An Adaptive Multi‐Grid Solver for Applications in Computer Graphics

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.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.