# Smooth spline surface generation over meshes of irregular topology

This source preferred by Jian Jun Zhang

**Authors: **Zheng, J.J., Zhang, J.J., Zhou, H.J. and Shen, L.G.

http://www.springerlink.com/content/j11651u471h27349/fulltext.pdf

**Journal:** The Visual Computer

**Volume:** 21

**Pages:** 858-864

**ISSN:** 0178-2789

**DOI:** 10.1007/s00371-005-0345-8

An efficient method for generating a smooth spline surface over an irregular mesh is presented in this paper. Similar to the methods proposed by [1, 2, 3, 4], this method generates a generalised bi-quadratic B-spline surface and achieves C1 smoothness. However, the rules to construct the control points for the proposed spline surfaces are much simpler and easier to follow. The construction process consists of two steps: subdividing the initial mesh once using the Catmull–Clark [5] subdivision rules and generating a collection of smoothly connected surface patches using the resultant mesh. As most of the final mesh is quadrilateral apart from the neighbourhood of the extraordinary points, most of the surface patches are regular quadratic B-splines. The neighbourhood of the extraordinary points is covered by quadratic Zheng–Ball patches [6].

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**Authors: **Zheng, J.J., Zhang, J.J., Zhou, H.J. and Shen, L.G.

**Journal:** Visual Computer

**Volume:** 21

**Issue:** 8-10

**Pages:** 858-864

**ISSN:** 0178-2789

**DOI:** 10.1007/s00371-005-0345-8

An efficient method for generating a smooth spline surface over an irregular mesh is presented in this paper. Similar to the methods proposed by [1, 2, 3, 4], this method generates a generalised bi-quadratic B-spline surface and achieves C 1 smoothness. However, the rules to construct the control points for the proposed spline surfaces are much simpler and easier to follow. The construction process consists of two steps: subdividing the initial mesh once using the Catmull-Clark [5] subdivision rules and generating a collection of smoothly connected surface patches using the resultant mesh. As most of the final mesh is quadrilateral apart from the neighbourhood of the extraordinary points, most of the surface patches are regular quadratic B-splines. The neighbourhood of the extraordinary points is covered by quadratic Zheng-Ball patches [6]. © Springer-Verlag 2005.