add support for prisms (new type of geometric_object) to libctlgeom

[HomerReid]

Added a new implementation of geometric_object for user-defined prisms, i.e. arbitrary planar polygons (given by user-defined list of vertices) extruded a user-defined thickness in a user-defined direction.
Example in utils/test-prism.c.

Sample code:

  vector3 v[4];
  v[0].x=-0.25; v[0].y=-0.5; v[0].z=-0.75;
  v[1].x=+0.25; v[1].y=-0.5; v[1].z=-0.75;
  v[2].x=+0.25; v[2].y=+0.5; v[2].z=-0.75;
  v[3].x=-0.25; v[3].y=+0.5; v[3].z=-0.75;
  geometric_object the_prism=make_prism(m, v, 4, 1.5, zhat);
  draw_prism(the_prism,"the_prism.out");                   

[stevengj]

This should be a const vector3 * since a copy is made of this vertex data.

[stevengj]

This is an inner-loop function for subpixel integration, so it shouldn't do any allocations via realloc or whatever.

Remember that subpixel averaging only needs to work in the limit where the pixels are very small compared to the object. So we shouldn't ever need to compute all of the intersections — maybe just the first and last intersection, should suffice, or knowing that it doesn't intersect at all.

[stevengj]

Change the intersect_line_with_object function to:

/* Compute the intersections with o of a line along p+s*d in the interval s in [a,b], returning
    the length of the s intersection in this interval.  (Note: o must not be a compound object.) */
double intersect_line_segment_with_object(vector3 p, vector3 d, geometric_object o, double a, double b)

To be more precise, define the function χ(s) = 1 if the point p+s*d is in the object, and χ(s) = 0 if the point p+s*d is not in the object. What we want is ∫ₐᵇ χ(s) ds.

[stevengj]

For the previously existing objects, intersect_line_segment_with_object is defined by

double s[2];
if (2 == intersect_line_with_object(p, d, o, s)) {
	  double ds = (s[0] < s[1]
		       ? MIN(s[1],b) - MAX(s[0],a)
		       : MIN(s[0],b) - MAX(s[1],a));
	  return (ds > 0 ? ds : 0.0);
}
else 
     return 0.0;

[stevengj]

overlap_integrand will now call:

return intersect_line_segment_with_object(p, data->dir, data->o, a0, b0) * scale_result;

instead of intersect_line_with_object

[stevengj]

cc @DerekK88, who has been playing with GDSII import for Meep.

[stevengj]

1. for technical reasons having to do with how Scheme code is compiled to use libctl, all the code needs to be in geom.c, so just paste prism.c at the end of this separated by /****************************************/ lines.

2. at the top of geom.c, add # define PRISM prism:: after the corresponding line for CYL in #ifdef CXX_CTL_IO, and add # define PRISM in the #else clause.

[stevengj]

Only make_prism should be exported — the other functions (except for make_prism) should be declared as static and removed from ctlgeom.h