeof obj.reuse !== "undefined")
self.copyObj(id, obj.reuse);
});
Object.keys(objs).forEach(function(key){
self.initSubscene(parseInt(key, 10));
});
this.setMouseHandlers();
this.initSphere();
this.onContextRestored = function(event) {
self.initGL();
self.drawScene();
};
this.onContextLost = function(event) {
if (!self.drawing)
this.gl = null;
event.preventDefault();
};
this.initGL0();
this.lazyLoadScene = function() {
if (typeof self.slide === "undefined")
self.slide = self.getSlide();
if (self.isInBrowserViewport()) {
if (!self.gl || self.gl.isContextLost())
self.initGL();
self.drawScene();
}
};
window.addEventListener("DOMContentLoaded", this.lazyLoadScene, false);
window.addEventListener("load", this.lazyLoadScene, false);
window.addEventListener("resize", this.lazyLoadScene, false);
window.addEventListener("scroll", this.lazyLoadScene, false);
this.slide = this.getSlide();
if (this.slide) {
if (typeof this.slide.rgl === "undefined")
this.slide.rgl = [this];
else
this.slide.rgl.push(this);
if (this.scene.context.rmarkdown) 
if (this.scene.context.rmarkdown === "ioslides_presentation") {
this.slide.setAttribute("slideenter", "this.rgl.forEach(function(scene) { scene.lazyLoadScene.call(window);})");
} else if (this.scene.context.rmarkdown === "slidy_presentation") {
// This method would also work in ioslides, but it gets triggered
// something like 5 times per slide for every slide change, so
// you'd need a quicker function than lazyLoadScene.
var MutationObserver = window.MutationObserver || window.WebKitMutationObserver || window.MozMutationObserver,
observer = new MutationObserver(function(mutations) {
mutations.forEach(function(mutation) {
self.slide.rgl.forEach(function(scene) { scene.lazyLoadScene.call(window); });});});
observer.observe(this.slide, { attributes: true, attributeFilter:["class"] });
}
}
};
/**
* Start the writeWebGL scene. This is only used by writeWebGL; rglwidget has
no debug element and does the drawing in rglwidget.js.
*/
rglwidgetClass.prototype.start = function() {
if (typeof this.prefix !== "undefined") {
this.debugelement = document.getElementById(this.prefix + "debug");
this.debug("");
}
this.drag = 0;
this.drawScene();
};
/**
* Display a debug message
* @param { string } msg - The message to display
* @param { Object } [img] - Image to insert before message
*/
rglwidgetClass.prototype.debug = function(msg, img) {
if (typeof this.debugelement !== "undefined" && this.debugelement !== null) {
this.debugelement.innerHTML = msg;
if (typeof img !== "undefined") {
this.debugelement.insertBefore(img, this.debugelement.firstChild);
}
} else if (msg !== "")
alert(msg);
};
/**
* Get the snapshot image of this scene
* @returns { Object } The img DOM element
*/
rglwidgetClass.prototype.getSnapshot = function() {
var img;
if (typeof this.scene.snapshot !== "undefined") {
img = document.createElement("img");
img.src = this.scene.snapshot;
img.alt = "Snapshot";
}
return img;
};
/**
* Initial test for WebGL
*/
rglwidgetClass.prototype.initGL0 = function() {
if (!window.WebGLRenderingContext){
alert("Your browser does not support WebGL. See http://get.webgl.org");
return;
}
};
/**
* If we are in an ioslides or slidy presentation, get the
* DOM element of the current slide
* @returns { Object }
*/
rglwidgetClass.prototype.getSlide = function() {
var result = this.el, done = false;
while (result && !done && this.scene.context.rmarkdown) {
switch(this.scene.context.rmarkdown) {
case "ioslides_presentation":
if (result.tagName === "SLIDE") return result;
break;
case "slidy_presentation":
if (result.tagName === "DIV" && result.classList.contains("slide"))
return result;
break;
default: return null;
}
result = result.parentElement;
}
return null;
};
/**
* Is this scene visible in the browser?
* @returns { boolean }
*/
rglwidgetClass.prototype.isInBrowserViewport = function() {
var rect = this.canvas.getBoundingClientRect(),
windHeight = (window.innerHeight || document.documentElement.clientHeight),
windWidth = (window.innerWidth || document.documentElement.clientWidth);
if (this.scene.context && this.scene.context.rmarkdown !== null) {
if (this.slide)
return (this.scene.context.rmarkdown === "ioslides_presentation" &&
this.slide.classList.contains("current")) ||
(this.scene.context.rmarkdown === "slidy_presentation" &&
!this.slide.classList.contains("hidden"));
}
return (
rect.top >= -windHeight &&
rect.left >= -windWidth &&
rect.bottom <= 2*windHeight &&
rect.right <= 2*windWidth);
};
/**
* Initialize WebGL
* @returns { Object } the WebGL context
*/
rglwidgetClass.prototype.initGL = function() {
var self = this;
if (this.gl) {
if (!this.drawing && this.gl.isContextLost())
this.restartCanvas();
else
return this.gl;
}
// if (!this.isInBrowserViewport()) return; Return what??? At this point we know this.gl is null.
this.canvas.addEventListener("webglcontextrestored",
this.onContextRestored, false);
this.canvas.addEventListener("webglcontextlost",
this.onContextLost, false);
this.gl = this.canvas.getContext("webgl", this.webGLoptions) ||
this.canvas.getContext("experimental-webgl", this.webGLoptions);
this.index_uint = this.gl.getExtension("OES_element_index_uint");
var save = this.startDrawing();
this.initSphereGL();
Object.keys(this.scene.objects).forEach(function(key){
self.initObj(parseInt(key, 10));
});
this.stopDrawing(save);
return this.gl;
};
/**
* Resize the display to match element
* @param { Object } el - DOM element to match
*/
rglwidgetClass.prototype.resize = function(el) {
this.canvas.width = el.width;
this.canvas.height = el.height;
};
/**
* Draw the whole scene
*/
rglwidgetClass.prototype.drawScene = function() {
var gl = this.gl || this.initGL(),
wasDrawing = this.startDrawing();
if (!wasDrawing) {
if (this.select.state !== "inactive")
this.selectionChanged();
gl.enable(gl.DEPTH_TEST);
gl.depthFunc(gl.LEQUAL);
gl.clearDepth(1.0);
gl.clearColor(1,1,1,1);
gl.depthMask(true); // Must be true before clearing depth buffer
gl.clear(gl.COLOR_BUFFER_BIT | gl.DEPTH_BUFFER_BIT);
this.drawSubscene(this.scene.rootSubscene, true);
this.drawSubscene(this.scene.rootSubscene, false);
}
this.stopDrawing(wasDrawing);
};
/**
* Change the displayed subset
* @param { Object } el - Element of the control; not used.
* @param { Object } control - The subset control data.
*/
rglwidgetClass.prototype.subsetSetter = function(el, control) {
if (typeof control.subscenes === "undefined" ||
control.subscenes === null)
control.subscenes = this.scene.rootSubscene;
var value = Math.round(control.value),
subscenes = [].concat(control.subscenes),
fullset = [].concat(control.fullset),
i, j, entries, subsceneid,
