n-Sided Patches and Subdivision Surfaces

Abstract

It is the base of surface blending and n-sided holes filling to construct n-sided patches. This chapter discusses three methods to construct n-sided patches. The first one is the manifold method. The control mesh of a manifold patch is constructed on the basis of the 5-ring submesh of an extraordinary vertex of a mesh with C-C subdivision connectivity.

Appendices

Remarks

Construction of n-sided patches is the fundamental of surface blending. It has important applications in CAD field and is a classical research content in CAGD field. Since the subdivision surface modeling technique has prevailed, the construction of n-sided patches is no more a difficult problem. Around the problem to construct n-sided patches by using the subdivision methods, researchers’ efforts focused on two aspects: one is how to construct patches with $G^{2}$ continuity and the other is how to blending other surfaces by using subdivision patches, from which many research works and literatures appear. This chapter classifies those methods in related subsections.

Exercises

• 1. Write program codes to extract an extraordinary point and its k-ring $(k= 1,2,3)$ from a Catmull–Clark subdivision mesh. The extraordinary point and its 3-ring can determine a uniform cubic B-spline surface ring. Compute the surface ring and render it.

• 2. Write program codes to subdivide an open mesh using the skirt-removed approach under the Catmull–Clark subdivision scheme.