]]>模型视图变换Ӟ法线向量要乘模型视图矩阵的逆{|矩?/title><link>http://m.shnenglu.com/flushthink/archive/2009/11/19/101380.html</link><dc:creator>tiny</dc:creator><author>tiny</author><pubDate>Thu, 19 Nov 2009 06:38:00 GMT</pubDate><guid>http://m.shnenglu.com/flushthink/archive/2009/11/19/101380.html</guid><wfw:comment>http://m.shnenglu.com/flushthink/comments/101380.html</wfw:comment><comments>http://m.shnenglu.com/flushthink/archive/2009/11/19/101380.html#Feedback</comments><slash:comments>4</slash:comments><wfw:commentRss>http://m.shnenglu.com/flushthink/comments/commentRss/101380.html</wfw:commentRss><trackback:ping>http://m.shnenglu.com/flushthink/services/trackbacks/101380.html</trackback:ping><description><![CDATA[早前一直被q个问题困惑Q但是自己推倒了很多遍也没推出来?br>哎，在gameres上搜?q前的谈话，后来在gamedev搜到了答案?br>其实在计机囑Ş学中Q只要是变换Q无论^U，旋{Q羃放，都是乘一个矩c?br>在模型视囑֏换时Q顶点乘模型视图变换矩阵Q而顶点对应的点法线向量Q或其他的法U向量）则要乘模型视囄늚逆{|矩c?br>点和法UK是向量，他们的区别是什么？无非点?lt;x, y, z>表示~省?lt;x, y, z, 1>Q而法U向量是<x, y, z>表示~省?lt;x, y, z, 0>。关于ؓ什么是q样Q不用我说了吧，2个顶点向量减下看看就知道了?br>从这Ҏ看，实不同Q或许就是这个不同，造成了变换的不同吧?br>法线向量只能保证方向的一致性，而不能保证位|的一致性，所以，所有线向量必须以面的Ş式进行变换，如下Q?br>
<h2>Transforming Planes</h2>
<p>If we have a plane vector <strong>n</strong> = [a, b, c, d] which describes a plane then for any point <strong>p</strong> = [x, y, z, 1] in that plane the follow equation holds:</p>
<p><strong>n</strong><sup>t</sup> <strong>p</strong> = ax + by + cz + d = 0 </p>
<p>If for a point <strong>p</strong> on the plane, we apply an invertible transformation <strong>R</strong> to get the transformed point <strong>p<sub>1</sub></strong>, then the plane vector <strong>n<sub>1</sub></strong> of the transformed plane is given by applying a corresponding transformation <strong>Q</strong> to the original plane vector <strong>n</strong> where <strong>Q</strong> is unknown.
<p><strong>p<sub>1</sub></strong> = <strong>R</strong> <strong>p</strong> <br><strong>n<sub>1</sub></strong> = <strong>Q</strong> <strong>n</strong> <br></p>
We can solve for <strong>Q</strong> by using the resulting plane equation: <br>
<p><strong>n<sub>1</sub></strong><sup>t</sup> <strong>p<sub>1</sub></strong> = 0 <br></p>
Begin by substituting for <strong>n<sub>1</sub></strong> and <strong>p<sub>1</sub></strong>: <br>
<p>(<strong>Q</strong> <strong>n</strong>)<sup>t</sup> (<strong>R</strong> <strong>p</strong>) = 0 <br><strong>n</strong><sup>t</sup> <strong>Q</strong><sup>t</sup> <strong>R</strong> <strong>p</strong> = 0 <br></p>
If <strong>Q</strong><sup>t</sup> <strong>R</strong> = <strong>I</strong> then <strong>n</strong><sup>t</sup> <strong>Q</strong><sup>t</sup> <strong>R</strong> <strong>p</strong> = <strong>n</strong><sup>t</sup> <strong>I</strong> <strong>p</strong> = <strong>n</strong><sup>t</sup> <strong>p</strong> = 0 which is given.<br>
<p><strong>Q</strong><sup>t</sup> <strong>R</strong> = <strong>I</strong> <br><strong>Q</strong><sup>t</sup> = <strong>R</strong><sup>-1</sup> <br><strong>Q</strong> = (<strong>R</strong><sup>-1</sup>)<sup>t</sup> <br></p>
Substituting <strong>Q</strong> back into our plane vector transformation equation we get: <br>
<p><strong>n<sub>1</sub></strong> = <strong>Q</strong> <strong>n</strong> = (<strong>R</strong><sup>-1</sup>)<sup>t</sup> <strong>n</strong> </p>
<img src ="http://m.shnenglu.com/flushthink/aggbug/101380.html" width = "1" height = "1" /><br><br><div align=right><a style="text-decoration:none;" href="http://m.shnenglu.com/flushthink/" target="_blank">tiny</a> 2009-11-19 14:38 <a href="http://m.shnenglu.com/flushthink/archive/2009/11/19/101380.html#Feedback" target="_blank" style="text-decoration:none;">发表评论</a></div>]]></description></item><item><title>compiler opthttp://m.shnenglu.com/flushthink/archive/2009/11/10/100551.htmltinytinyMon, 09 Nov 2009 23:25:00 GMThttp://m.shnenglu.com/flushthink/archive/2009/11/10/100551.htmlhttp://m.shnenglu.com/flushthink/comments/100551.htmlhttp://m.shnenglu.com/flushthink/archive/2009/11/10/100551.html#Feedback0http://m.shnenglu.com/flushthink/comments/commentRss/100551.htmlhttp://m.shnenglu.com/flushthink/services/trackbacks/100551.html公司的^台只~译了release版，我们必drelease下写具体实现。（依赖release写debug会出问题Q?br>可恶的是Q我的代码对象层ơ颇多，所以我写了很多函敎ͼq些函数在release版本下默认是内联的?br>p样造成了悲剧，q多的内联，把调试器都晃晕了Q烦性，我把~译优化关了Q发现dll膨胀?倍?br>
