Almost isometric mesh parameterization through abstract domains

In this paper we propose a robust, automatic technique to build a global hi-quality parameterization of a two-manifold triangular mesh. An adaptively chosen 2D domain of the parameterization is built as par t of the process. The produced parameterization exhibits very low isometric distor tion, because it is globally optimized to preser ve both areas and angles. The domain is a collection of equilateral triangular 2D regions enriched with explicit adjacency relationships (it is abstract in the sense that no 3D embedding is necessary). It is tailored to minimize isometric distor tion, resulting in excellent parameterization qualities, even when meshes with complex shape and topology are mapped into domains composed of a small number of large continuous regions. Moreover, this domain is in turn remapped into a collection of 2D square regions, unlocking many advantages found in quad-based domains (e.g. ease of packing). The technique is tested on a variety of cases, including challenging ones, and compares ver y favorably with known approaches.