adds = [], deletes = [],
ismissing = function(x) {
return fullset.indexOf(x) < 0;
},
tointeger = function(x) {
return parseInt(x, 10);
};
if (isNaN(value))
value = control.value = 0;
if (control.accumulate)
for (i=0; i <= value; i++)
adds = adds.concat(control.subsets[i]);
else
adds = adds.concat(control.subsets[value]);
deletes = fullset.filter(function(x) { return adds.indexOf(x) < 0; });
for (i = 0; i < subscenes.length; i++) {
subsceneid = subscenes[i];
if (typeof this.getObj(subsceneid) === "undefined")
this.alertOnce("typeof object is undefined");
for (j = 0; j < adds.length; j++)
this.addToSubscene(adds[j], subsceneid);
for (j = 0; j < deletes.length; j++)
this.delFromSubscene(deletes[j], subsceneid);
}
};
/**
* Change the requested property
* @param { Object } el - Element of the control; not used.
* @param { Object } control - The property setter control data.
*/
rglwidgetClass.prototype.propertySetter = function(el, control)  {
var value = control.value,
values = [].concat(control.values),
svals = [].concat(control.param),
direct = values[0] === null,
entries = [].concat(control.entries),
ncol = entries.length,
nrow = values.length/ncol,
properties = this.repeatToLen(control.properties, ncol),
objids = this.repeatToLen(control.objids, ncol),
property, objid = objids[0],
obj = this.getObj(objid),
propvals, i, v1, v2, p, entry, gl, needsBinding,
newprop, newid,
getPropvals = function() {
if (property === "userMatrix")
return obj.par3d.userMatrix.getAsArray();
else if (property === "scale" || property === "FOV" || property === "zoom")
return [].concat(obj.par3d[property]);
else
return [].concat(obj[property]);
};
putPropvals = function(newvals) {
if (newvals.length == 1)
newvals = newvals[0];
if (property === "userMatrix")
obj.par3d.userMatrix.load(newvals);
else if (property === "scale" || property === "FOV" || property === "zoom")
obj.par3d[property] = newvals;
else
obj[property] = newvals;
};
if (direct && typeof value === "undefined")
return;
if (control.interp) {
values = values.slice(0, ncol).concat(values).
concat(values.slice(ncol*(nrow-1), ncol*nrow));
svals = [-Infinity].concat(svals).concat(Infinity);
for (i = 1; i < svals.length; i++) {
if (value <= svals[i]) {
if (svals[i] === Infinity)
p = 1;
else
p = (svals[i] - value)/(svals[i] - svals[i-1]);
break;
}
}
} else if (!direct) {
value = Math.round(value);
}
for (j=0; j<entries.length; j++) {
entry = entries[j];
newprop = properties[j];
newid = objids[j];
if (newprop !== property || newid != objid) {
if (typeof property !== "undefined")
putPropvals(propvals);
property = newprop;
objid = newid;
obj = this.getObj(objid);
propvals = getPropvals();
}
if (control.interp) {
v1 = values[ncol*(i-1) + j];
v2 = values[ncol*i + j];
this.setElement(propvals, entry, p*v1 + (1-p)*v2);
} else if (!direct) {
this.setElement(propvals, entry, values[ncol*value + j]);
} else {
this.setElement(propvals, entry, value[j]);
}
}
putPropvals(propvals);
needsBinding = [];
for (j=0; j < entries.length; j++) {
if (properties[j] === "values" &&
needsBinding.indexOf(objids[j]) === -1) {
needsBinding.push(objids[j]);
}
}
for (j=0; j < needsBinding.length; j++) {
gl = this.gl || this.initGL();
obj = this.getObj(needsBinding[j]);
gl.bindBuffer(gl.ARRAY_BUFFER, obj.buf);
gl.bufferData(gl.ARRAY_BUFFER, obj.values, gl.STATIC_DRAW);
}
};
/**
* Change the requested vertices
* @param { Object } el - Element of the control; not used.
* @param { Object } control - The vertext setter control data.
*/
rglwidgetClass.prototype.vertexSetter = function(el, control)  {
var svals = [].concat(control.param),
j, k, p, a, propvals, stride, ofs, obj, entry,
attrib,
ofss    = {x:"vofs", y:"vofs", z:"vofs",
red:"cofs", green:"cofs", blue:"cofs",
alpha:"cofs", radii:"radofs",
nx:"nofs", ny:"nofs", nz:"nofs",
ox:"oofs", oy:"oofs", oz:"oofs",
ts:"tofs", tt:"tofs"},
pos     = {x:0, y:1, z:2,
red:0, green:1, blue:2,
alpha:3,radii:0,
nx:0, ny:1, nz:2,
ox:0, oy:1, oz:2,
ts:0, tt:1},
values = control.values,
direct = values === null,
ncol,
interp = control.interp,
vertices = [].concat(control.vertices),
attributes = [].concat(control.attributes),
value = control.value, newval, aliases, alias;
ncol = Math.max(vertices.length, attributes.length);
if (!ncol)
return;
vertices = this.repeatToLen(vertices, ncol);
attributes = this.repeatToLen(attributes, ncol);
if (direct)
interp = false;
/* JSON doesn't pass Infinity */
svals[0] = -Infinity;
svals[svals.length - 1] = Infinity;
for (j = 1; j < svals.length; j++) {
if (value <= svals[j]) {
if (interp) {
if (svals[j] === Infinity)
p = 1;
else
p = (svals[j] - value)/(svals[j] - svals[j-1]);
} else {
if (svals[j] - value > value - svals[j-1])
j = j - 1;
}
break;
}
}
obj = this.getObj(control.objid);
// First, make sure color attributes vary in original
if (typeof obj.vOffsets !== "undefined") {
varies = true;
for (k = 0; k < ncol; k++) {
attrib = attributes[k];
if (typeof attrib !== "undefined") {
ofs = obj.vOffsets[ofss[attrib]];
if (ofs < 0) {
switch(attrib) {
case "alpha":
case "red":
case "green":
case "blue":
obj.colors = [obj.colors[0], obj.colors[0]];
break;
}
varies = false;
}
}
}
if (!varies)
this.initObj(control.objid);
}
propvals = obj.values;
aliases = obj.alias;
if (typeof aliases === "undefined")
aliases = [];
for (k=0; k<ncol; k++) {
if (direct) {
newval = value;
} else if (interp) {
newval = p*values[j-1][k] + (1-p)*values[j][k];
} else {
newval = values[j][k];
}      	
attrib = attributes[k];
vertex = vertices[k];
alias = aliases[vertex];
if (obj.type === "planes" || obj.type === "clipplanes") {
ofs = ["nx", "ny", "nz", "offset"].indexOf(attrib);
if (ofs >= 0) {
if (ofs < 3) {
if (obj.normals[vertex][ofs] != newval) {  // Assume no aliases here...
obj.normals[vertex][ofs] = newval;
obj.initialized = false;
}
} else {
if (obj.offsets[vertex][0] != newval) {
obj.offsets[vertex][0] = newval;
obj.initialized = false;
}
}
continue;
}
}
// Not a plane setting...
ofs = obj.vOffsets[ofss[attrib]];
if (ofs < 0)
this.alertOnce("Attribute '"+attrib+"' not found in object "+control.objid);
else {
stride = obj.vOffsets.stride;
ofs = ofs + pos[attrib];
entry = vertex*stride + ofs;
propvals[entry] = newval;
if (typeof alias !== "undefined")
for (a = 0; a < alias.length; a++)
propvals[alias[a]*stride + ofs] = newval;
}
}
if (typeof obj.buf !== "undefined") {
var gl = this.gl || this.initGL();
gl.bindBuffer(gl.ARRAY_BUFFER, obj.buf);
gl.bufferData(gl.ARRAY_BUFFER, propvals, gl.STATIC_DRAW);
}
};
/**
* Change the requested vertex properties by age
* @param { Object } el - Element of the control; not used.
