Efficient computation of constrained parameterizations on parallel platforms

• Published in: Computers & graphics Vol. 37; no. 6; pp. 596 - 607
• Main Authors: Athanasiadis, Theodoros, Zioupos, Georgios, Fudos, Ioannis
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Oxford Elsevier Ltd 01.10.2013; Elsevier
• Subjects: Applied sciences; Artificial intelligence; Computational efficiency; Computer science; control theory; systems; Computer systems and distributed systems. User interface; Constrained parameterization; Constraints; Exact sciences and technology; GPU; Interactive; Massively parallel platforms; Mesh parameterization; Non linear solver; Parametrization; Pattern recognition. Digital image processing. Computational geometry; Platforms; Real time; Smoothing; Software; Solvers; Tesselation; Non linear solver; Tesselation; Massively parallel platforms; Constrained parameterization; GPU; Mesh parameterization; High performance; Isometry; Constraint; Parameterization; Real time; Distributed computing; Spectrum; Parallel system; Graphic processing unit; Massive parallelism; Non linear effect; Parallelization; Mesh generation; Mechanical deformation
• ISSN: 0097-8493; 1873-7684
• DOI: 10.1016/j.cag.2013.05.023

Constrained isometric planar parameterizations are central to a broad spectrum of applications. In this work, we present a non linear solver developed on OpenCL that is efficiently parallelizable on modern massively parallel architectures. We establish how parameterization relates to mesh smoothing and show how to efficiently and robustly solve the planar mesh parameterization problem with constraints. Furthermore, we demonstrate the applicability of our approach to real-time cut-and-paste editing and interactive mesh deformation. [Display omitted] •Establishes the relation between mesh smoothing and parameterization techniques.•Derives a simplified formulation for the isometric parameterization problem.•Presents an efficient parallel implementation of a non-linear solver.•Presents an iterative topological untangling process for constrained parameterization.•Demonstrates the applicability of our approach on feature cut-and-paste design.