Local Geodesic Parametrization: An Ant's Perspective

Two dimensional parameterizations of meshes is a dynamic field of

research. Most works focus on parameterizing complete surfaces,

attempting to satisfy various constraints on distances and angles and

produce a 2D map with minimal errors. Except for developable surfaces

no single map can be devoid of errors, and a parametrization

produced for one purpose usually doesn't suit others.

This work presents a different viewpoint. We try and acquire

the perspective of an ant living on the surface. The point on which

it stands is the center of its world, and importance diminishes from

there onward. Distances and angles measured relative to its position

have higher importance than those measured elsewhere. Hence, the

local parametrization of the geodesic neighborhood should convey

this perspective by mostly preserving geodesic distances from the

center. We present a method for producing such overlapping localparametrization

for each vertex on the mesh. Our method provides

an accurate rendition of the local area of each vertex and can be

used for several purposes, including clustering algorithms which

focus on local areas of the surface within a certain window such as

Mean Shift.

In  Mathematical Foundations of Scientific Visualization, Computer Graphics, and Massive Data Exploration, (Series: Mathematics and Visualization)

Publisher  Springer

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