* @param { Object } control - The age setter control data.
*/
rglwidgetClass.prototype.ageSetter = function(el, control) {
var objids = [].concat(control.objids),
nobjs = objids.length,
time = control.value,
births = [].concat(control.births),
ages = [].concat(control.ages),
steps = births.length,
j = Array(steps),
p = Array(steps),
i, k, age, j0, propvals, stride, ofs, objid, obj,
attrib, dim, varies, alias, aliases, a, d,
attribs = ["colors", "alpha", "radii", "vertices",
"normals", "origins", "texcoords",
"x", "y", "z",
"red", "green", "blue"],
ofss    = ["cofs", "cofs", "radofs", "vofs",
"nofs", "oofs", "tofs",
"vofs", "vofs", "vofs",
"cofs", "cofs", "cofs"],
dims    = [3,1,1,3,
3,2,2,
1,1,1,
1,1,1],
pos     = [0,3,0,0,
0,0,0,
0,1,2,
0,1,2];
/* Infinity doesn't make it through JSON */
ages[0] = -Infinity;
ages[ages.length-1] = Infinity;
for (i = 0; i < steps; i++) {
if (births[i] !== null) {  // NA in R becomes null
age = time - births[i];
for (j0 = 1; age > ages[j0]; j0++);
if (ages[j0] == Infinity)
p[i] = 1;
else if (ages[j0] > ages[j0-1])
p[i] = (ages[j0] - age)/(ages[j0] - ages[j0-1]);
else
p[i] = 0;
j[i] = j0;
}
}
// First, make sure color attributes vary in original
for (l = 0; l < nobjs; l++) {
objid = objids[l];
obj = this.getObj(objid);
varies = true;
if (typeof obj.vOffsets === "undefined")
continue;
for (k = 0; k < attribs.length; k++) {
attrib = control[attribs[k]];
if (typeof attrib !== "undefined") {
ofs = obj.vOffsets[ofss[k]];
if (ofs < 0) {
switch(attribs[k]) {
case "colors":
case "alpha":
case "red":
case "green":
case "blue":
obj.colors = [obj.colors[0], obj.colors[0]];
break;
}
varies = false;
}
}
}
if (!varies)
this.initObj(objid);
}
for (l = 0; l < nobjs; l++) {
objid = objids[l];
obj = this.getObj(objid);
if (typeof obj.vOffsets === "undefined")
continue;
aliases = obj.alias;
if (typeof aliases === "undefined")
aliases = [];
propvals = obj.values;
stride = obj.vOffsets.stride;
for (k = 0; k < attribs.length; k++) {
attrib = control[attribs[k]];
if (typeof attrib !== "undefined") {
ofs = obj.vOffsets[ofss[k]];
if (ofs >= 0) {
dim = dims[k];
ofs = ofs + pos[k];
for (i = 0; i < steps; i++) {
alias = aliases[i];
if (births[i] !== null) {
for (d=0; d < dim; d++) {
propvals[i*stride + ofs + d] = p[i]*attrib[dim*(j[i]-1) + d] + (1-p[i])*attrib[dim*j[i] + d];
if (typeof alias !== "undefined")
for (a=0; a < alias.length; a++)
propvals[alias[a]*stride + ofs + d] = propvals[i*stride + ofs + d];
}
}
}
} else
this.alertOnce("\'"+attribs[k]+"\' property not found in object "+objid);
}
}
obj.values = propvals;
if (typeof obj.buf !== "undefined") {
gl = this.gl || this.initGL();
gl.bindBuffer(gl.ARRAY_BUFFER, obj.buf);
gl.bufferData(gl.ARRAY_BUFFER, obj.values, gl.STATIC_DRAW);
}
}
};
/**
* Bridge to old style control
* @param { Object } el - Element of the control; not used.
* @param { Object } control - The bridge control data.
*/
rglwidgetClass.prototype.oldBridge = function(el, control) {
var attrname, global = window[control.prefix + "rgl"];
if (global)
for (attrname in global)
this[attrname] = global[attrname];
window[control.prefix + "rgl"] = this;
};
/**
* Set up a player control
* @param { Object } el - The player control element
* @param { Object } control - The player data.
*/
rglwidgetClass.prototype.Player = function(el, control) {
var
self = this,
components = [].concat(control.components),
buttonLabels = [].concat(control.buttonLabels),
Tick = function() { /* "this" will be a timer */
var i,
nominal = this.value,
slider = this.Slider,
labels = this.outputLabels,
output = this.Output,
step;
if (typeof slider !== "undefined" && nominal != slider.value)
slider.value = nominal;
if (typeof output !== "undefined") {
step = Math.round((nominal - output.sliderMin)/output.sliderStep);
if (labels !== null) {
output.innerHTML = labels[step];
} else {
step = step*output.sliderStep + output.sliderMin;
output.innerHTML = step.toPrecision(output.outputPrecision);
}
}
for (i=0; i < this.actions.length; i++) {
this.actions[i].value = nominal;
}
self.applyControls(el, this.actions, false);
self.drawScene();
},
OnSliderInput = function() { /* "this" will be the slider */
this.rgltimer.value = Number(this.value);
this.rgltimer.Tick();
},
addSlider = function(min, max, step, value) {
var slider = document.createElement("input");
slider.type = "range";
slider.min = min;
slider.max = max;
slider.step = step;
slider.value = value;
slider.oninput = OnSliderInput;
slider.sliderActions = control.actions;
slider.sliderScene = this;
slider.className = "rgl-slider";
slider.id = el.id + "-slider";
el.rgltimer.Slider = slider;
slider.rgltimer = el.rgltimer;
el.appendChild(slider);
},
addLabel = function(labels, min, step, precision) {
var output = document.createElement("output");
output.sliderMin = min;
output.sliderStep = step;
output.outputPrecision = precision;
output.className = "rgl-label";
output.id = el.id + "-label";
el.rgltimer.Output = output;
el.rgltimer.outputLabels = labels;
el.appendChild(output);
},
addButton = function(which, label, active) {
var button = document.createElement("input"),
onclicks = {Reverse: function() { this.rgltimer.reverse();},
Play: function() { this.rgltimer.play();
this.value = this.rgltimer.enabled ? this.inactiveValue : this.activeValue; },
Slower: function() { this.rgltimer.slower(); },
Faster: function() { this.rgltimer.faster(); },
Reset: function() { this.rgltimer.reset(); },
Step:  function() { this.rgltimer.step(); }
};
button.rgltimer = el.rgltimer;
button.type = "button";
button.value = label;
button.activeValue = label;
button.inactiveValue = active;
if (which === "Play")
button.rgltimer.PlayButton = button;
button.onclick = onclicks[which];
button.className = "rgl-button";
button.id = el.id + "-" + which;
el.appendChild(button);
};
if (typeof control.reinit !== "undefined" && control.reinit !== null) {
control.actions.reinit = control.reinit;
}
el.rgltimer = new rgltimerClass(Tick, control.start, control.interval, control.stop,
control.step, control.value, control.rate, control.loop, control.actions);
for (var i=0; i < components.length; i++) {
switch(components[i]) {
case "Slider": addSlider(control.start, control.stop,
control.step, control.value);
break;
case "Label": addLabel(control.labels, control.start,
control.step, control.precision);
break;
default:
addButton(components[i], buttonLabels[i], control.pause);
}
}
el.rgltimer.Tick();
};
/**
* Apply all registered controls
* @param { Object } el - DOM element of the control
* @param { Object } x - List of actions to apply
* @param { boolean } [draw=true] - Whether to redraw after applying
*/
