The applications of texture mapping in computer graphics and image distortion (warping) in image processing share a core of fundamental techniques. We explore two of these techniques, the two-dimensional geometric mappings that arise in the parameterization and projection of textures onto surfaces, and the filters necessary to eliminate aliasing when an image is resampled during texture mapping or warping. With respect to mappings, this work presents a tutorial on three common classes of mapping: the affine, bilinear, and projective. For resampling, this work develops a new theory describing the ideal, space variant intialiazing filter for signals warped and resampled according to an arbitrary mapping. Efficient implementations of the mapping and filtering techniques are discussed and demonstrated.