Matrix animation and polar decomposition
Proceedings of the conference on Graphics interface '92
As-rigid-as-possible shape interpolation
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Linear combination of transformations
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Similarity and Affine Invariant Distances Between 2D Point Sets
IEEE Transactions on Pattern Analysis and Machine Intelligence
Proceedings of the 2005 ACM symposium on Solid and physical modeling
ACM SIGGRAPH 2005 Papers
As-rigid-as-possible shape manipulation
ACM SIGGRAPH 2005 Papers
On Linear Variational Surface Deformation Methods
IEEE Transactions on Visualization and Computer Graphics
Rigid shape interpolation using normal equations
NPAR '08 Proceedings of the 6th international symposium on Non-photorealistic animation and rendering
Compatible Embedding for 2D Shape Animation
IEEE Transactions on Visualization and Computer Graphics
Bounded biharmonic weights for real-time deformation
ACM SIGGRAPH 2011 papers
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This paper gives a simple mathematical framework for 2D shape interpolation methods that preserve rigidity. An interpolation technique in this framework works for given the source and target 2D shapes, which are compatibly triangulated. Focusing on the local affine maps between the corresponding triangles, we describe a global transformation as a piecewise affine map. Several existing rigid shape interpolation techniques are discussed and mathematically analyzed through this framework. This gives us not only a useful comprehensive understanding of existing approaches, but also new algorithms and a few improvements of previous approaches.