A matrix approach to the analysis of recursively generated B-spline surfaces
Computer-Aided Design
Estimating subdivision depths for rational curves and surfaces
ACM Transactions on Graphics (TOG)
Efficient, fair interpolation using Catmull-Clark surfaces
SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
Non-uniform recursive subdivision surfaces
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Exact evaluation of Catmull-Clark subdivision surfaces at arbitrary parameter values
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Sharp, quantitative bounds on the distance between a polynomial piece and its Bézier control polygon
Computer Aided Geometric Design - Special issue dedicated to Paul de Faget de Casteljau
Best bounds on the approximation of polynomials and splines by their control structure
Computer Aided Geometric Design
A bound on the approximation of a Catmull--Clark subdivision surface by its limit mesh
Computer Aided Geometric Design
The distance of a subdivision surface to its control polyhedron
Journal of Approximation Theory
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In this paper, both general and exponential bounds of the distance between a uniform Catmull-Clark surface and its control polyhedron are derived. The exponential bound is independent of the process of subdivision and can be evaluated without recursive subdivision. Based on the exponential bound, we can predict the depth of subdivision within a user-specified error tolerance. This is quite useful and important for pre-computing the subdivision depth of subdivision surfaces in many engineering applications such as surface/surface intersection, mesh generation, numerical control machining and surface rendering.