rglwidgetClass.prototype.applyControls = function(el, x, draw) {
var self = this, reinit = x.reinit, i, control, type;
for (i = 0; i < x.length; i++) {
control = x[i];
type = control.type;
self[type](el, control);
}
if (typeof reinit !== "undefined" && reinit !== null) {
reinit = [].concat(reinit);
for (i = 0; i < reinit.length; i++)
self.getObj(reinit[i]).initialized = false;
}
if (typeof draw === "undefined" || draw)
self.drawScene();
};
/**
* Handler for scene change
* @param { Object } message - What sort of scene change to do?
*/
rglwidgetClass.prototype.sceneChangeHandler = function(message) {
var self = document.getElementById(message.elementId).rglinstance,
objs = message.objects, mat = message.material,
root = message.rootSubscene,
initSubs = message.initSubscenes,
redraw = message.redrawScene,
skipRedraw = message.skipRedraw,
deletes, subs, allsubs = [], i,j;
if (typeof message.delete !== "undefined") {
deletes = [].concat(message.delete);
if (typeof message.delfromSubscenes !== "undefined")
subs = [].concat(message.delfromSubscenes);
else
subs = [];
for (i = 0; i < deletes.length; i++) {
for (j = 0; j < subs.length; j++) {
self.delFromSubscene(deletes[i], subs[j]);
}
delete self.scene.objects[deletes[i]];
}
}
if (typeof objs !== "undefined") {
Object.keys(objs).forEach(function(key){
key = parseInt(key, 10);
self.scene.objects[key] = objs[key];
self.initObj(key);
var obj = self.getObj(key),
subs = [].concat(obj.inSubscenes), k;
allsubs = allsubs.concat(subs);
for (k = 0; k < subs.length; k++)
self.addToSubscene(key, subs[k]);
});
}
if (typeof mat !== "undefined") {
self.scene.material = mat;
}
if (typeof root !== "undefined") {
self.scene.rootSubscene = root;
}
if (typeof initSubs !== "undefined")
allsubs = allsubs.concat(initSubs);
allsubs = self.unique(allsubs);
for (i = 0; i < allsubs.length; i++) {
self.initSubscene(allsubs[i]);
}
if (typeof skipRedraw !== "undefined") {
root = self.getObj(self.scene.rootSubscene);
root.par3d.skipRedraw = skipRedraw;
}
if (redraw)
self.drawScene();
};
/**
* Set mouse mode for a subscene
* @param { string } mode - name of mode
* @param { number } button - button number (1 to 3)
* @param { number } subscene - subscene id number
* @param { number } stayActive - if truthy, don't clear brush
*/
rglwidgetClass.prototype.setMouseMode = function(mode, button, subscene, stayActive) {
var sub = this.getObj(subscene),
which = ["left", "right", "middle"][button - 1];
if (!stayActive && sub.par3d.mouseMode[which] === "selecting")
this.clearBrush(null);
sub.par3d.mouseMode[which] = mode;
};
/**
* The class of an rgl timer object
* @class
*/
/**
* Construct an rgltimerClass object
* @constructor
* @param { function } Tick - action when timer fires
* @param { number } startTime - nominal start time in seconds
* @param { number } interval - seconds between updates
* @param { number } stopTime - nominal stop time in seconds
* @param { number } stepSize - nominal step size
* @param { number } value - current nominal time
* @param { number } rate - nominal units per second
* @param { string } loop - "none", "cycle" or "oscillate"
* @param { Object } actions - list of actions
*/
rgltimerClass = function(Tick, startTime, interval, stopTime, stepSize, value, rate, loop, actions) {
this.enabled = false;
this.timerId = 0;
/** nominal start time in seconds */
this.startTime = startTime;   
/** current nominal time */      
this.value = value;
/** seconds between updates */                 
this.interval = interval;
/** nominal stop time */           
this.stopTime = stopTime;
/** nominal step size */           
this.stepSize = stepSize;
/** nominal units per second */           
this.rate = rate;
/** "none", "cycle", or "oscillate" */                   
this.loop = loop;
/** real world start time */                   
this.realStart = undefined;
/** multiplier for fast-forward or reverse */         
this.multiplier = 1;                
this.actions = actions;
this.Tick = Tick;
};
/**
* Start playing timer object
*/
rgltimerClass.prototype.play = function() {
if (this.enabled) {
this.enabled = false;
window.clearInterval(this.timerId);
this.timerId = 0;
return;
}
var tick = function(self) {
var now = new Date();
self.value = self.multiplier*self.rate*(now - self.realStart)/1000 + self.startTime;
self.forceToRange();
if (typeof self.Tick !== "undefined") {
self.Tick(self.value);
}
};
this.realStart = new Date() - 1000*(this.value - this.startTime)/this.rate/this.multiplier;
this.timerId = window.setInterval(tick, 1000*this.interval, this);
this.enabled = true;
};
/**
* Force value into legal range
*/
rgltimerClass.prototype.forceToRange = function() {
if (this.value > this.stopTime + this.stepSize/2 || this.value < this.startTime - this.stepSize/2) {
if (!this.loop) {
this.reset();
} else {
var cycle = this.stopTime - this.startTime + this.stepSize,
newval = (this.value - this.startTime) % cycle + this.startTime;
if (newval < this.startTime) {
newval += cycle;
}
this.realStart += (this.value - newval)*1000/this.multiplier/this.rate;
this.value = newval;
}
}
};
/**
* Reset to start values
*/
rgltimerClass.prototype.reset = function() {
this.value = this.startTime;
this.newmultiplier(1);
if (typeof this.Tick !== "undefined") {
this.Tick(this.value);
}
if (this.enabled)
this.play();  /* really pause... */
if (typeof this.PlayButton !== "undefined")
this.PlayButton.value = "Play";
};
/**
* Increase the multiplier to play faster
*/
rgltimerClass.prototype.faster = function() {
this.newmultiplier(Math.SQRT2*this.multiplier);
};
/**
* Decrease the multiplier to play slower
*/
rgltimerClass.prototype.slower = function() {
this.newmultiplier(this.multiplier/Math.SQRT2);
};
/**
* Change sign of multiplier to reverse direction
*/
rgltimerClass.prototype.reverse = function() {
this.newmultiplier(-this.multiplier);
};
/**
* Set multiplier for play speed
* @param { number } newmult - new value
*/
rgltimerClass.prototype.newmultiplier = function(newmult) {
if (newmult != this.multiplier) {
this.realStart += 1000*(this.value - this.startTime)/this.rate*(1/this.multiplier - 1/newmult);
this.multiplier = newmult;
}
};
/**
* Take one step
*/
rgltimerClass.prototype.step = function() {
this.value += this.rate*this.multiplier;
this.forceToRange();
if (typeof this.Tick !== "undefined")
this.Tick(this.value);
};</script>
<div id="testgldiv" class="rglWebGL"></div>
<script type="text/javascript">
var testgldiv = document.getElementById("testgldiv"),
testglrgl = new rglwidgetClass();
testgldiv.width = 505;
testgldiv.height = 505;
testglrgl.initialize(testgldiv,
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---

