An alternative method for constructing interpolatory subdivision from approximating subdivision

作者：Li, Xin; Zheng, Jianmin^*

来源：Computer Aided Geometric Design, 2012, 29(7): 474-484.

DOI：10.1016/j.cagd.2012.03.008

• Geometric modeling
• Subdivision algorithms
• Approximating subdivision
• Interpolatory subdivision

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.

• 出版日期2012-10
• 单位南阳理工学院; 中国科学技术大学