An alternative method for constructing interpolatory subdivision from approximating subdivision

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• 作者：Xin Li^a ; Jianmin Zheng^b ; ^{asjmzheng@ntu.edu.sg} ;
• 关键词：Geometric modeling ; Subdivision algorithms ; Approximating subdivision ; Interpolatory subdivision
• 刊名：Computer Aided Geometric Design
• 出版年：2012
• 期刊代码：20_01678396
• 类别：cp
• 出版时间：October, 2012
• 卷：29
• 期：7
• 页码：474-484
• 文件大小：1452 K

摘要

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始s interpolatory scheme, and Loop subdivision and the butterfly algorithm.