Principal Warps: Thin-Plate Splines and the Decomposition of Deformations
IEEE Transactions on Pattern Analysis and Machine Intelligence
On compatible triangulations of simple polygons
Computational Geometry: Theory and Applications
SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
A Delaunay refinement algorithm for quality 2-dimensional mesh generation
SODA '93 Selected papers from the fourth annual ACM SIAM symposium on Discrete algorithms
Multiresolution analysis of arbitrary meshes
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Optimal point placement for mesh smoothing
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
As-rigid-as-possible shape interpolation
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Texture mapping progressive meshes
Proceedings of the 28th 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
Bounded-distortion piecewise mesh parameterization
Proceedings of the conference on Visualization '02
Triangle: Engineering a 2D Quality Mesh Generator and Delaunay Triangulator
FCRC '96/WACG '96 Selected papers from the Workshop on Applied Computational Geormetry, Towards Geometric Engineering
One-to-one piecewise linear mappings over triangulations
Mathematics of Computation
ABF++: fast and robust angle based flattening
ACM Transactions on Graphics (TOG)
As-rigid-as-possible shape manipulation
ACM SIGGRAPH 2005 Papers
Discrete conformal mappings via circle patterns
ACM Transactions on Graphics (TOG)
Image deformation using moving least squares
ACM SIGGRAPH 2006 Papers
As-rigid-as-possible surface modeling
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Mesh parameterization methods and their applications
Foundations and Trends® in Computer Graphics and Vision
Conformal equivalence of triangle meshes
ACM SIGGRAPH 2008 papers
ACM SIGGRAPH 2008 papers
On Numerical Algorithms for the Solution of a Beltrami Equation
SIAM Journal on Numerical Analysis
Surface Quasi-Conformal Mapping by Solving Beltrami Equations
Proceedings of the 13th IMA International Conference on Mathematics of Surfaces XIII
Discrete one-forms on meshes and applications to 3D mesh parameterization
Computer Aided Geometric Design
A local/global approach to mesh parameterization
SGP '08 Proceedings of the Symposium on Geometry Processing
Discrete surface Ricci flow: theory and applications
Proceedings of the 12th IMA international conference on Mathematics of surfaces XII
A simple geometric model for elastic deformations
ACM SIGGRAPH 2010 papers
Controllable conformal maps for shape deformation and interpolation
ACM SIGGRAPH 2010 papers
Bounded biharmonic weights for real-time deformation
ACM SIGGRAPH 2011 papers
Registration for 3D surfaces with large deformations using quasi-conformal curvature flow
CVPR '11 Proceedings of the 2011 IEEE Conference on Computer Vision and Pattern Recognition
Simple formulas for quasiconformal plane deformations
ACM Transactions on Graphics (TOG)
Injective and bounded distortion mappings in 3D
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
Planar shape interpolation with bounded distortion
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
Integer-grid maps for reliable quad meshing
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
SGP '13 Proceedings of the Eleventh Eurographics/ACMSIGGRAPH Symposium on Geometry Processing
Bijective composite mean value mappings
SGP '13 Proceedings of the Eleventh Eurographics/ACMSIGGRAPH Symposium on Geometry Processing
Consistent volumetric discretizations inside self-intersecting surfaces
SGP '13 Proceedings of the Eleventh Eurographics/ACMSIGGRAPH Symposium on Geometry Processing
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The problem of mapping triangular meshes into the plane is fundamental in geometric modeling, where planar deformations and surface parameterizations are two prominent examples. Current methods for triangular mesh mappings cannot, in general, control the worst case distortion of all triangles nor guarantee injectivity. This paper introduces a constructive definition of generic convex spaces of piecewise linear mappings with guarantees on the maximal conformal distortion, as-well as local and global injectivity of their maps. It is shown how common geometric processing objective functionals can be restricted to these new spaces, rather than to the entire space of piecewise linear mappings, to provide a bounded distortion version of popular algorithms.