Thursday, February 17, 2022

Nelson's word today was 'concert', so I drew a cowboy serenading us with his guitar-
Back to work on my oval world polygon/world peach polyhedron! The 2D version maps nicely to the 3D version, but I need to figure out the 3D version to get the area of each triangle terrain tile. Each point therefore has a 2D horizontal and vertical component for my 2D ‘oval world polygon’ and an XYZ component for the ‘world peach polyhedron’, P5D. Each triangle has three vertices and an area, which we can derive from the magnitude of the cross product of the vectors formed by two of the sides, p0-p1 x p0-p2. I can subdivide the OWP by rows of triangle strips, starting with a triangle fan at the north pole and ending with another triangle fan at the south pole.

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