Tracing Field-Coherent Quad Layouts

• Published in: Computer graphics forum Vol. 35; no. 7; pp. 485 - 496
• Main Authors: Pietroni, Nico, Puppo, Enrico, Marcias, Giorgio, Roberto, Roberto, Cignoni, Paolo
• Format: Journal Article
• Language: English
• Published: Oxford Blackwell Publishing Ltd 01.10.2016
• Subjects: Alignment; Analysis; Categories and Subject Descriptors (according to ACM CCS); Formulations; Geodesy; I.3.3 [Computer Graphics]: Picture/Image Generation-Line and curve generation; Image processing systems; Layouts; Parametrization; Singularities; State of the art; Studies; Topological manifolds; Triangles
• ISSN: 0167-7055; 1467-8659
• DOI: 10.1111/cgf.13045

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.