Screen-space versus object space interpolation
This applet shows two points A and B projected on a camera plane (horizontal blue line) from a center of projection C. It shows that the middle of projection is not the projection of the middle. In other words, interpolating in screen space (=middle of projection) is not perspective correct:
If A is red and B is green and you color the point between a=P(A) and b=P(B) in image by interpolating between red and green using interpolation in image space, you will get incorrect colors.
That Java applet is powered by the excellent free software GeoNext.