TY - JOUR
T1 - Consistent functional cross field design for mesh quadrangulation
AU - Azencot, Omri
AU - Corman, Etienne
AU - Ben-Chen, Mirela
AU - Ovsjanikov, Maks
N1 - Funding Information:
This work was supported in part by the Marie-Curie CIG-334283, a CNRS chaire d’excellence, chaire Jean Marjoulet from Ecole Polytechnique, FUI project TANDEM 2, a grant from the Direction Générale de l’Armement (DGA) and a Google Focused Research Award, European Research Council (ERC starting grant No. 714776 “OPREP”), the Israel Science Foundation (grant No. 699/12), and an Adams Fellowship. We thank Daniele Panozzo and Matthias Vestner for supplying the code for their methods. In addition, we thank Keenan Crane, AIM@Shape, SCAPE, and TOSCA for the models. Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from permissions@acm.org. © 2017 ACM. 0730-0301/2017/7-ART92 $15.00 DOI: http://dx.doi.org/10.1145/3072959.3073696
Publisher Copyright:
© 2017 ACM.
PY - 2017/1/1
Y1 - 2017/1/1
N2 - We propose a novel technique for computing consistent cross fields on a pair of triangle meshes given an input correspondence, which we use as guiding fields for approximately consistent quadrangulations. Unlike the majority of existing methods our approach does not assume that the meshes share the same connectivity or even have the same number of vertices, and furthermore does not place any restrictions on the topology (genus) of the shapes. Importantly, our method is robust with respect to small perturbations of the given correspondence, as it only relies on the transportation of real-valued functions and thus avoids the costly and error-prone estimation of the map differential. Key to this robustness is a novel formulation, which relies on the previously-proposed notion of power vectors, and we show how consistency can be enforced without pre-alignment of local basis frames, in which these power vectors are computed. We demonstrate that using the same formulation we can both compute a quadrangulation that would respect a given symmetry on the same shape or a map across a pair of shapes. We provide quantitative and qualitative comparison of our method with several baselines and show that it both provides more accurate results and allows to handle more general cases than existing techniques.
AB - We propose a novel technique for computing consistent cross fields on a pair of triangle meshes given an input correspondence, which we use as guiding fields for approximately consistent quadrangulations. Unlike the majority of existing methods our approach does not assume that the meshes share the same connectivity or even have the same number of vertices, and furthermore does not place any restrictions on the topology (genus) of the shapes. Importantly, our method is robust with respect to small perturbations of the given correspondence, as it only relies on the transportation of real-valued functions and thus avoids the costly and error-prone estimation of the map differential. Key to this robustness is a novel formulation, which relies on the previously-proposed notion of power vectors, and we show how consistency can be enforced without pre-alignment of local basis frames, in which these power vectors are computed. We demonstrate that using the same formulation we can both compute a quadrangulation that would respect a given symmetry on the same shape or a map across a pair of shapes. We provide quantitative and qualitative comparison of our method with several baselines and show that it both provides more accurate results and allows to handle more general cases than existing techniques.
KW - Consistent remeshing
KW - Correspondence
KW - Cross field design
KW - Quad remeshing
UR - http://www.scopus.com/inward/record.url?scp=85030761612&partnerID=8YFLogxK
U2 - 10.1145/3072959.3073696
DO - 10.1145/3072959.3073696
M3 - Conference article
AN - SCOPUS:85030761612
SN - 0730-0301
VL - 36
JO - ACM Transactions on Graphics
JF - ACM Transactions on Graphics
IS - 4
M1 - 92
T2 - ACM SIGGRAPH 2017
Y2 - 30 July 2017 through 3 August 2017
ER -