For a coneВ pointing up you typically make a separate vertex for each triangle meeting at the tip, with a separate normal. This is a common object, but is surprisingly messy. Another example is the coneВ and having a normal per vertex. However, this problem isnвЂ™t limited to spheres, and isnвЂ™t limited to textures. That works for texturing, if you can afford to fold the spherical mapping into the pixel shader.

The other, ultimate solutionВ is that you could compute the UV location per pixel, not per vertex. The artifacts areВ still there, but contained in a smaller area. One is to tessellate more: the more lines of latitude you make, the smaller the problem areas at the poles become. There are two ways I know to improveВ the rendering. The triangles that are rendered here are somewhat arbitrary вЂ“ at least the triangles along the top edge have a symmetry to them. Again, all the triangles with edges along the bottom of the texture will collapse to zero area, and half of the texture in the strip will not be rendered. I showВ a different tessellation along the bottom strip of the texture, a more traditional way to generate the UV coordinates and triangles. So any red triangles added will collapse theyвЂ™ll have zero area, as their two points along the top edge are co-located. Recall that all points along the upper edge of the texture are located at the same position in world space, the north pole of the model itself. Even if you form these triangles, adding them to the mesh, they wonвЂ™t appear. The sawtooth of triangles will display one half of the texture in this strip, but will not display the triangles covered in red. WhatвЂ™s interesting about this tessellation is that it leaves out half of the horizontal strip of texture near the pole. This gives a tessellation at the north pole something like this: One way around this is to look at the other vertices in the triangle (i.e., those not at the pole) and averageВ the U values they have. ItвЂ™s like asking what longitude youвЂ™re at when youвЂ™re sitting at the north pole вЂ“ you can take your pick, since none is correct. Part of the problem is that getting a good U value at each pole is problematic: U is essentially undefined. The only problem is that you canвЂ™t get exactly the right answer at the poles. Pretty straightforward, right? Compute the UV coordinates at the vertices and let the rasterizer do the work.

YouвЂ™re mapping a latitude-longitude texture on to a sphere.

Tessellation triangle texture