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Dave Blake

Tessellating a segment of a sphere

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I am working on 2D rendering of various azimuthal projections (gnomonic, equidistant, orthographic etc.) of a sphere. The colour of the sphere generally varies with position, but one distinct colour boundary lies exactly along a great circle. I need to cover the equivalent region in my projected "map" of the sphere with an even triangular mesh. I could do with some help on this. One approach would be to approximate the boundary of the region (projected great circle, edge of sphere and any clipping by rectangular viewport) with a polygon and tessellate that. Suggestions for simple algorithms for tessellation of concave/convex polygons most welcome (I am a nubie to tessellation). However, I have tried another route: cover the sphere in a geodesic mesh derived from the bisection of an icosahedron (orientated such that there are vertices along the bounding great circle). This produces a nice evenly spaced triangulation, but I run into problems on the map at the projected edge of the sphere where triangles are only partly in view (depending on the angle it is viewed from). Maybe my adventure into geodesics has been a waste of time :( I am hoping that I can somehow adjust the geodesic mesh, to fit not only the colour boundary great circle but also the edge great circle that delimits the current view point of the sphere. Any advise, is this folly? I have not taken viewport clipping onto account here either, and an even triangulation on the sphere may not be so good when projected.

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