Dynamic Catmull-Clark Subdivision Surfaces

Koiter's Thin Shells on Catmull-Clark Limit Surfaces

We present a discretization of Koiter’s model of elastic thin shells based on a finite element that employs limit surfaces of Catmull–Clark’s subdivision scheme. The discretization can directly be applied to control grids of Catmull–Clark subdivision surfaces, and, therefore, integrates modeling of Catmull–Clark subdivision surfaces with analysis and optimization of elastic thin shells. To test...

Exact Evaluation Of Catmull-Clark Subdivision Surfaces At Arbitrary Parameter Value

In this paper we disprove the belief widespread within the computer graphics community that Catmull-Clark subdivision surfaces cannot be evaluated directly without explicitly subdividing. We show that the surface and all its derivatives can be evaluated in terms of a set of eigenbasis functions which depend only on the subdivision scheme and we derive analytical expressions for these basis func...

Approximating catmull-clark subdivision surfaces with bicubic patches

Generalized Catmull-Clark Subdivision

The Catmull-Clark subdivision algorithm consists of an operator that can be decomposed into a refinement operator and a successively executed smoothing operator, where the refinement operator splits each face with m vertices into m quadrilateral subfaces and the smoothing operator replaces each internal vertex with an affine combination of its neighboring vertices and itself. Over regular meshe...

Exact Evaluation of NURSS at Arbitrary Parameter Values

Convergence and continuity analyses as well as exact evaluation of non-uniform subdivision surfaces at arbitrary parameter values have been very difficult because the subdivision matrix varies at each iteration step, unlike uniform subdivision surfaces. Using eigenanalysis and convergence properties of non-uniform subdivision surfaces that have been given by authors recently, a parameterization...

Evaluation of Loop Subdivision Surfaces

This paper describes a technique to evaluate Loop subdivision surfaces at arbitrary parameter values. The method is a straightforward extension of our evaluation work for Catmull-Clark surfaces. The same ideas are applied here, with the differences being in the details only.