Distortion or Aliasing of a UV Sphere

Question

I am trying to map a texture on a UV sphere. I created an algorithm to generate the vertices of the sphere and the UV texture coordinates for each vertex. How I do fix the distortion or aliasing? The formulas I used to generate the vertices of the sphere are: x = rsinΦcosθ y = rcosΦ z = -rsinΦsinθ

The formulas used to generate the UV texture coordinates for each vertex are: θ = arctan(z / x) / 2π Φ = arcos(y) / π

I am using Direct3D 12 to render the sphere.

Answer 1

This problem might occur, because the most left vertices and the most right vertices are connected while the UV coordinates (texture coordinates) are 1(right) and 0(left)... so the whole texture is interpolated within the small area. (See figure 1)

Figure 1: This is what you have right now. The green triangles are correct, the red triangles show the problem you have...

You can add an additional vertex column on the right, where the vertex positions are the same as the most left vertices. (see Figure 2)

Figure 2: This is what you need. The orange vertices have the same position as the blue vertices. So this column of vertices is duplicated. But the texture coordinates are different. The blue vertices have a texture coordinate (x) = 0 and the orange vertices have a texture coordinate (x) = 1.