Metric Reconstruction Driven by Density Functions and its Applications

As an important tool for controlling the local significance of a surface, density functions are widely used in many computer graphics occasions, ranging from sampling to remeshing.However, the weighted geodesic distance induced from an arbitrarily given density function generally doesn't satisfy the triangle inequality, and degenerate cases often occur.This leads to difficulties in solving geometry processing problems.In this paper, we propose a novel technique to transform an arbitrary input density function to a non-degenerate metric by re-configuring the edge lengths of the mesh, which facilitates further geometry processing tasks.In order to demonstrate the usefulness and effectiveness of our algorithm, we construct a new metric from mean curvatures, employ exact geodesic algorithm to compute distances, and finally obtain high-quality adaptive sampling and remeshing results with the help of the new metric.