POV-Ray

Attached to Project: POV-Ray
Opened by Christoph Lipka - 2011-01-04
Last edited by Christoph Lipka - 2011-02-26

polygon objects comprised of multiple “sub-polygons” don’t work properly if start/end points of sub-polygons do not exactly match, as can be demonstrated by the following code:

#default { texture { pigment { rgb 1 } finish { ambient 1.0} } }

camera {
  orthographic
  up 3.5*y
  right 3.5*x*image_width/image_height
  location  <0,0,-4>
  look_at   <0,0,0>
}

polygon { 8,
  // outer triangle
  0.70 * < cos(  0 *pi/180),sin(  0 *pi/180),0>
  0.70 * < cos(120 *pi/180),sin(120 *pi/180),0>
  0.70 * < cos(240 *pi/180),sin(240 *pi/180),0>
  0.70 * < cos(360 *pi/180),sin(360 *pi/180),0>

  // inner triangle
  0.35 * < cos(  0 *pi/180),sin(  0 *pi/180),0>
  0.35 * < cos(120 *pi/180),sin(120 *pi/180),0>
  0.35 * < cos(240 *pi/180),sin(240 *pi/180),0>
  0.35 * < cos(360 *pi/180),sin(360 *pi/180),0>
}

Note that the end points /should/ be identical. There are however some minor rounding differences, which mess up polygon computations. Compare with the following code, which leads to the desired results:

polygon { 8,
  // outer triangle
  0.70 * < cos(  0 *pi/180),sin(  0 *pi/180),0>
  0.70 * < cos(120 *pi/180),sin(120 *pi/180),0>
  0.70 * < cos(240 *pi/180),sin(240 *pi/180),0>
  0.70 * < cos(  0 *pi/180),sin(  0 *pi/180),0>

  // inner triangle
  0.35 * < cos(  0 *pi/180),sin(  0 *pi/180),0>
  0.35 * < cos(120 *pi/180),sin(120 *pi/180),0>
  0.35 * < cos(240 *pi/180),sin(240 *pi/180),0>
  0.35 * < cos(  0 *pi/180),sin(  0 *pi/180),0>
}

Code inspection shows that the polygon insideness testing code tests for precise equality of the points, whereas the general policy of POV-Ray is to accept slight rounding differences.