3daa/project_math.html at master · bmaltzan/3daa · GitHub

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<html><head><title>3d ray tracing animation applet: some math</title>

</head>
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<font size=5><p>Some Math</font>

<font size=4><p>Cross Product</font><font size=3 face="Arial">
<br>The cross product of two vectors is another vector at 90&#186; (or perpendicular) to both.

<p>In the raytracer code used in this simulator, the cross product is used to find a
triangle's normal, and in determining the dimensions of the image created.

<p>The simulator uses a cross product in the 3d wireframe.  The cross product of a
'ray' cast into the scene and the view up vector gives a convenient viewpoint to
observe the ray.

<p>Code to determine, and normalize, the cross product of two vectors:
<pre>
   private final T3d crossp(T3d a,T3d b){
      T3d o= new T3d();
      double d;
      o.x= a.y*b.z - a.z*b.y;
      o.y= a.z*b.x - a.x*b.z;
      o.z= a.x*b.y - a.y*b.x;
      d= Math.sqrt(o.x*o.x + o.y*o.y + o.z*o.z);
      o.x/= d;
      o.y/= d;
      o.z/= d;
      return o;
   }
</pre>

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<font size=4><p>Cross Product</font><font size=3 face="Arial">


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