TryUMph: Geometries and Meshes

This dataset accompanies the TryUMph algorithm of Rangarajan and Lew for constructing planar meshes that conform to curved geometries with universal meshes. The dataset provides the geometry test database used in testing the algorithm, computed meshes, and performance metrics. Contents Geometry database — 578 planar geometries bounded by spline curves (line segments and quadratic/cubic Bézier curves), spanning 20,963 curves and 62,236 control points. The set is topologically diverse: about three-quarters are multiply connected (holes and/or disjoint components), corner sharpness ranges from nearly smooth down to roughly 1°, and the number of curves per geometry ranges from 2 to 317 (median 30). Each geometry is a plain-text .fset file; the format is documented in the accompanying README. Static meshing — single-frame meshing of every geometry under two quadtree-sizing criteria (per-feature "local" medial sizing and global "nonlocal" medial sizing). For each geometry and each criterion, the deposit includes per-geometry statistics (trys, timing, element quality, boundary conformity) and the computed meshes (background, quadtree, and conforming working meshes) in legacy VTK format, plus corpus-wide summary tables. Moving meshing — meshing under prescribed motion: a rigid-rotation sweep (0°–360°) of every geometry with per-frame statistics, and a non-rigid, time-varying affine deformation of a representative geometry, meshed both incrementally (reusing the previous frame) and from scratch, with full per-frame meshes. See the top-level README for structure, file formats, and reproduction details. The geometries are a curated subset derived from the image-based geometry collection distributed with the TriWild project (Hu et al., TriWild: Robust Triangulation with Curve Constraints, ACM Transactions on Graphics / SIGGRAPH, 2019). Please cite that work in addition to this dataset.