# Lessons learnt

- With 2 variables we can do a 2-dimensional (2D) scatter plot.
  - This can be interpreted very easily
- With 3 variables we can do a 3D scatter plot
  - This doesn't look great on a flat screen
  - We get more insight by *rotating* the plot
- What about 5 variables? What about 100 variables?

---

# Principal components

- Later on we will cover the method of *principal components*.
--

- This can be used to combine the variables into a single index.
--

- This single index explains most of the variation in the data.
--

- On the next slide we plot the first principal component on a map of the USA.

---

# One PC on a map

---

# Multidimensional Scaling

- Two states close to one another on the scatterplot had similar levels of income, and life expectancy.
--

- Can we do something similar but for all five variables.
--

- The method of *multidimensional scaling* finds two coordinates so that states close to one another on the scatterplot are close to one another across all five characteristics.

---

#Multidimensional Scaling

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---

# Factor Analysis

- Later on we will attempt to attach possible interpretations to these constructed variables.
--

- This is the objective of factor modelling.
--

- In this context *factor* refers to a latent construct that cannot be directly observed but can be measured via its correlation with observable data.

---

# Cluster Analysis

- Even from the simple analysis so far, it appears that similar states can placed into a small number of groups.
--

- The use of algorithms that achieve this task is known as *cluster analysis*.
--

- It is extremely useful across a number of business disciplines.
--

- On the following slide we group the states into two clusters and present them in different colors.

---

# Cluster Analysis: Example

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---
class: inverse, middle, center

# A broad understanding of data.

---

# Numerical Data

- So far we looked at *numerical* data 
  - This is also called *metric* data or *ratio* data
- The differences and ratios between values of the variable have some meaningful interpretation.
--

- A state with a mean income of $5000 has twice as much income as a state with a mean income of $2500.

---

# Non-metric data

- *Categorical* (or *nominal*) Data
  - The value of the variable does not measure the *size* of some characteristic.
- *Ordinal* data
  - Different values of the variable measure *more* or *less* of a characteristic but not *how much* more or *how much* less.

