Interpolants Induced by Marching Cases

Visualization depends among other things on the interpolant used in generating images. One way to assess this is to construct case tables for Marching Cubes that represent the chosen interpolant accuracy. Instead, we show how to construct the interpolants induced by Marching Cases for comparison and assessment, how to extend this approach to Marching Squares, Cubes and Hypercubes, and how to construct an interpolant which is computationally equivalent to the digital rules conventionally used in image processing. Furthermore, we demonstrate that unlike tetrahedral meshes, geometric measurements over multi-linear mesh cells are inherently non-linear and cannot be summed as in the Contour Spectrum