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An Adaptive Multi‐Grid Solver for Applications in Computer Graphics
Author(s) -
Kazhdan Misha,
Hoppe Hugues
Publication year - 2019
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.13449
Subject(s) - solver , computer science , computer graphics , image stitching , grid , pointwise , domain (mathematical analysis) , computational science , discretization , regular grid , computer graphics (images) , mesh generation , algorithm , theoretical computer science , finite element method , computer vision , mathematics , geometry , programming language , mathematical analysis , physics , thermodynamics
Abstract A key processing step in numerous computer graphics applications is the solution of a linear system discretized over a spatial domain. Often, the linear system can be represented using an adaptive domain tessellation, either because the solution will only be sampled sparsely, or because the solution is known to be ‘interesting’ (e.g. high frequency) only in localized regions. In this work, we propose an adaptive, finite elements, multi‐grid solver capable of efficiently solving such linear systems. Our solver is designed to be general‐purpose, supporting finite elements of different degrees, across different dimensions and supporting both integrated and pointwise constraints. We demonstrate the efficacy of our solver in applications including surface reconstruction, image stitching and Euclidean Distance Transform calculation.