Interpolation by geometric algorithm

We present a novel geometric algorithm to construct a smooth surface that interpolates a triangular or a quadrilateral mesh of arbitrary topological type formed by n vertices. Although our method can be applied to B-spline surfaces and subdivision surfaces of all kinds, we illustrate our algorithm focusing on Loop subdivision surfaces as most of the meshes are in triangular form. We start our algorithm by assuming that the given triangular mesh is a control net of a Loop subdivision surface. The control points are iteratively updated globally by a simple local point-surface distance computation and an offsetting procedure without solving a linear system. The complexity of our algorithm is O(mn) where n is the number of vertices and m is the number of iterations. The number of iterations m depends on the fineness of the mesh and accuracy required. Key words: geometric algorithm, surface interpolation, Loop subdivision surface, Catmull-Clark subdivision surface, B-spline curves and su...

• Type: Journal
• Year: 2007
• Where: CAD
• Authors: Takashi Maekawa, Yasunori Matsumoto, Ken Namiki
• Keywords: Algorithm, CAD 2007, Loop Subdivision, Loop Subdivision Surface, Theoretical Computer Science