Local Surface Parameterizations via Smoothed Geodesic Splines

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.