Subdivision interpolating implicit surfaces

Interpolating implicit surfaces using radial basis functions can directly specify surface points and surface normals with closed form solutions, so they are elegantly used in surface reconstruction and shape morphing. This paper presents subdivision interpolating implicit surfaces, a new progressive subdivision tessellation scheme for interpolating implicit surfaces controlled by a triangular mesh with arbitrary topology. We use a recursive polyhedral subdivision scheme to subdivide the control triangular mesh, and the new generated vertices are mapped to the implicit surface using Newton iteration. A multiresolution surface representation is automatically built with the proposed approach. Based on this approach, a newly surface modeling tool with more flexible control is developed by blending the interpolating subdivision surfaces with the subdivision interpolating implicit surfaces. r 2003 Elsevier Ltd. All rights reserved.