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Tracing Field‐Coherent Quad Layouts
Author(s) -
Pietroni Nico,
Puppo Enrico,
Marcias Giorgio,
Scopigno Roberto,
Cigi Paolo
Publication year - 2016
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/cgf.13045
Subject(s) - geodesic , parametrization (atmospheric modeling) , surface (topology) , computer science , tracing , field (mathematics) , algorithm , polygon mesh , gravitational singularity , binary number , computer graphics (images) , computational science , topology (electrical circuits) , geometry , mathematics , mathematical analysis , physics , combinatorics , pure mathematics , optics , arithmetic , radiative transfer , operating system
Given a cross field over a triangulated surface we present a practical and robust method to compute a field aligned coarse quad layout over the surface. The method works directly on a triangle mesh without requiring any parametrization and it is based on a new technique for tracing field‐coherent geodesic paths directly on a triangle mesh, and on a new relaxed formulation of a binary LP problem, which allows us to extract both conforming quad layouts and coarser layouts containing t‐junctions. Our method is easy to implement, very robust, and, being directly based on the input cross field, it is able to generate better aligned layouts, even with complicated fields containing many singularities. We show results on a number of datasets and comparisons with state‐of‐the‐art methods.