Mathematical Model of Catmull-Clark Subdivision Scheme on Regular Mesh

DOI

10.2991/amcce-17.2017.31How to use a DOI?

Keywords

Subdivision, interpolation, mathematical expression, B-spline surface.

Abstract

In order to further simplify the research of limit surface properties and establish a unified mathematical model. According to Catmull-Clark subdivision method in the regular mesh at the subdivision rules, a method of calculating the mathematical expression of limit surface by interpolation was presented by using the subdivision method which is described by the curves and surfaces interpolation theory. And according to the process of solving, we prove that the limit surface which generated by the Catmull-Clark subdivision method in the regular mesh is a bi-cubic B-spline surface.

Copyright

© 2017, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Shu-qun Liu
AU  - Bei Zhang
PY  - 2017/03
DA  - 2017/03
TI  - Mathematical Model of Catmull-Clark Subdivision Scheme on Regular Mesh
BT  - Proceedings of the 2017 2nd International Conference on Automation, Mechanical Control and Computational Engineering (AMCCE 2017)
PB  - Atlantis Press
SP  - 180
EP  - 186
SN  - 2352-5401
UR  - https://doi.org/10.2991/amcce-17.2017.31
DO  - 10.2991/amcce-17.2017.31
ID  - Liu2017/03
ER  -