Mapping Surfaces with Earcut

by   Marco Livesu, et al.

Mapping a shape to some parametric domain is a fundamental tool in graphics and scientific computing. In practice, a map between two shapes is commonly represented by two meshes with same connectivity and different embedding. The standard approach is to input a meshing of one of the two domains plus a function that projects its boundary to the other domain, and then solve for the position of the interior vertices. Inspired by basic principles in mesh generation, in this paper we present the reader a novel point of view on mesh parameterization: we consider connectivity as an additional unknown, and assume that our inputs are just two boundaries that enclose the domains we want to connect. We compute the map by simultaneously growing the same mesh inside both shapes.This change in perspective allows us to recast the parameterization problem as a mesh generation problem, granting access to a wide set of mature tools that are typically not used in this setting. Our practical outcome is a provably robust yet trivial to implement algorithm that maps any planar shape with simple topology to a homotopic domain that is weakly visible from an inner convex kernel. Furthermore, we speculate on a possible extension of the proposed ideas to volumetric maps, listing the major challenges that arise. Differently from prior methods, for which we show that a volumetric extension is not possible, our analysis leaves us reasoneable hopes that the robust generation of volumetric maps via compatible mesh generation could be obtained in the future.


page 1

page 2

page 3

page 4

page 5

page 6

page 7

page 8


Volumetric Parameterization of the Placenta to a Flattened Template

We present a volumetric mesh-based algorithm for parameterizing the plac...

Advancing Front Mapping

We present Advancing Front Mapping (AFM), a provably robust algorithm fo...

Foldover-free maps in 50 lines of code

Mapping a triangulated surface to 2D space (or a tetrahedral mesh to 3D ...

A Dataset and Benchmark for Mesh Parameterization

UV parameterization is a core task in computer graphics, with applicatio...

Placental Flattening via Volumetric Parameterization

We present a volumetric mesh-based algorithm for flattening the placenta...

Volumetric Spline Parameterization for Isogeometric Analysis

Given the spline representation of the boundary of a three dimensional d...

The 3D Motorcycle Complex for Structured Volume Decomposition

The so-called motorcycle graph has been employed in recent years for var...

Please sign up or login with your details

Forgot password? Click here to reset