Nonlinear interpolation between slices

The topic of interpolation between slices has been an intriguing problem for many years, as it offers means to visualize and investigate a three-dimensional object given only by its level sets. A slice consists of multiple non-intersecting simple contours, each defined by a cyclic list of vertices. An interpolation solution matches between a number of such slices (two or more at a time), providing means to create a closed surface connecting these slices, or the equivalent morph from one slice to another. We offer a method to incorporate the influence of more than two slices at each point in the reconstructed surface. We investigate the flow of the surface from one slice to the next by matching vertices and extracting differential geometric quantities from that matching. Interpolating these quantities with surface patches then allows a nonlinear reconstruction which produces a free-form, nonintersecting surface. No assumptions aremade about the input, such as on the number of contours in each slice, their geometric similarity, their nesting hierarchy, etc., and the proposed algorithm handles automatically all branching and hierarchical structures. The resulting surface is smooth and does not require further subdivision measures.