An alternative method for constructing interpolatory subdivision from approximating subdivision

Authors:
Xin Li;Jianmin Zheng
Affiliations:
Department of Mathematics, University of Science and Technology of China, Hefei, Anhui, PR China;School of Computer Engineering, Nanyang Technological University, N4, #02a-32, Nanyang Avenue, Singapore 639798, Singapore
Venue:
Computer Aided Geometric Design
Year:
2012

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Abstract

This paper presents a new perspective for constructing interpolatory subdivision from primal approximating subdivision. The basic idea is constructing the subdivision rule for new inserted vertices of a new interpolatory subdivision scheme based on an approximating subdivision algorithm applied to a local configuration of the mesh with one vertex updated for interpolation of the vertex. This idea is demonstrated by presenting two new interpolatory subdivision schemes based on Catmull-Clark subdivision for an arbitrary polygonal mesh and Loop subdivision for a triangular mesh, respectively. These algorithms are simple and have a small stencil for computing new points. The new perspective also shows a link between those classic approximating and interpolatory subdivision algorithms such as cubic B-spline curve subdivision and the four-point interpolatory subdivision, Catmull-Clark subdivision and Kobbelt@?s interpolatory scheme, and Loop subdivision and the butterfly algorithm.