Shape Space Exploration of Constrained Meshes

Yong-Liang Yang KAUST Yi-Jun Yang KAUST Helmut Pottmann KAUST/TU Vienna Niloy Mitra KAUST/TU Vienna

Geometric Modeling and Processing mathscidoc:1608.16072

ACM Transactions on Graphics, 30, (6), 124:1--124:12, 2011.12
We present a general computational framework to locally characterize any shape space of meshes implicitly prescribed by a collection of non-linear constraints. We computationally access such manifolds, typically of high dimension and co-dimension, through first and second order approximants, namely tangent spaces and quadratically parameterized osculant surfaces. Exploration and navigation of desirable subspaces of the shape space with regard to application specific quality measures are enabled using approximants that are intrinsic to the underlying manifold and directly computable in the parameter space of the osculant surface. We demonstrate our framework on shape spaces of planar quad (PQ) meshes, where each mesh face is constrained to be (nearly) planar, and circular meshes, where each face has a circumcircle. We evaluate our framework for navigation and design exploration on a variety of inputs, while keeping context specific properties such as fairness, proximity to a reference surface, etc.
shape space, manifold navigation, design exploration, computational differential geometry, constrained mesh
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  title={Shape Space Exploration of Constrained Meshes},
  author={Yong-Liang Yang, Yi-Jun Yang, Helmut Pottmann, and Niloy Mitra},
  booktitle={ACM Transactions on Graphics},
Yong-Liang Yang, Yi-Jun Yang, Helmut Pottmann, and Niloy Mitra. Shape Space Exploration of Constrained Meshes. 2011. Vol. 30. In ACM Transactions on Graphics. pp.124:1--124:12.
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