OpenGL: Mapping texture on a sphere using spherical coordinates

Question

I have a texture of the earth which I want to map onto a sphere. As it is a unit sphere and the model itself has no texture coordinates, the easiest thing I could think of is to just calculate spherical coordinates for each vertex and use them as texture coordinates.

textureCoordinatesVarying = vec2(atan(modelPositionVarying.y, modelPositionVarying.x)/(2*M_PI)+.5, acos(modelPositionVarying.z/sqrt(length(modelPositionVarying.xyz)))/M_PI);

When doing this in the fragment shader, this works fine, as I calculate the texture coordinates from the (interpolated) vertex positions.

But when I do this in the vertex shader, which I also would do if the model itself has texture coordinates, I get the result as shown in the image below. The vertices are shown as points and a texture coordinate (u) lower than 0.5 is red while all others are blue.

So it looks like that the texture coordinate (u) of two adjacent red/blue vertices have value (almost) 1.0 and 0.0. The variably is then smoothly interpolated and therefore yields values somewhere between 0.0 and 1.0. This of course is wrong, because the value should either be 1.0 or 0.0 but nothing in between.

Is there a way to work with spherical coordinates as texture coordinates without getting those effects shown above? (if possible, without changing the model)

Answer 1

This is a common problem. The seams between two texture coordinate topologies, where you want the texture coordinate to seamlessly wrap from 1.0 to 0.0 requires the mesh to properly handle this. To do this, the mesh must duplicate every vertex along the seam. One of the vertices will have a 0.0 texture coordinate and will be connected to the vertices coming from the right (in your example). The other will have a 1.0 texture coordinate and will be connected to the vertices coming from the left (in your example).

This is a mesh problem, and it is best to solve it in the mesh itself. The same position needs two different texture coordinates, so you must duplicate the position in question.

Alternatively, you could have the fragment shader generate the texture coordinate from an interpolated vertex normal. Of course, this is more computationally expensive, as it requires doing a conversion from a direction to a pair of angles (and then to the [0, 1] texture coordinate range).