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Build a hexahedron from 6 triangles(!), setting its 2 vertices at the poles of the sphere, and the other 3 vertices equally around the equator. Then iteratively or recursively subdivide all triangles, projecting the new vertices at the sphere surface (!). Triangle subdivision can be done by replacing an original triangle by 4 new ones, adding new vertices in ...


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To expand on @Makogan and @lightxbulb's answers/comments: There are several reasons for using triangles as the basic primitive. (Non-degenerate) triangles are guaranteed to be planar. This means that an individual single triangle cannot obscure itself (in terms of hidden surface removal) and thus cannot form an internal silhouette edge (when being ...


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A literal triangle, as in 3 vertices connected by 3 edges. They are the basic building block for any other shape, any polygon can be represented with a set of triangles (called triangulation).


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When do they actually discard points that have a z component smaller than the near clipping plane? For actual rendering hardware, they don't. Clipping happens in clip space, before the NDC transform. "Points" outside of the clipping volume are never seen by the rasterizer (in theory, at least. In practice, guard-band clipping is often used to minimize the ...


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