Exact Evaluation of Catmull-Clark Subdivision Surfaces Near B-Spline Boundaries

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

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...

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...

Construction of Minimal Catmull-Clark's Subdivision Surfaces with Given Boundaries

Minimal surface is an important class of surfaces. They are widely used in the areas such as architecture, art and natural science etc.. On the other hand, subdivision technology has always been active in computer aided design since its invention. The flexibility and high quality of the subdivision surface makes them a powerful tool in geometry modeling and surface designing. In this paper, we ...