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veiledinviolet · 3 months ago

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Spherical hex¹ grid based on a class II Goldberg polyhedron, generated using the inverse of Lee's conformal projection of the sphere upon a regular icosahedron [1, pp. 62–65]. When the camera is close to the surface, stereographic projection is applied to flatten the surface.

¹ All faces are hexagonal except for twelve pentagons required by the Euler characteristic of the 2-sphere.

[1] L.P. Lee, “Conformal Projections Based on Elliptic Function”, url: https://archive.org/details/conformalproject0000leel

#computer graphics #i am very pleased with the transition of the stereographic projection #it's actually pretty simple; just exponential smoothing of the denominator #btw i do Not understand Lee's math; i just copied his series #it generally looks good; but at the vertices of the principal icosahedron the series diverges and you can see numerical inaccuracies #i might try some more to improve this aspect in future #next though i'll clean up the code a bit; then implement adjacency

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