---
# Beer Data

<div style="border: 1px solid #ddd; padding: 0px; overflow-y: scroll; height:500px; "><table class="table table-striped table-hover table-condensed" style="margin-left: auto; margin-right: auto;">
 <thead>
  <tr>
   <th style="text-align:left;position: sticky; top:0; background-color: #FFFFFF;"> beer </th>
   <th style="text-align:left;position: sticky; top:0; background-color: #FFFFFF;"> rating </th>
   <th style="text-align:left;position: sticky; top:0; background-color: #FFFFFF;"> origin </th>
   <th style="text-align:left;position: sticky; top:0; background-color: #FFFFFF;"> avail </th>
   <th style="text-align:right;position: sticky; top:0; background-color: #FFFFFF;"> price </th>
   <th style="text-align:right;position: sticky; top:0; background-color: #FFFFFF;"> cost </th>
   <th style="text-align:right;position: sticky; top:0; background-color: #FFFFFF;"> calories </th>
   <th style="text-align:right;position: sticky; top:0; background-color: #FFFFFF;"> sodium </th>
   <th style="text-align:right;position: sticky; top:0; background-color: #FFFFFF;"> alcohol </th>
   <th style="text-align:left;position: sticky; top:0; background-color: #FFFFFF;"> light </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> Budweiser Light </td>
   <td style="text-align:left;"> Good </td>
   <td style="text-align:left;"> USA </td>
   <td style="text-align:left;"> National </td>
   <td style="text-align:right;"> 2.63 </td>
   <td style="text-align:right;"> 0.44 </td>
   <td style="text-align:right;"> 113 </td>
   <td style="text-align:right;"> 8 </td>
   <td style="text-align:right;"> 3.7 </td>
   <td style="text-align:left;"> LIGHT </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Coors Light </td>
   <td style="text-align:left;"> Good </td>
   <td style="text-align:left;"> USA </td>
   <td style="text-align:left;"> Regional </td>
   <td style="text-align:right;"> 2.73 </td>
   <td style="text-align:right;"> 0.46 </td>
   <td style="text-align:right;"> 102 </td>
   <td style="text-align:right;"> 15 </td>
   <td style="text-align:right;"> 4.1 </td>
   <td style="text-align:left;"> LIGHT </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Michelob Light </td>
   <td style="text-align:left;"> Good </td>
   <td style="text-align:left;"> USA </td>
   <td style="text-align:left;"> National </td>
   <td style="text-align:right;"> 2.99 </td>
   <td style="text-align:right;"> 0.50 </td>
   <td style="text-align:right;"> 135 </td>
   <td style="text-align:right;"> 11 </td>
   <td style="text-align:right;"> 4.2 </td>
   <td style="text-align:left;"> LIGHT </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Miller Light </td>
   <td style="text-align:left;"> Good </td>
   <td style="text-align:left;"> USA </td>
   <td style="text-align:left;"> National </td>
   <td style="text-align:right;"> 2.55 </td>
   <td style="text-align:right;"> 0.43 </td>
   <td style="text-align:right;"> 99 </td>
   <td style="text-align:right;"> 10 </td>
   <td style="text-align:right;"> 4.3 </td>
   <td style="text-align:left;"> LIGHT </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Olympia Gold Light </td>
   <td style="text-align:left;"> Fair </td>
   <td style="text-align:left;"> USA </td>
   <td style="text-align:left;"> Regional </td>
   <td style="text-align:right;"> 2.75 </td>
   <td style="text-align:right;"> 0.46 </td>
   <td style="text-align:right;"> 72 </td>
   <td style="text-align:right;"> 6 </td>
   <td style="text-align:right;"> 2.9 </td>
   <td style="text-align:left;"> LIGHT </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Pabst Extra Light </td>
   <td style="text-align:left;"> Fair </td>
   <td style="text-align:left;"> USA </td>
   <td style="text-align:left;"> National </td>
   <td style="text-align:right;"> 2.29 </td>
   <td style="text-align:right;"> 0.38 </td>
   <td style="text-align:right;"> 68 </td>
   <td style="text-align:right;"> 15 </td>
   <td style="text-align:right;"> 2.3 </td>
   <td style="text-align:left;"> LIGHT </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Schlitz Light </td>
   <td style="text-align:left;"> Fair </td>
   <td style="text-align:left;"> USA </td>
   <td style="text-align:left;"> National </td>
   <td style="text-align:right;"> 2.79 </td>
   <td style="text-align:right;"> 0.47 </td>
   <td style="text-align:right;"> 97 </td>
   <td style="text-align:right;"> 7 </td>
   <td style="text-align:right;"> 4.2 </td>
   <td style="text-align:left;"> LIGHT </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Anchor Steam </td>
   <td style="text-align:left;"> VeryGood </td>
   <td style="text-align:left;"> USA </td>
   <td style="text-align:left;"> Regional </td>
   <td style="text-align:right;"> 7.19 </td>
   <td style="text-align:right;"> 1.20 </td>
   <td style="text-align:right;"> 154 </td>
   <td style="text-align:right;"> 17 </td>
   <td style="text-align:right;"> 4.7 </td>
   <td style="text-align:left;"> NONLIGHT </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Augsberger </td>
   <td style="text-align:left;"> Good </td>
   <td style="text-align:left;"> USA </td>
   <td style="text-align:left;"> Regional </td>
   <td style="text-align:right;"> 2.39 </td>
   <td style="text-align:right;"> 0.40 </td>
   <td style="text-align:right;"> 175 </td>
   <td style="text-align:right;"> 24 </td>
   <td style="text-align:right;"> 5.5 </td>
   <td style="text-align:left;"> NONLIGHT </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Becks </td>
   <td style="text-align:left;"> Good </td>
   <td style="text-align:left;"> Germany </td>
   <td style="text-align:left;"> Regional </td>
   <td style="text-align:right;"> 4.55 </td>
   <td style="text-align:right;"> 0.76 </td>
   <td style="text-align:right;"> 150 </td>
   <td style="text-align:right;"> 19 </td>
   <td style="text-align:right;"> 4.7 </td>
   <td style="text-align:left;"> NONLIGHT </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Blatz </td>
   <td style="text-align:left;"> Fair </td>
   <td style="text-align:left;"> USA </td>
   <td style="text-align:left;"> Regional </td>
   <td style="text-align:right;"> 1.79 </td>
   <td style="text-align:right;"> 0.30 </td>
   <td style="text-align:right;"> 144 </td>
   <td style="text-align:right;"> 13 </td>
   <td style="text-align:right;"> 4.6 </td>
   <td style="text-align:left;"> NONLIGHT </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Budweiser </td>
   <td style="text-align:left;"> VeryGood </td>
   <td style="text-align:left;"> USA </td>
   <td style="text-align:left;"> National </td>
   <td style="text-align:right;"> 2.59 </td>
   <td style="text-align:right;"> 0.43 </td>
   <td style="text-align:right;"> 144 </td>
   <td style="text-align:right;"> 15 </td>
   <td style="text-align:right;"> 4.7 </td>
   <td style="text-align:left;"> NONLIGHT </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Coors </td>
   <td style="text-align:left;"> Good </td>
   <td style="text-align:left;"> USA </td>
   <td style="text-align:left;"> Regional </td>
   <td style="text-align:right;"> 2.65 </td>
   <td style="text-align:right;"> 0.44 </td>
   <td style="text-align:right;"> 140 </td>
   <td style="text-align:right;"> 18 </td>
   <td style="text-align:right;"> 4.6 </td>
   <td style="text-align:left;"> NONLIGHT </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Dos Equis </td>
   <td style="text-align:left;"> Good </td>
   <td style="text-align:left;"> Mexico </td>
   <td style="text-align:left;"> Regional </td>
   <td style="text-align:right;"> 4.22 </td>
   <td style="text-align:right;"> 0.70 </td>
   <td style="text-align:right;"> 145 </td>
   <td style="text-align:right;"> 14 </td>
   <td style="text-align:right;"> 4.5 </td>
   <td style="text-align:left;"> NONLIGHT </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Hamms </td>
   <td style="text-align:left;"> Fair </td>
   <td style="text-align:left;"> USA </td>
   <td style="text-align:left;"> Regional </td>
   <td style="text-align:right;"> 2.59 </td>
   <td style="text-align:right;"> 0.43 </td>
   <td style="text-align:right;"> 136 </td>
   <td style="text-align:right;"> 19 </td>
   <td style="text-align:right;"> 4.4 </td>
   <td style="text-align:left;"> NONLIGHT </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Heilmans Old Style </td>
   <td style="text-align:left;"> Fair </td>
   <td style="text-align:left;"> USA </td>
   <td style="text-align:left;"> Regional </td>
   <td style="text-align:right;"> 2.59 </td>
   <td style="text-align:right;"> 0.43 </td>
   <td style="text-align:right;"> 144 </td>
   <td style="text-align:right;"> 24 </td>
   <td style="text-align:right;"> 4.9 </td>
   <td style="text-align:left;"> NONLIGHT </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Heineken </td>
   <td style="text-align:left;"> VeryGood </td>
   <td style="text-align:left;"> Holland </td>
