Texture mapping on a cylinder - c++

Question

I want to apply an uniform checkerboard texture to a cylinder surface of height h, and semiradii (a,b).
I've implemented this shader:
Vertex shader:
varying vec2 texture_coordinate;
float twopi = 6.283185307;
float pi=3.141592654;
float ra = 1.5;
float rb= 1.0;
void main()
{
// Transforming The Vertex
gl_Position = gl_ModelViewProjectionMatrix * gl_Vertex;
// -pi/2 < theta < pi/2
float theta = (atan2( rb*gl_Vertex.y , ra*gl_Vertex.x)+pi*0.5)/pi;
// Passing The Texture Coordinate Of Texture Unit 0 To The Fragment Shader
texture_coordinate = vec2( theta , -(-gl_Vertex.z+0.5) );
}
Fragment shader:
varying vec2 texture_coordinate;
uniform sampler2D my_color_texture;
void main()
{
// Sampling The Texture And Passing It To The Frame Buffer
gl_FragColor = texture2D(my_color_texture, texture_coordinate);
}
while on client side I've specified the following options:
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MIN_FILTER, GL_LINEAR);
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MAG_FILTER, GL_LINEAR);
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_S, GL_REPEAT);
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_T, GL_REPEAT);
My texture is a 3768x1200 checkerboard. Now I would like that the texture is applied in order to keep the checkerboard uniform (squares without stretch), but I obtain a correct aspect ratio only in the less curved part of the surface, while on the more curved parts the tiles are stretched.
I would like to understand how to apply the texture without distorting and stretching it, maybe by repeating the texture instead of stretching it.
I also have a problem of strange flickering on the borders of the texture, where the two borders intersect, how to solve it (it can be seen in the second image)?

Answer 1

You can modify the texture coordinates to "shrink" it on an object a bit. What you can't do is to parametrize the texture coordinates to scale non-linearly.
So, the options are:
Quantize the sampling, modifying texture coordinates to better accomodate the non-circularity (dynamic, but quality is low when using low-poly tesselation; it's the simplest solution to implement, though).
Use fragment shader to scale texture coordinates non-linearly (possibly a bit more complicated, but dynamic and giving quite good results, depending on the texture size, filtering used and the texture contents(!))
Modify the texture (static solution - will work only for given Ra/Rb ratio. However, the quality will be the best possible).
As to the flickering on the borders, you have to generate mipmaps for your textures.
Let me know if you need more information.