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Optimizing Isometric Mesh of Parametric Surface

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Until now I always sampled my parametric surfaces on a grid. However, while the control points for parametric surfaces (i.e. NURBS) usually lie on a grid, the surface UVs of the sampled points don't have to. The problem with grids is in thin areas or pole areas where the polygons converge and many are wasted: It is preferable to use "isometric" meshing - where the triangles attempt to be the same size. A simple, fast to execute and "fast" to implement (40 hours) approach (when you have parametric surfaces) is to simply prorate each slice by the radius and then perform N to M stitching on each slice to the neighbor: This approach uses between 25% and 75% of the polygons of the grid approach. However the problem is that all of the slices start at 12:00 and in extreme cases it creates this effect: I'm wondering how to balance it? Some ideas: 1) Grid based - the surface UV's should look like graph paper that was cut with scissors, where each vertex snaps to the grid, and portions are on the edges. 2) Padding approach - pad the edges to balance things, introducing smaller triangles on the edges of open areas. On closed areas, this gave the polar regions a spiraled look that was an improvement. I presume that ideally I would postfilter the mesh and allow points to to lie off of the slice boundaries themselves?

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