   <td style="text-align:left;"> National </td>
   <td style="text-align:right;"> 4.59 </td>
   <td style="text-align:right;"> 0.77 </td>
   <td style="text-align:right;"> 152 </td>
   <td style="text-align:right;"> 11 </td>
   <td style="text-align:right;"> 5.0 </td>
   <td style="text-align:left;"> NONLIGHT </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Henry Weinhard </td>
   <td style="text-align:left;"> VeryGood </td>
   <td style="text-align:left;"> USA </td>
   <td style="text-align:left;"> Regional </td>
   <td style="text-align:right;"> 3.65 </td>
   <td style="text-align:right;"> 0.61 </td>
   <td style="text-align:right;"> 149 </td>
   <td style="text-align:right;"> 7 </td>
   <td style="text-align:right;"> 4.7 </td>
   <td style="text-align:left;"> NONLIGHT </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Kirin </td>
   <td style="text-align:left;"> Good </td>
   <td style="text-align:left;"> Japan </td>
   <td style="text-align:left;"> Regional </td>
   <td style="text-align:right;"> 4.75 </td>
   <td style="text-align:right;"> 0.79 </td>
   <td style="text-align:right;"> 149 </td>
   <td style="text-align:right;"> 6 </td>
   <td style="text-align:right;"> 5.0 </td>
   <td style="text-align:left;"> NONLIGHT </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Kronenbourg </td>
   <td style="text-align:left;"> VeryGood </td>
   <td style="text-align:left;"> France </td>
   <td style="text-align:left;"> Regional </td>
   <td style="text-align:right;"> 4.39 </td>
   <td style="text-align:right;"> 0.73 </td>
   <td style="text-align:right;"> 170 </td>
   <td style="text-align:right;"> 7 </td>
   <td style="text-align:right;"> 5.2 </td>
   <td style="text-align:left;"> NONLIGHT </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Labatts </td>
   <td style="text-align:left;"> VeryGood </td>
   <td style="text-align:left;"> Canada </td>
   <td style="text-align:left;"> Regional </td>
   <td style="text-align:right;"> 3.15 </td>
   <td style="text-align:right;"> 0.53 </td>
   <td style="text-align:right;"> 147 </td>
   <td style="text-align:right;"> 17 </td>
   <td style="text-align:right;"> 5.0 </td>
   <td style="text-align:left;"> NONLIGHT </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Lowenbrau </td>
   <td style="text-align:left;"> VeryGood </td>
   <td style="text-align:left;"> USA </td>
   <td style="text-align:left;"> National </td>
   <td style="text-align:right;"> 2.89 </td>
   <td style="text-align:right;"> 0.48 </td>
   <td style="text-align:right;"> 157 </td>
   <td style="text-align:right;"> 15 </td>
   <td style="text-align:right;"> 4.9 </td>
   <td style="text-align:left;"> NONLIGHT </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Michelob </td>
   <td style="text-align:left;"> VeryGood </td>
   <td style="text-align:left;"> USA </td>
   <td style="text-align:left;"> National </td>
   <td style="text-align:right;"> 2.99 </td>
   <td style="text-align:right;"> 0.50 </td>
   <td style="text-align:right;"> 162 </td>
   <td style="text-align:right;"> 10 </td>
   <td style="text-align:right;"> 5.0 </td>
   <td style="text-align:left;"> NONLIGHT </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Miller High Life </td>
   <td style="text-align:left;"> VeryGood </td>
   <td style="text-align:left;"> USA </td>
   <td style="text-align:left;"> National </td>
   <td style="text-align:right;"> 2.49 </td>
   <td style="text-align:right;"> 0.42 </td>
   <td style="text-align:right;"> 149 </td>
   <td style="text-align:right;"> 17 </td>
   <td style="text-align:right;"> 4.7 </td>
   <td style="text-align:left;"> NONLIGHT </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Molson </td>
   <td style="text-align:left;"> VeryGood </td>
   <td style="text-align:left;"> Canada </td>
   <td style="text-align:left;"> Regional </td>
   <td style="text-align:right;"> 3.35 </td>
   <td style="text-align:right;"> 0.56 </td>
   <td style="text-align:right;"> 154 </td>
   <td style="text-align:right;"> 17 </td>
   <td style="text-align:right;"> 5.1 </td>
   <td style="text-align:left;"> NONLIGHT </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Old Milwaukee </td>
   <td style="text-align:left;"> Good </td>
   <td style="text-align:left;"> USA </td>
   <td style="text-align:left;"> Regional </td>
   <td style="text-align:right;"> 1.69 </td>
   <td style="text-align:right;"> 0.28 </td>
   <td style="text-align:right;"> 145 </td>
   <td style="text-align:right;"> 23 </td>
   <td style="text-align:right;"> 4.6 </td>
   <td style="text-align:left;"> NONLIGHT </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Olympia </td>
   <td style="text-align:left;"> Good </td>
   <td style="text-align:left;"> USA </td>
   <td style="text-align:left;"> Regional </td>
   <td style="text-align:right;"> 2.65 </td>
   <td style="text-align:right;"> 0.44 </td>
   <td style="text-align:right;"> 153 </td>
   <td style="text-align:right;"> 27 </td>
   <td style="text-align:right;"> 4.6 </td>
   <td style="text-align:left;"> NONLIGHT </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Pabst Blue Ribbon </td>
   <td style="text-align:left;"> Good </td>
   <td style="text-align:left;"> USA </td>
   <td style="text-align:left;"> National </td>
   <td style="text-align:right;"> 2.29 </td>
   <td style="text-align:right;"> 0.38 </td>
   <td style="text-align:right;"> 152 </td>
   <td style="text-align:right;"> 8 </td>
   <td style="text-align:right;"> 4.9 </td>
   <td style="text-align:left;"> NONLIGHT </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Rolling Rock </td>
   <td style="text-align:left;"> Fair </td>
   <td style="text-align:left;"> USA </td>
   <td style="text-align:left;"> Regional </td>
   <td style="text-align:right;"> 2.15 </td>
   <td style="text-align:right;"> 0.36 </td>
   <td style="text-align:right;"> 144 </td>
   <td style="text-align:right;"> 8 </td>
   <td style="text-align:right;"> 4.7 </td>
   <td style="text-align:left;"> NONLIGHT </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Schlitz </td>
   <td style="text-align:left;"> VeryGood </td>
   <td style="text-align:left;"> USA </td>
   <td style="text-align:left;"> National </td>
   <td style="text-align:right;"> 2.59 </td>
   <td style="text-align:right;"> 0.43 </td>
   <td style="text-align:right;"> 151 </td>
   <td style="text-align:right;"> 19 </td>
   <td style="text-align:right;"> 4.9 </td>
   <td style="text-align:left;"> NONLIGHT </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Schmidts </td>
   <td style="text-align:left;"> Good </td>
   <td style="text-align:left;"> USA </td>
   <td style="text-align:left;"> Regional </td>
   <td style="text-align:right;"> 1.79 </td>
   <td style="text-align:right;"> 0.30 </td>
   <td style="text-align:right;"> 147 </td>
   <td style="text-align:right;"> 7 </td>
   <td style="text-align:right;"> 4.7 </td>
   <td style="text-align:left;"> NONLIGHT </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Scotch Buy (Safeway) </td>
   <td style="text-align:left;"> Fair </td>
   <td style="text-align:left;"> USA </td>
   <td style="text-align:left;"> Regional </td>
   <td style="text-align:right;"> 1.59 </td>
   <td style="text-align:right;"> 0.27 </td>
   <td style="text-align:right;"> 145 </td>
   <td style="text-align:right;"> 18 </td>
   <td style="text-align:right;"> 4.5 </td>
   <td style="text-align:left;"> NONLIGHT </td>
  </tr>
  <tr>
   <td style="text-align:left;"> St Pauli Girl </td>
   <td style="text-align:left;"> Fair </td>
   <td style="text-align:left;"> Germany </td>
   <td style="text-align:left;"> Regional </td>
   <td style="text-align:right;"> 4.59 </td>
   <td style="text-align:right;"> 0.77 </td>
   <td style="text-align:right;"> 144 </td>
   <td style="text-align:right;"> 21 </td>
   <td style="text-align:right;"> 4.7 </td>
   <td style="text-align:left;"> NONLIGHT </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Strohs Bohemian Style </td>
   <td style="text-align:left;"> Good </td>
   <td style="text-align:left;"> USA </td>
   <td style="text-align:left;"> Regional </td>
   <td style="text-align:right;"> 2.49 </td>
   <td style="text-align:right;"> 0.42 </td>
   <td style="text-align:right;"> 149 </td>
   <td style="text-align:right;"> 27 </td>
   <td style="text-align:right;"> 4.7 </td>
   <td style="text-align:left;"> NONLIGHT </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Tuborg </td>
   <td style="text-align:left;"> Fair </td>
   <td style="text-align:left;"> USA </td>
   <td style="text-align:left;"> Regional </td>
   <td style="text-align:right;"> 2.59 </td>
   <td style="text-align:right;"> 0.43 </td>
   <td style="text-align:right;"> 155 </td>
   <td style="text-align:right;"> 13 </td>
   <td style="text-align:right;"> 5.0 </td>
   <td style="text-align:left;"> NONLIGHT </td>
  </tr>
</tbody>
</table></div>

