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
One-to-one piecewise linear mappings over triangulations
Mathematics of Computation
Convex Optimization
Sweepers: Swept User-Defined Tools for Modeling by Deformation
SMI '04 Proceedings of the Shape Modeling International 2004
Swirling-Sweepers: Constant-Volume Modeling
PG '04 Proceedings of the Computer Graphics and Applications, 12th Pacific Conference
Invertible finite elements for robust simulation of large deformation
SCA '04 Proceedings of the 2004 ACM SIGGRAPH/Eurographics symposium on Computer animation
Point based animation of elastic, plastic and melting objects
SCA '04 Proceedings of the 2004 ACM SIGGRAPH/Eurographics symposium on Computer animation
ABF++: fast and robust angle based flattening
ACM Transactions on Graphics (TOG)
Meshless deformations based on shape matching
ACM SIGGRAPH 2005 Papers
Mathematical Programming: Series A and B
Proceedings of the 4th international symposium on Non-photorealistic animation and rendering
Vector field based shape deformations
ACM SIGGRAPH 2006 Papers
Kinodynamic skinning using volume-preserving deformations
SCA '07 Proceedings of the 2007 ACM SIGGRAPH/Eurographics symposium on Computer animation
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
On Linear Variational Surface Deformation Methods
IEEE Transactions on Visualization and Computer Graphics
ACM SIGGRAPH 2009 papers
Meshless modeling of deformable shapes and their motion
Proceedings of the 2008 ACM SIGGRAPH/Eurographics Symposium on Computer Animation
A simple geometric model for elastic deformations
ACM SIGGRAPH 2010 papers
Volumetric modeling with diffusion surfaces
ACM SIGGRAPH Asia 2010 papers
Interference-aware geometric modeling
Proceedings of the 2011 SIGGRAPH Asia Conference
Bounded distortion mapping spaces for triangular meshes
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
Global parametrization by incremental flattening
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
Computing Extremal Quasiconformal Maps
Computer Graphics Forum
Simulation of complex nonlinear elastic bodies using lattice deformers
ACM Transactions on Graphics (TOG) - Proceedings of ACM SIGGRAPH Asia 2012
Energetically consistent invertible elasticity
EUROSCA'12 Proceedings of the 11th ACM SIGGRAPH / Eurographics conference on Computer Animation
Consistent volumetric discretizations inside self-intersecting surfaces
SGP '13 Proceedings of the Eleventh Eurographics/ACMSIGGRAPH Symposium on Geometry Processing
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Mappings and deformations are ubiquitous in geometry processing, shape modeling, and animation. Numerous deformation energies have been proposed to tackle problems like mesh parameterization and volumetric deformations. We present an algorithm that modifies any deformation energy to guarantee a locally injective mapping, i.e., without inverted elements. Our formulation can be used to compute continuous planar or volumetric piecewise-linear maps and it uses a barrier term to prevent inverted elements. Differently from previous methods, we carefully design both the barrier term and the associated numerical techniques to be able to provide immediate feedback to the user, enabling interactive manipulation of inversion-free mappings. Stress tests show that our method robustly handles extreme deformations where previous techniques converge very slowly or even fail. We demonstrate that enforcing local injectivity increases fidelity of the results in applications such as shape deformation and parameterization.