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
Matrix animation and polar decomposition
Proceedings of the conference on Graphics interface '92
A signal processing approach to fair surface design
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Mesh Smoothing Using A Posteriori Error Estimates
SIAM Journal on Numerical Analysis
Interactive multi-resolution modeling on arbitrary meshes
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
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
Bounded-distortion piecewise mesh parameterization
Proceedings of the conference on Visualization '02
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Deformation transfer for triangle meshes
ACM SIGGRAPH 2004 Papers
Mesh editing with poisson-based gradient field manipulation
ACM SIGGRAPH 2004 Papers
Cross-parameterization and compatible remeshing of 3D models
ACM SIGGRAPH 2004 Papers
Feature-based surface parameterization and texture mapping
ACM Transactions on Graphics (TOG)
Simplification and improvement of tetrahedral models for simulation
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Linear rotation-invariant coordinates for meshes
ACM SIGGRAPH 2005 Papers
ACM SIGGRAPH 2005 Papers
Large mesh deformation using the volumetric graph Laplacian
ACM SIGGRAPH 2005 Papers
Variational tetrahedral meshing
ACM SIGGRAPH 2005 Papers
Mesh quilting for geometric texture synthesis
ACM SIGGRAPH 2006 Papers
Subspace gradient domain mesh deformation
ACM SIGGRAPH 2006 Papers
Volume and shape preservation via moving frame manipulation
ACM Transactions on Graphics (TOG)
Tetrahedral mass spring model for fast soft tissue deformation
IS4TM'03 Proceedings of the 2003 international conference on Surgery simulation and soft tissue modeling
Robust mesh editing using Laplacian coordinates
Graphical Models
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We present a novel least scaling distortion metric to measure the deformation distortion for tetrahedral meshes. The stretch-like metric is a combination of Jacobian matrix norm and tetrahedron volume and has the properties of good shape preservation and rotation invariance. Based on our metric, we propose a uniform non-linear optimization solution to a variety of tetrahedral mesh manipulation applications including shape deformation, interpolation, deformation transfer, and deformation learning. Our approach can produce volume preserving and flip free tetrahedral mesh results, which performs much better than the previous tetrahedral manipulation approaches. We also demonstrate an efficient and practical application using free-form deformation technique. The object is embedded in a rough control tetrahedral mesh and deformed by editing the tetrahedral mesh with various constraints. Each vertex of the object can be obtained by its barycentric coordinates according to its embedding tetrahedron of the control tetrahedral mesh.