Joint-dependent local deformations for hand animation and object grasping
Proceedings on Graphics interface '88
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
Computer Aided Geometric Design
A two-dimensional interpolation function for irregularly-spaced data
ACM '68 Proceedings of the 1968 23rd ACM national conference
An intuitive framework for real-time freeform modeling
ACM SIGGRAPH 2004 Papers
Mean value coordinates for closed triangular meshes
ACM SIGGRAPH 2005 Papers
As-rigid-as-possible shape manipulation
ACM SIGGRAPH 2005 Papers
Image deformation using moving least squares
ACM SIGGRAPH 2006 Papers
Inverse kinematics for reduced deformable models
ACM SIGGRAPH 2006 Papers
Harmonic coordinates for character articulation
ACM SIGGRAPH 2007 papers
Automatic rigging and animation of 3D characters
ACM SIGGRAPH 2007 papers
Embedded deformation for shape manipulation
ACM SIGGRAPH 2007 papers
Mesh puppetry: cascading optimization of mesh deformation with inverse kinematics
ACM SIGGRAPH 2007 papers
PriMo: coupled prisms for intuitive surface modeling
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
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
Geometric skinning with approximate dual quaternion blending
ACM Transactions on Graphics (TOG)
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Changing an object's shape is a basic operation in computer graphics, necessary for transforming raster images, vector graphics, geometric models, and animated characters. The fastest approaches for such object deformation involve linearly blending a small number of given affine transformations, typically each associated with bones of an internal skeleton, vertices of an enclosing cage, or a collection of loose point handles. Unfortunately, linear blending schemes are not always easy to use because they may require manually painting influence weights or modeling closed polyhedral cages around the input object. Our goal is to make the design and control of deformations simpler by allowing the user to work freely with the most convenient combination of handle types. We develop linear blending weights that produce smooth and intuitive deformations for points, bones, and cages of arbitrary topology. Our weights, called bounded biharmonic weights, minimize the Laplacian energy subject to bound constraints. Doing so spreads the influences of the handles in a shape-aware and localized manner, even for objects with complex and concave boundaries. The variational weight optimization also makes it possible to customize the weights so that they preserve the shape of specified essential object features. We demonstrate successful use of our blending weights for real-time deformation of 2D and 3D shapes.