Conformal Spherical Parametrization for High Genus Surfaces
نویسندگان
چکیده
Surface parameterization establishes bijective maps from a surface onto a topologically equivalent standard domain. It is well known that the spherical parameterization is limited to genus-zero surfaces. In this work, we design a new parameter domain, two-layered sphere, and present a framework for mapping high genus surfaces onto sphere. This setup allows us to transfer the existing applications based on general spherical parameterization to the field of high genus surfaces, such as remeshing, consistent parameterization, shape analysis, and so on. Our method is based on Riemann surface theory. We construct meromorphic functions on surfaces: for genus one surfaces, we apply Weierstrass P-functions; for high genus surfaces, we compute the quotient between two holomorphic one-forms. Our method of spherical parameterization is theoretically sound and practically efficient. It makes the subsequent applications on high genus surfaces very promising.
منابع مشابه
Spherical Parametrization of Genus-Zero Meshes using the Lagrange-Newton Method
This paper addresses the problem of spherical parametrization, i.e., mapping a given polygonal surface of genus-zero onto a unit sphere. We construct an improved algorithm for parametrization of genus-zero meshes and aim to obtain high-quality surfaces fitting with PHT-splines. This parametrization consists of minimizing discrete harmonic energy subject to spherical constraints and solving the ...
متن کاملA Landmark-Based Brain Conformal Parametrization with Automatic Landmark Tracking Technique
In this paper, we present algorithms to automatically detect and match landmark curves on cortical surfaces to get an optimized brain conformal parametrization. First, we propose an automatic landmark curve tracing method based on the principal directions of the local Weingarten matrix. Our algorithm obtains a hypothesized landmark curves using the Chan-Vese segmentation method, which solves a ...
متن کاملParametrization for Surfaces with Arbitrary Topologies
Surface parametrization is a fundamental problem in computer graphics. It is essential for operations such as texture mapping, texture synthesis, interactive 3D painting, remeshing, multi-resolution analysis and mesh compression. Conformal parameterization, which preserves angles, has many nice properties such as having no local distortion on textures, and being independent of triangulation or ...
متن کاملExplicit Parametrization of Delaunay Surfaces in Space Forms via Loop Group Methods
We compute explicit conformal parametrizations of Delaunay surfaces in each of the three space forms Euclidean 3-space , spherical 3-space 3 and hyperbolic 3-space 3 by using the generalized Weierstrass type representation for constant mean curvature (CMC) surfaces established by J. Dorfmeister, F. Pedit and H. Wu.
متن کاملSpherical Conformal Parameterization of Genus-0 Point Clouds for Meshing
Point cloud is the most fundamental representation of 3D geometric objects. Analyzing and processing point cloud surfaces is important in computer graphics and computer vision. However, most of the existing algorithms for surface analysis require connectivity information. Therefore, it is desirable to develop a mesh structure on point clouds. This task can be simplified with the aid of a parame...
متن کامل