What does "region to be shaded" mean in the PCF paper?

Question

I am reading the percentage closer filtering (PCF) paper by Reeves, W. et al. (https://graphics.pixar.com/library/ShadowMaps/paper.pdf).

At at section 3.2, it mentioned that "each shading calculation represents some region on a surface". And "each region to be shaded is mapped to a region in the shadow map".

For my understanding, using Opengl fragment shader, for each shading calculation, we just operate on each pixel. We do the shadow calculation on each pixel in the camera image.

Can anyone explain what does that "region to be shaded" mean? Thanks!

Answer 1

Texture mapping is the process of providing a mapping from the surface to a location on the texture. That is, given a particular point on a surface, you can find a specific point in a texture that corresponds to it. Giving positions a UV texture coordinate is a common means of defining a texture mapping, but you can use a function of arbitrary complexity.

Texture mapping is at least theoretically reversible. That is, given a particular texel, you can use the texture mapping to determine where on an object that texel appears. Of course, not every texture mapping is reversible. Some mapping cause a texel to be used in multiple locations on a surface, and not every mapping uses every texel in the texture.

But the important part of the reverse mapping operation is this: a texel maps to some area of the surface, not a single point.

Shadow mapping is a form of texture mapping. It defines a mapping from the scene to a texture by performing perspective projection of the points in the scene onto the surface of a texture, based on a light position.

If you reverse this mapping, a texel in the shadow map maps to an area in the scene. This is the "region in the scene".