Curve and surface fitting with splines
Curve and surface fitting with splines
A signal processing approach to fair surface design
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Implicit fairing of irregular meshes using diffusion and curvature flow
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Multiresolution signal processing for meshes
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion
Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion
Non-iterative, feature-preserving mesh smoothing
ACM SIGGRAPH 2003 Papers
ACM SIGGRAPH 2003 Papers
Geometry-Aware Bases for Shape Approximation
IEEE Transactions on Visualization and Computer Graphics
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
Constraint-based fairing of surface meshes
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Discovering Process Models from Unlabelled Event Logs
BPM '09 Proceedings of the 7th International Conference on Business Process Management
Physics-inspired upsampling for cloth simulation in games
ACM SIGGRAPH 2011 papers
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In Sorkine et al. proposed a least squares based representation of meshes, which is suitable for compression and modeling. In this paper we look at this representation from the viewpoint of Tikhonov regularization. We show that this viewpoint yields a smoothing algorithm, which can be seen as shape approximation using weighted geometry aware bases, where the weighting factor is determined by the algorithm. The algorithm combines the Laplacian smoothing approach with the smoothing spline approach, where a global deviation constraint is imposed on the approximation. We use the generalized Laplacian matrix to measure smoothness and show how it can be modified in order to obtain smoothing behavior similar to that of curvature flow and feature preserving smoothing algorithms. The method is applicable to meshes, polygonal curves and point clouds in arbitrary dimensional spaces.