Math behind Tex2D in HLSL

Question

Could someone explain the math behind the function Tex2D in HLSL?

One of the examples is: given a quad with 4 vertices, the texture coordinates are (0,0) (0,1) (1,0) (1,1) on it and the texture's width and height are 640 and 480. How is the shader able to determine the number of times of sampling to be performed? If it is to map texels to pixels directly, does it mean that the shader needs to perform 640*480 times of sampling with the texture coordinates increasing in some kind of gradients? Also, I would appreciate if you could provide more references and articles on this topic.

Thanks.

Answer 1

After the vertex shader the rasterizer "converts" triangles into pixels. Each pixel is associated with a screen position, and the vertex attributes of the triangles (eg: texture coordinates) are interpolated across the triangles and an interpolated value is stored in each pixel according to the pixel position.

The pixel shader runs once per pixel (in most cases).

The number of times the texture is sampled per pixel depends on the sampler used. If you use a point sampler the texture is sampled once, 4 times if you use a bilinear sampler and a few more if you use more complex samplers.

So if you're drawing a fullscreen quad, the texture you're sampling is the same size of the render target and you're using a point sampler the texture will be sampled width*height times (once per pixel).

You can think about textures as an 2-dimensional array of texels. tex2D simply returns the texel at the requested position performing some kind of interpolation depending on the sampler used (texture coordinates are usually relative to the texture size so the hardware will convert them to absolute coordinates).

This link might be useful: Rasterization