Periodic global parameterization
- 1 October 2006
- journal article
- Published by Association for Computing Machinery (ACM) in ACM Transactions on Graphics
- Vol. 25 (4), 1460-1485
- https://doi.org/10.1145/1183287.1183297
Abstract
We present a new globally smooth parameterization method for the triangulated surfaces of arbitrary topology. Given two orthogonal piecewise linear vector fields defined over the input mesh (typically the estimated principal curvature directions), our method computes two piecewise linear periodic functions, aligned with the input vector fields, by minimizing an objective function. The bivariate function they define is a smooth parameterization almost everywhere on the surface, except in the vicinity of singular vertices, edges, and triangles, where the derivatives of the parameterization vanish. We extract a quadrilateral chart layout from the parameterization function and propose an automatic procedure to detect the singularities, and fix them by splitting and reparameterizing the containing charts. Our method can construct both quasiconformal (angle preserving) and quasi-isometric (angle and area preserving) parameterizations. The more restrictive class of quasi-isometric parameterizations is constructed at the expense of introducing more singularities. The constructed parameterizations can be used for a variety of geometry processing applications. Since we can align the parameterization with the principal curvature directions, our result is particularly suitable for surface fitting and remeshing.Keywords
This publication has 13 references indexed in Scilit:
- Multilevel Solvers for Unstructured Surface MeshesSIAM Journal on Scientific Computing, 2005
- A simple manifold-based construction of surfaces of arbitrary smoothnessPublished by Association for Computing Machinery (ACM) ,2004
- Anisotropic polygonal remeshingPublished by Association for Computing Machinery (ACM) ,2003
- Discrete multiscale vector field decompositionPublished by Association for Computing Machinery (ACM) ,2003
- Globally smooth parameterizations with low distortionPublished by Association for Computing Machinery (ACM) ,2003
- Fundamentals of spherical parameterization for 3D meshesACM Transactions on Graphics, 2003
- Least squares conformal maps for automatic texture atlas generationACM Transactions on Graphics, 2002
- Parameterization of Faceted Surfaces for Meshing using Angle-Based FlatteningEngineering with Computers, 2001
- Are Bilinear Quadrilaterals Better Than Linear Triangles?SIAM Journal on Scientific Computing, 2000
- Parametrization and smooth approximation of surface triangulationsComputer Aided Geometric Design, 1997