Planar 2-pass texture mapping and warping

The 2-pass tranformation replaces a 2-D (2-dimensional) transformation with a sequence of orthogonal, simpler 1-D transformation. It may be used for the closely related processes of texture mapping and warping in computer graphics and image processing. First, texture maps onto planar quadric and superquadric surfaces and, second, planar bicubic and biquadratic warps of images are shown to be 2-pass transformable. A distinction between serial and parallel warps is introduced to solve a confusion in terms between computer graphics and image processing. It is shown that an n-th order serial polynomial warp is equivalent to an (n2+n)-th order parallel polynomial warp. It is also shown that the serial equivalent to a parallel polynomial warp is generally not a polynomial warp, being more complicated than a polynomial. The unusual problem of bottlenecking and the usual one of antialiasing are discussed in the 2-pass context.