Progressive Interpolation based on Catmull-Clark Subdivision Surfaces

Approximating catmull-clark subdivision surfaces with bicubic patches

A Generalized Scheme for the Interpolation of Arbitrarily Intersecting Curves by Catmull-Clark Subdivision Surfaces

This paper presents a scheme for interpolating intersecting uniform cubic B-spline curves by Catmull-Clark subdivision surfaces. The curves are represented by polygonal complexes and the neighborhoods of intersection points are modeled by X-Configurations. When these structures are embedded within a control polyhedron, the corresponding curves will automatically be interpolated by the surface l...

Deforming Subdivision Surfaces

We introduce a new algorithm for fitting a Catmull-Clark subdivision surface to a given shape within a prescribed tolerance, based on the method of quasi-interpolation. The fitting algorithm is fast, local and scalable since it does not require the solution of linear systems. Its convergence rate is optimal for regular meshes and our experiments show that it behaves very well for irregular mesh...

Inscribed Approximation based Adaptive Tessellation of Catmull-Clark Subdivision Surfaces

Catmull-Clark subdivision scheme provides a powerful method for building smooth and complex surfaces. But the number of faces in the uniformly refined meshes increases exponentially with respect to subdivision depth. Adaptive tessellation reduces the number of faces needed to yield a smooth approximation to the limit surface and, consequently, makes the rendering process more efficient. In this...

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...