Using partial differential equations to generate free-form surfaces: 91787
Computer-Aided Design
Functional optimization for fair surface design
SIGGRAPH '92 Proceedings of the 19th 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 signal processing approach to fair surface design
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Parametrization and smooth approximation of surface triangulations
Computer Aided Geometric Design
Interactive multi-resolution modeling on arbitrary meshes
Proceedings of the 25th 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
On the design of CGAL a computational geometry algorithms library
Software—Practice & Experience - Special issue on discrete algorithm engineering
Reconstruction and representation of 3D objects with radial basis functions
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Level set surface editing operators
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Interactive geometry remeshing
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Least squares conformal maps for automatic texture atlas generation
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Generating Fair Meshes with G1 Boundary Conditions
GMP '00 Proceedings of the Geometric Modeling and Processing 2000
Polyhedral Surface Smoothing with Simultaneous Mesh Regularization
GMP '00 Proceedings of the Geometric Modeling and Processing 2000
Geometric fairing of irregular meshes for free-form surface design
Computer Aided Geometric Design
Smooth surface reconstruction via natural neighbour interpolation of distance functions
Computational Geometry: Theory and Applications
Mesh editing with poisson-based gradient field manipulation
ACM SIGGRAPH 2004 Papers
Optimal Global Conformal Surface Parameterization
VIS '04 Proceedings of the conference on Visualization '04
A remeshing approach to multiresolution modeling
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
ABF++: fast and robust angle based flattening
ACM Transactions on Graphics (TOG)
Master-element vector irradiance for large tessellated models
GRAPHITE '05 Proceedings of the 3rd international conference on Computer graphics and interactive techniques in Australasia and South East Asia
Template-based mesh completion
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
Mesh parameterization methods and their applications
Foundations and Trends® in Computer Graphics and Vision
Mesh parameterization: theory and practice
ACM SIGGRAPH ASIA 2008 courses
Fixing geometric errors on polygonal models: a survey
Journal of Computer Science and Technology
Technical Section: Automatic hole-filling of CAD models with feature-preserving
Computers and Graphics
Intuitive shape modeling by shading design
SG'05 Proceedings of the 5th international conference on Smart Graphics
Design-driven quadrangulation of closed 3D curves
ACM Transactions on Graphics (TOG) - Proceedings of ACM SIGGRAPH Asia 2012
Field-guided registration for feature-conforming shape composition
ACM Transactions on Graphics (TOG) - Proceedings of ACM SIGGRAPH Asia 2012
Template deformation for point cloud fitting
SPBG'06 Proceedings of the 3rd Eurographics / IEEE VGTC conference on Point-Based Graphics
Polygon mesh repairing: An application perspective
ACM Computing Surveys (CSUR)
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Shape optimization and surface fairing for polygon meshes have been active research areas for the last few years. Existing approaches either require the border of the surface to be fixed, or are only applicable to closed surfaces. In this paper, we propose a new approach, that computes natural boundaries. This makes it possible not only to smooth an existing geometry, but also to extrapolate its shape beyond the existing border. Our approach is based on a global parameterization of the surface and on a minimization of the squared curvatures, discretized on the edges of the surface. The so-constructed surface is an approximation of a minimal energy surface (MES). Using a global parameterization makes it possible to completely decouple the outer fairness (surface smoothness) from the inner fairness (mesh quality). In addition, the parameter space provides the user with a new means of controlling the shape of the surface. When used as a geometry filter, our approach computes a smoothed mesh that is discrete conformal to the original one. This allows smoothing textured meshes without introducing distortions.