DC Field | Value | Language |
dc.contributor.author | Campen, Marcel | |
dc.contributor.author | Shen, Hanxiao | |
dc.contributor.author | Zhou, Jiaran | |
dc.contributor.author | Zorin, Denis | |
dc.date.accessioned | 2021-12-23T16:16:09Z | - |
dc.date.available | 2021-12-23T16:16:09Z | - |
dc.date.issued | 2020 | |
dc.identifier.issn | 07300301 | |
dc.identifier.uri | https://osnascholar.ub.uni-osnabrueck.de/handle/unios/11748 | - |
dc.description.abstract | Seamless global parametrization of surfaces is a key operation in geometry processing, e.g., for high-quality quad mesh generation. A common approach is to prescribe the parametric domain structure, in particular, the locations of parametrization singularities (cones), and solve a non-convex optimization problem minimizing a distortion measure, with local injectivity imposed through either constraints or barrier terms. In both cases, an initial valid parametrization is essential to serve as a feasible starting point for obtaining an optimized solution. While convexified versions of the constraints eliminate this initialization requirement, they narrow the range of solutions, causing some problem instances that actually do have a solution to become infeasible. We demonstrate that for arbitrary given sets of topologically admissible parametric cones with prescribed curvature, a global seamless parametrization always exists (with the exception of one well-known case). Importantly, our proof is constructive and directly leads to a general algorithm for computing such parametrizations. Most distinctively, this algorithm is bootstrapped with a convex optimization problem (solving for a conformal map), in tandem with a simple linear equation system (determining a seamless modification of this map). This initial map can then serve as a valid starting point and be optimized for low distortion using existing injectivity preserving methods. | |
dc.description.sponsorship | [NSF IIS-1320635]; [NSF DMS1436591]; H. Shen and D. Zorin are supported by Awards No. NSF IIS-1320635, No. NSF DMS1436591, and a gift from Adobe. | |
dc.language.iso | en | |
dc.publisher | ASSOC COMPUTING MACHINERY | |
dc.relation.ispartof | ACM TRANSACTIONS ON GRAPHICS | |
dc.subject | Computer Science | |
dc.subject | Computer Science, Software Engineering | |
dc.subject | cone metric | |
dc.subject | Conformal | |
dc.subject | DISCRETE | |
dc.subject | holonomy | |
dc.subject | SURFACES | |
dc.subject | THEOREM | |
dc.title | Seamless Parametrization with Arbitrary Cones for Arbitrary Genus | |
dc.type | journal article | |
dc.identifier.doi | 10.1145/3360511 | |
dc.identifier.isi | ISI:000535714800002 | |
dc.description.volume | 39 | |
dc.description.issue | 1 | |
dc.contributor.orcid | 0000-0003-2340-3462 | |
dc.contributor.orcid | 0000-0002-2943-2806 | |
dc.contributor.researcherid | ABB-8625-2021 | |
dc.identifier.eissn | 15577368 | |
dc.publisher.place | 2 PENN PLAZA, STE 701, NEW YORK, NY 10121-0701 USA | |
dcterms.isPartOf.abbreviation | ACM Trans. Graph. | |
dcterms.oaStatus | Green Submitted, Bronze | |
crisitem.author.dept | FB 06 - Mathematik/Informatik | - |
crisitem.author.deptid | fb06 | - |
crisitem.author.orcid | 0000-0003-2340-3462 | - |
crisitem.author.parentorg | Universität Osnabrück | - |
crisitem.author.netid | CaMa281 | - |