Free-form shape design using triangulated surfaces
SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
Minimal surfaces and Sobolev gradients
SIAM Journal on Scientific Computing
Shape preserving interpolation by space curves
Computer Aided Geometric Design
Sobolev Gradients and the Ginzburg--Landau Functional
SIAM Journal on Scientific Computing
The Barzilai and Borwein Gradient Method for the Large Scale Unconstrained Minimization Problem
SIAM Journal on Optimization
Generating Fair Meshes with G1 Boundary Conditions
GMP '00 Proceedings of the Geometric Modeling and Processing 2000
Shape-preserving interpolation by fair discrete G3 space curves
Computer Aided Geometric Design
Shape-preserving interpolation by fair discrete G 3 space curves
Computer Aided Geometric Design
Application of Sobolev gradient method to Poisson-Boltzmann system
Journal of Computational Physics
Nonlinear elasticity registration and sobolev gradients
WBIR'10 Proceedings of the 4th international conference on Biomedical image registration
Approximate solutions to Poisson-Boltzmann systems with Sobolev gradients
Journal of Computational Physics
Computers & Mathematics with Applications
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We have devised a new method for constructing discrete approximations to fair curves and surfaces by directly minimizing an arbitrarily selected fairness functional subject to geometric constraints. The nonlinear optimization problem is solved efficiently by a Sobolev gradient method. We first describe the method in general terms and then present results which demonstrate its effectiveness for constructing minimum variation curves which interpolate specified control points, tangent vectors, and/or curvature vectors.