Axioms and variational problems in surface parameterization
For a surface patch on a smooth, two-dimensional surface in R^3, low-distortion parameterizations are described in terms of minimizers of suitable energy functionals. Appropriate distortion measures are derived from principles of rational mechanics, ...
Developable surface fitting to point clouds
Given a set of data points as measurements from a developable surface, the present paper investigates the recognition and reconstruction of these objects. We investigate the set of estimated tangent planes of the data points and show that classical ...
Rational quadratic approximation to real algebraic curves
An algorithm is proposed to give a global approximation of an implicit real plane algebraic curve with rational quadratic B-spline curves. The algorithm consists of four steps: topology determination, curve segmentation, segment approximation and curve ...
Lifting curve parameterization methods to isosurfaces
We describe a new technique for the parameterization of surfaces which applies to the isosurfaces produced by the marching cubes algorithm. The technique is motivated by methods of parameterization for curves including the centripetal and chord length ...
Discrete Laplace--Beltrami operators and their convergence
The convergence property of the discrete Laplace-Beltrami operators is the foundation of convergence analysis of the numerical simulation process of some geometric partial differential equations which involve the operator. In this paper we propose ...