Curves and surfaces for computer aided geometric design (3rd ed.): a practical guide
Curves and surfaces for computer aided geometric design (3rd ed.): a practical guide
Efficient, fair interpolation using Catmull-Clark surfaces
SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
Piecewise smooth surface reconstruction
SIGGRAPH '94 Proceedings of the 21st 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
Subdivision depth computation for extra-ordinary catmull-clark subdivision surface patches
CGI'06 Proceedings of the 24th international conference on Advances in Computer Graphics
GMP'06 Proceedings of the 4th international conference on Geometric Modeling and Processing
Robustness of Boolean Operations on Subdivision-Surface Models
Numerical Validation in Current Hardware Architectures
The distance of a subdivision surface to its control polyhedron
Journal of Approximation Theory
Bounding the distance between a loop subdivision surface and its limit mesh
GMP'08 Proceedings of the 5th international conference on Advances in geometric modeling and processing
Beyond Catmull–Clark? A Survey of Advances in Subdivision Surface Methods
Computer Graphics Forum
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In geometry processing a refined control mesh is often used to approximate a Catmull-Clark subdivision surface (CCSS). By pushing the control points to their limit positions, a limit mesh of the subdivision surface is obtained. We present a bound on the distance between a CCSS patch and its limit face in terms of the maximum norm of the second order differences of the control points. The bound shows that the limit mesh may approximate the limit surface better than the corresponding control mesh in general. Consequently, for a given error tolerance, fewer subdivision steps are needed if the refined control mesh is replaced with the corresponding limit mesh.