Local Surface Parameterizations via Smoothed Geodesic Splines

TL;DR

This paper introduces a versatile method for local surface parameterizations using smoothed geodesic splines, applicable to various surface representations, enabling high-quality local texturing and curve drawing.

Contribution

It presents a novel two-stage spline-based approach for local surface parameterizations that works with multiple surface representations, including implicit functions and point clouds.

Findings

Supports diverse surface types such as signed distance functions and neural implicits.

Produces high-quality local parameterizations demonstrated on various examples.

Enables applications in local texturing and surface curve drawing.

Abstract

We present a general method for computing local parameterizations rooted at a point on a surface, where the surface is described only through a signed implicit function and a corresponding projection function. Using a two-stage process, we compute several points radially emanating from the map origin, and interpolate between them with a spline surface. The narrow interface of our method allows it to support several kinds of geometry such as signed distance functions, general analytic implicit functions, triangle meshes, neural implicits, and point clouds. We demonstrate the high quality of our generated parameterizations on a variety of examples, and show applications in local texturing and surface curve drawing.