---

# Questions for you

- How many variables in the Beer dataset?
- Which are metric?
- Which are nominal?
- Which are ordinal?

---

# Discussion

- Price is an example of a numerical variable.
- Country of Origin is an example of a nominal variable:
  - You can not have more or less *France-ness* or *Mexico-ness*
- Rating is an example of an ordinal variable:
  - A very *good beer* is better than a *good* beer but we do not know how much better.

---

# Cross tab

- A useful tool for exploring non-metric variables is the cross tab.
--

- Cross tabs that are small can be very useful in providing some indication of the relationships between categorical variables. 
--

- Since most Beers in our dataset are from the US, the following cross tab only looks at US beers against beers from all other countries combined.

---

# Cross Tab: Rating v Origin

International v US
<table>
 <thead>
  <tr>
   <th style="text-align:left;">   </th>
   <th style="text-align:right;"> Int. </th>
   <th style="text-align:right;"> US </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> VeryGood </td>
   <td style="text-align:right;"> 4 </td>
   <td style="text-align:right;"> 7 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Good </td>
   <td style="text-align:right;"> 3 </td>
   <td style="text-align:right;"> 11 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Fair </td>
   <td style="text-align:right;"> 1 </td>
   <td style="text-align:right;"> 9 </td>
  </tr>
</tbody>
</table>

Is there a relationship between origin and rating?

---

# Using all countries

<div style="border: 1px solid #ddd; padding: 0px; overflow-y: scroll; height:300px; "><table class="table table-striped table-hover table-condensed" style="margin-left: auto; margin-right: auto;">
 <thead>
  <tr>
   <th style="text-align:left;position: sticky; top:0; background-color: #FFFFFF;">   </th>
   <th style="text-align:right;position: sticky; top:0; background-color: #FFFFFF;"> USA </th>
   <th style="text-align:right;position: sticky; top:0; background-color: #FFFFFF;"> Canada </th>
   <th style="text-align:right;position: sticky; top:0; background-color: #FFFFFF;"> France </th>
   <th style="text-align:right;position: sticky; top:0; background-color: #FFFFFF;"> Holland </th>
   <th style="text-align:right;position: sticky; top:0; background-color: #FFFFFF;"> Mexico </th>
   <th style="text-align:right;position: sticky; top:0; background-color: #FFFFFF;"> Germany </th>
   <th style="text-align:right;position: sticky; top:0; background-color: #FFFFFF;"> Japan </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> VeryGood </td>
   <td style="text-align:right;"> 7 </td>
   <td style="text-align:right;"> 2 </td>
   <td style="text-align:right;"> 1 </td>
   <td style="text-align:right;"> 1 </td>
   <td style="text-align:right;"> 0 </td>
   <td style="text-align:right;"> 0 </td>
   <td style="text-align:right;"> 0 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Good </td>
   <td style="text-align:right;"> 11 </td>
   <td style="text-align:right;"> 0 </td>
   <td style="text-align:right;"> 0 </td>
   <td style="text-align:right;"> 0 </td>
   <td style="text-align:right;"> 1 </td>
   <td style="text-align:right;"> 1 </td>
   <td style="text-align:right;"> 1 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Fair </td>
   <td style="text-align:right;"> 9 </td>
   <td style="text-align:right;"> 0 </td>
   <td style="text-align:right;"> 0 </td>
   <td style="text-align:right;"> 0 </td>
   <td style="text-align:right;"> 0 </td>
   <td style="text-align:right;"> 1 </td>
   <td style="text-align:right;"> 0 </td>
  </tr>
</tbody>
</table></div>

Is it as easy to find a relationship now?

---

#Correspondence Analysis

- Large cross tabulations can be summarised and visualised with a technique known as *Correspondence Analysis*.
--

- This technique is mostly used to visualise the relationship between two variables.
--

- The problem is considered *high-dimensional* since the number of categories rather than the number of variables is large.
--

- On the next slide is the output from correspondence analysis

---

# Correspondence Analysis

---

# Other data

- Data comes in even more unusual forms. 
  - The list of your favourite musicians on Spotify
  - The words used in online reviews of hotels
  - A ranking of pairs of products from most similar to most dissimilar
--

- All of these types of data can be analysed using methods covered in the unit.