Shape space exploration of constrained meshes

Handle URI:
http://hdl.handle.net/10754/575912
Title:
Shape space exploration of constrained meshes
Authors:
Yang, Yongliang; Yang, Yijun; Pottmann, Helmut ( 0000-0002-3195-9316 ) ; Mitra, Niloy J. ( 0000-0002-2597-0914 )
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. © 2011 ACM.
KAUST Department:
Visual Computing Center (VCC); Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Applied Mathematics and Computational Science Program
Publisher:
Association for Computing Machinery (ACM)
Journal:
Proceedings of the 2011 SIGGRAPH Asia Conference on - SA '11
Issue Date:
12-Dec-2011
DOI:
10.1145/2024156.2024158; 10.1145/2070752.2024158; 10.1145/2070781.2024158
Type:
Article
ISSN:
07300301
Sponsors:
We thank Daniel Piker for providing the starting "rheotomic" mesh used as the input mesh in Figure 1 and for the starting flat meshes in the upper two rows of Figure 18. We thank Johannes Wallner for his many useful comments and suggestions, Alexander Schiftner, Mathias Hobinger and Michael Eigensatz for their help and valuable comments, and the anonymous reviewers for their feedback. We are grateful to Heinz Schmiedhofer for the final renderings. The work has been partially supported by Austrian Science Fund (FWF) grant P23735-N13 and Austrian Science Promotion Agency (FFG) grant 813391.
Appears in Collections:
Articles; Applied Mathematics and Computational Science Program; Applied Mathematics and Computational Science Program; Visual Computing Center (VCC); Visual Computing Center (VCC); Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorYang, Yongliangen
dc.contributor.authorYang, Yijunen
dc.contributor.authorPottmann, Helmuten
dc.contributor.authorMitra, Niloy J.en
dc.date.accessioned2015-08-25T06:19:16Zen
dc.date.available2015-08-25T06:19:16Zen
dc.date.issued2011-12-12en
dc.identifier.issn07300301en
dc.identifier.doi10.1145/2024156.2024158en
dc.identifier.doi10.1145/2070752.2024158en
dc.identifier.doi10.1145/2070781.2024158en
dc.identifier.urihttp://hdl.handle.net/10754/575912en
dc.description.abstractWe 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.en
dc.description.sponsorshipWe thank Daniel Piker for providing the starting "rheotomic" mesh used as the input mesh in Figure 1 and for the starting flat meshes in the upper two rows of Figure 18. We thank Johannes Wallner for his many useful comments and suggestions, Alexander Schiftner, Mathias Hobinger and Michael Eigensatz for their help and valuable comments, and the anonymous reviewers for their feedback. We are grateful to Heinz Schmiedhofer for the final renderings. The work has been partially supported by Austrian Science Fund (FWF) grant P23735-N13 and Austrian Science Promotion Agency (FFG) grant 813391.en
dc.publisherAssociation for Computing Machinery (ACM)en
dc.subjectConstrained meshen
dc.subjectDesign explorationen
dc.subjectManifold navigationen
dc.subjectShape spaceen
dc.titleShape space exploration of constrained meshesen
dc.typeArticleen
dc.contributor.departmentVisual Computing Center (VCC)en
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.identifier.journalProceedings of the 2011 SIGGRAPH Asia Conference on - SA '11en
kaust.authorYang, Yongliangen
kaust.authorYang, Yijunen
kaust.authorPottmann, Helmuten
kaust.authorMitra, Niloy J.en
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