Stripe Embedding: Efficient Maps with Exact Numeric Computation
DescriptionWe consider the fundamental problem of injectively mapping a surface mesh with disk topology onto a boundary constrained convex domain. We start from the basic observation that mapping a strip of triangles onto a rectangular shape always yields a valid embedding if the vertices that bound the strip are sorted coherently along the sides of the rectangle. Based on this intuition we propose a straightforward algorithm, called Stripe Embedding, that operates by decomposing the input mesh into a set of triangle strips and then embeds each strip into the target domain by means of linear interpolation between two previously embedded vertices. Thanks to its simplicity, Stripe Embedding is extremely efficient and permits to switch to an exact implementation without almost increasing its running times. Stripe Embedding is up to three orders of magnitude faster than the Tutte embedding for same numerical model and, even when implemented with costly rational numbers, it is faster than any floating point implementation of prior methods at any scale.
Author
Event Type
Technical Papers
TimeTuesday, 3 December 20241:23pm - 1:34pm JST
LocationHall B5 (1), B Block, Level 5
