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The stretch energy is an energy functional particularly defined for the measurement of the area distortion for simplicial mapping, which has been applied to efficiently compute area-preserving parameterizations of simplicial surfaces. The stretch energy has a nice geometric interpretation that is helpful for the generalization of the functional to higher dimensional manifold mappings. On the application aspect, parameterizations of simplicial surfaces have been widely applied in computer graphics that aim to efficiently compute a diffeomorphism between a simplicial surface and a canonical domain. This provides the surface with a unified coordinate system that simplifies various image and geometry processing tasks such as alignment and blending of images and surfaces. In this talk, I will introduce the theoretical foundation of stretch energy minimization for the computation of area-preserving parameterizations of simplicial surfaces. Applications in image and surface blending and area-preserving deformations will be demonstrated to highlight the practical utility of the parameterizations.

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