GUIDED CATMULL-CLARK SUBDIVISION

Jianzhong Wang, jwangf@uky.edu

Fuhua Cheng, cheng@cs.uky.edu

The Catmull-Clark subdivision scheme for extraordinary patches is modified. The limit surface is curvature continuous at extraordinary points and C2 continuous elsewhere. With the new

scheme, one can generate a high quality subdivision surface with only bi-cubic B-spline patches.

In this paper we have shown that the guided subdivision scheme guarantees curvature continuity at extraordinary vertices of a Catmull-Clark subdivision surface. In contrast to previous works on extraordinary vertices, our scheme is purely subdivision based and uses only regular bi-cubic subdivision. This avoids the hassle to recompute eigenvalues and eigenbases for every valence in the original CCSS subdivision surface, instead the eigenstructures of our scheme have eigenvalues of 1 ,1/2, 1/4, 1/8, 1/16, 1/32, 1/64 (the eigenvalues for regular bi-cubic subdivision), so the scheme has a unique eigenbase for any valence.

Besides, the guided subdivison surface is flexible, we can adjust the shape of the subdivison surface by fine-tuning the determining control meshes as far as the choice of control points fulfill the requirement set forth in this paper. The linear system for choosing the control points of 2N determining control meshes is underdetermined, so this leaves rooms for changing the shape of subdivision surface without sacrificing the curvature continuity.

This paper is currently under review. The followings are some examples generated by using this scheme.

Limit surface for extraordinary point of valence 3 with its enlarged mesh structure

Limit surface for extraordinary point of valence 5 with its enlarged mesh structure

Limit surface for extraordinary point of valence 6 with its enlarged mesh structure

Limit surface for extraordinary point of valence 7 with its enlarged mesh structure

Limit surface for extraordinary point of valence 8 with its enlarged mesh structure