I have a triangle that is extended in space and each edge is refracted differently, creating a 5 sided polytope. The initial and final triangles are the view radii segments of a frustum. We need to get the u and v along the triangle and the w depth in between the triangles of a point inside the polytope.

  • $\begingroup$ You also can use Transfinite interpolation where you take the refracted triangle as a four sides polygon by having vertices at sides. en.wikipedia.org/wiki/Transfinite_interpolation $\endgroup$ – ali Jun 7 '18 at 6:35
  • $\begingroup$ or this link:ebrary.free.fr/Mesh%20Generation/… $\endgroup$ – ali Jun 7 '18 at 8:11
  • $\begingroup$ I'm not clear on what shape you're trying to parameterize. Is it an oblique triangular prism? What's a refracted edge? Are the triangles parallel? Could you draw a picture of the shape? $\endgroup$ – gilgamec May 3 '19 at 7:45

I think I can do this using trilinear interpolation and treating two vertices on each side as merged and using my own volume calculations. I just need to interpolate some values given by the three points and a z. http://bmia.bmt.tue.nl/People/BRomeny/Courses/8C080/Interpolation.pdf

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