Free-form deformation of solid geometric models
SIGGRAPH '86 Proceedings of the 13th annual conference on Computer graphics and interactive techniques
Extended free-form deformation: a sculpturing tool for 3D geometric modeling
SIGGRAPH '90 Proceedings of the 17th annual conference on Computer graphics and interactive techniques
Multiresolution analysis of arbitrary meshes
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Proceedings of the 2002 ACM SIGGRAPH/Eurographics symposium on Computer animation
Least squares conformal maps for automatic texture atlas generation
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
One-to-one piecewise linear mappings over triangulations
Mathematics of Computation
Invertible finite elements for robust simulation of large deformation
SCA '04 Proceedings of the 2004 ACM SIGGRAPH/Eurographics symposium on Computer animation
Mean value coordinates for closed triangular meshes
ACM SIGGRAPH 2005 Papers
Variational tetrahedral meshing
ACM SIGGRAPH 2005 Papers
Harmonic volumetric mapping for solid modeling applications
Proceedings of the 2007 ACM symposium on Solid and physical modeling
Isosurface stuffing: fast tetrahedral meshes with good dihedral angles
ACM SIGGRAPH 2007 papers
Harmonic coordinates for character articulation
ACM SIGGRAPH 2007 papers
As-rigid-as-possible surface modeling
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
On Linear Variational Surface Deformation Methods
IEEE Transactions on Visualization and Computer Graphics
ACM SIGGRAPH 2008 papers
Numerical Geometry of Non-Rigid Shapes
Numerical Geometry of Non-Rigid Shapes
Variational harmonic maps for space deformation
ACM SIGGRAPH 2009 papers
Computer Aided Geometric Design - Special issue: Geometric modelling and differential geometry
A local/global approach to mesh parameterization
SGP '08 Proceedings of the Symposium on Geometry Processing
A simple geometric model for elastic deformations
ACM SIGGRAPH 2010 papers
Bounded biharmonic weights for real-time deformation
ACM SIGGRAPH 2011 papers
Parameterization of star-shaped volumes using green's functions
GMP'10 Proceedings of the 6th international conference on Advances in Geometric Modeling and Processing
Bounded distortion mapping spaces for triangular meshes
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
Computing Extremal Quasiconformal Maps
Computer Graphics Forum
Biharmonic Volumetric Mapping Using Fundamental Solutions
IEEE Transactions on Visualization and Computer Graphics
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We introduce an efficient algorithm for producing provably injective mappings of tetrahedral meshes with strict bounds on their tetrahedra aspect-ratio distortion. The algorithm takes as input a simplicial map (e.g., produced by some common deformation or volumetric parameterization technique) and projects it on the space of injective and bounded-distortion simplicial maps. Namely, finds a similar map that is both bijective and bounded-distortion. As far as we are aware, this is the first algorithm to produce injective or bounded-distortion simplicial maps of tetrahedral meshes. The construction of the algorithm was made possible due to a novel closed-form solution to the problem of finding the closest orientation-preserving bounded-distortion matrix to an arbitrary matrix in three (and higher) dimensions. The algorithm is shown to have quadratic convergence, usually not requiring more than a handful of iterations to converge. Furthermore, it is readily generalized to simplicial maps of any dimension, including mixed dimensions. Finally, it can deal with different distortion spaces, such as bounded isometric distortion. During experiments we found the algorithm useful for producing bijective and bounded-distortion volume parameterizations and deformations of tetrahedral meshes, and improving tetrahedral meshes, increasing the tetrahedra quality produced by state-of-the-art techniques.