Method for fairing B-spline surfaces
Computer-Aided Design
Functional optimization for fair surface design
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Efficient, fair interpolation using Catmull-Clark surfaces
SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
Free-form shape design using triangulated surfaces
SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
A unified approach to subdivision algorithms near extraordinary vertices
Computer Aided Geometric Design
A signal processing approach to fair surface design
SIGGRAPH '95 Proceedings of the 22nd 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
ACM Transactions on Mathematical Software (TOMS)
Fairing Recursive Subdivision Surfaces with Curve Interpolation Constraints
SMI '01 Proceedings of the International Conference on Shape Modeling & Applications
Stationary subdivision and multiresolution surface representations
Stationary subdivision and multiresolution surface representations
Modeling with multiresolution subdivision surfaces
ACM SIGGRAPH 2006 Courses
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In this paper we present a new algorithm for solving the data dependent fairing problem for subdivision surfaces, using Catmull-Clark surfaces as an example. Earlier approaches to subdivision surface fairing encountered problems with singularities in the parametrization of the surface. We address these issues through the use of the characteristic map parametrization, leading to well defined membrane and bending energies even at irregular vertices. Combining this approach with ideas from data-dependent energy operators we are able to express the associated nonlinear stiffness matrices for Catmull-Clark surfaces as linear combinations of precomputed energy matrices. This machinery also provides exact, inexpensive gradients and Hessians of the new energy operators. With these the nonlinear minimization problem can be solved in a stable and efficient way using Steihaug's Newton/CG trust-region method. We compare properties of linear and nonlinear methods through a number of examples and report on the performance of the algorithm.