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Title: Which cross fields can be quadrangulated?: global parameterization from prescribed holonomy signatures
We describe a method for the generation of seamless surface parametrizations with guaranteed local injectivity and full control over holonomy. Previous methods guarantee only one of the two. Local injectivity is required to enable these parametrizations' use in applications such as surface quadrangulation and spline construction. Holonomy control is crucial to enable guidance or prescription of the parametrization's isocurves based on directional information, in particular from cross-fields or feature curves, and more generally to constrain the parametrization topologically. To this end we investigate the relation between cross-field topology and seamless parametrization topology. Leveraging previous results on locally injective parametrization and combining them with insights on this relation in terms of holonomy, we propose an algorithm that meets these requirements. A key component relies on the insight that arbitrary surface cut graphs, as required for global parametrization, can be homeomorphically modified to assume almost any set of turning numbers with respect to a given target cross-field.  more » « less
Award ID(s):
1835712 1652515 1901091
NSF-PAR ID:
10357186
Author(s) / Creator(s):
; ; ; ; ;
Date Published:
Journal Name:
ACM Transactions on Graphics
Volume:
41
Issue:
4
ISSN:
0730-0301
Page Range / eLocation ID:
1 to 12
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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