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This paper describes a method for fast simplification of surface meshes.Whereas past methods focus on visual appearance, our goal is to solve equationson the surface. Hence, rather than approximate the extrinsic geometry, weconstruct a coarse intrinsic triangulation of the input domain. In the spiritof the quadric error metric (QEM), we perform greedy decimation whileagglomerating global information about approximation error. In lieu ofextrinsic quadrics, however, we store intrinsic tangent vectors that track howfar curvature "drifts" during simplification. This process also yields abijective map between the fine and coarse mesh, and prolongation operators forboth scalar- and vector-valued data. Moreover, we obtain hard guarantees onelement quality via intrinsic retriangulation - a feature unique to theintrinsic setting. The overall payoff is a "black box" approach to geometryprocessing, which decouples mesh resolution from the size of matrices used tosolve equations. We show how our method benefits several fundamental tasks,including geometric multigrid, all-pairs geodesic distance, mean curvatureflow, geodesic Voronoi diagrams, and the discrete exponential map.

Surface Simplification using Intrinsic Error Metrics