Hierarchical Multiresolution Reconstruction of Shell Surfaces

Several naturally occurring as well as manufactured objects have shell-like structures, that is, their boundaries consist of surfaces with thickness. In this paper we call these shell structures "fat surfaces". We present an adaptive, hierarchical Hh-multiresolution reconstruction algorithm to model fat surface objects from a matched triangulation pair. Fat surfaces are constructed by the contours of trivariate functions defined on prism scaffolds. In the H-direction, a hierarchical representation of the scaffold is constructed. For any adaptively extracted scaffold from the hierarchy, a sequence of functions in the h-direction (regularly subdivided mesh) is constructed so that their contours approximate the input shell to within a given error epsilon. The fat surfaces can be made to capture sharp curve creases on the shell while being C sup 1 smooth everywhere else. We also allow function values to be attached to the input vertices of the shell triangulations, so that physical data fileds defined on the shell can be visualized and texture mapping can be performed. Using an interval of iso-contours of smooth trivariate spline functions, rather than a pair of inner and outer surface splines, one avoids the need for interference checks between the inner and outer surface boundaries.