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Shape Space Exploration of . . .
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@MISC{Yang_shapespace,
author = {Yong-liang Yang and Yi-jun Yang and Helmut Pottmann and Niloy J. Mitra},
title = {Shape Space Exploration of . . .},
year = {}
}
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Abstract
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.
Keyphrases
shape space shape space exploration osculant surface parameter space circular mesh second order approximants general computational framework mesh face tangent space desirable subspace planar quad access manifold high dimension reference surface context specific property design exploration application specific quality measure non-linear constraint
