We can now use this expression for s to interpolate arbitrary parameters,
such as texture indices (u, v), over our 3-space triangle. This is accomplished
substituting our solution for s given t into the parameter interploation.
Therefore, if we premultiply all parameters that we wish to interpolate in
3-space by their corresponding w value and add a new plane equation to interpolate
the w values themselves, we can interpolate the numerators and denominator in
screen-space. We then need to perform a divide a each step to get to map the
screen-space interpolants to their corresponding 3-space values.
For obvious reasons this method of interpolation is called perspective-correct
interpolation. The fact is, the name could be shortened to simply correct interpolation.
You should be aware that not all 3-D graphics APIs implement perspective-correct
interpolation.
