Define: Interpolation

Background

This tutorial demonstrates a very important part of the 3D pipeline - the interpolation that the rasterizer performs on variables that come out of the vertex shader. 

• As you have already seen, in order to get something meaningful on the screen you need to designate one of the VS output variables as 'gl_Position'. 
• This is a 4-vector that contains the homogenuous coordinates of the vertex. 
• The XYZ components of that vector are divided by the W component (a process known as perspective divide and is dealt with in the tutorial dedicated to that subject) and any component which goes outside the normalized box ([-1,1]) gets clipped. 
• The result is transformed to screen space coordinates and then the triangle (or any other supported primitive type) is rendered to screen by the rasterizer.

• The rasterizer performs interpolation between the three triangle vertices (either going line by line or any other technique) and "visits" each pixel inside the triangle by executing the fragment shader. 
• The fragment shader is expected to return a pixel color which the rasterizer places in the color buffer for display (after passing a few additional tests like depth test, etc). Any other variable which comes out of the vertex shader does not go through the steps above. If the fragment shader does not explicitly requests that variable (and you can mix and match multiple fragment shaders with the same vertex shader) then a common driver optimization will be to drop any instructions in the VS that only affect this variable (for that particular shader program that combines this VS and FS pair). 
• However, if the FS does use that variable the rasterizer interpolates it during rasterization and each FS invocation is provided a the interpolated value that matches that specific location. This usually means that the values for pixels that are right next to each other will be a bit different (though as the triangle becomes further and further away from the camera that becomes less likely).

Two very common variables that often rely on this interpolation are the triangle normal and texture coordinates. 

• The vertex normal is usually calculated as the average between the triangle normals of all triangles that include that vertex. If that object is not completely flat this usually means that the three vertex normals of each triangle will be different from each other. In that case we rely on interpolation to calculate the specific normal at each pixel. That normal is used in lighting calculations in order to generate a more believable representation of lighting effects. 
• The case for texture coordinates is similar. These coordinates are part of the model and are specified per vertex. In order to "cover" the triangle with a texture you need to perform the sample operation for each pixel and specify the correct texture coordinates for that pixel. These coordinates are the result of the interpolation.

In this tutorial we will see the effects of interpolation by interpolating different colors across the triangle face. Since I'm lazy we will generate the color in the VS. A more tedious approach is to supply it from the vertex buffer. Usually you don't supply colors from the vertex buffer. You supply texture coordinates and sample a color from a texture. That color is later processed by the lighting calculations.