Towards a robust and portable pipeline for quad meshing: Topological initialization of injective integer grid maps

Advancing Front Surface Mapping

“…A successful strategy to further enlarge the family of domains that can be considered is map composition. Methods in this category internally use the Tutte embedding, generating mappings to strictly convex domains that are then combined to obtain more general mappings to manifolds of arbitrary genus [Liv20c, LBG*08, GJGQ05, KS04, SAPH04], grid spaces for quad remeshing [Liv23], and even non‐convex planar polygons that may also partially overlap [WZ14]. Being internally based on Tutte, all these methods inherit the same theoretical guarantees of correctness.…”

“…While mappings of this kind are seldom directly useful for downstream applications due to the high geometric distortion they may contain, methods for the robust solution of this problem are internally used in many higher level pipelines, which employ these constructions to create valid initial maps that are subsequently improved based on the needs of the application at hand. Various representative examples of this strategy can be found in the literature, spanning from the robust computation of correspondences between shapes [KS04, SAPH04, SJZP19], to morphing [PSS01] and the generation of low‐distortion planar maps for uv mapping, remeshing, and other applications [KSG03, LSS*98, SS15, RPPSH17, LYNF18, FW22, Liv23].…”