Shape space exploration of constrained meshes

Citation data:

ACM Transactions on Graphics, ISSN: 0730-0301, Vol: 30, Issue: 6, Page: 1-12

Publication Year:
2011
Usage 13
Abstract Views 12
Link-outs 1
Citations 52
Citation Indexes 52
Repository URL:
http://hdl.handle.net/10754/575752; http://hdl.handle.net/10754/575912
DOI:
10.1145/2024156.2024158; 10.1145/2070781.2024158; 10.1145/2070752.2024158
Author(s):
Yang, Yong-Liang; Yang, Yi-Jun; Pottmann, Helmut; Mitra, Niloy J.
Publisher(s):
Association for Computing Machinery (ACM); Association for Computing Machinery
Tags:
Computer Science; Constrained mesh; Design exploration; Manifold navigation; Shape space
article description
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. © 2011 ACM.