An algorithm to improve parameterizations of rational Bézier surfaces using rational bilinear reparameterization

Authors:
Yi-Jun Yang;Wei Zeng;Cheng-Lei Yang;Bailin Deng;Xiang-Xu Meng;S. Sitharama Iyengar
Affiliations:
School of Computer Science & Technology, Shandong University, Jinan, China;School of Computing & Information Sciences, Florida International University, USA;School of Computer Science & Technology, Shandong University, Jinan, China;Computer Graphics and Geometry Laboratory, EPFL, Switzerland;School of Computer Science & Technology, Shandong University, Jinan, China;School of Computing & Information Sciences, Florida International University, USA
Venue:
Computer-Aided Design
Year:
2013

Citing 14
Cited 1

Real rational curves are not “unit speed”

Computer Aided Geometric Design
The NURBS book

The NURBS book
Tessellation of trimmed NURB surfaces

Computer Aided Geometric Design
A vegetarian approach to optimal parameterizations

Computer Aided Geometric Design
NURBS: From Projective Geometry to Practical Use

NURBS: From Projective Geometry to Practical Use
Incremental rendering of deformable trimmed NURBS surfaces

Proceedings of the ACM symposium on Virtual reality software and technology
Levenberg-Marquardt methods with strong local convergence properties for solving nonlinear equations with convex constraints

Journal of Computational and Applied Mathematics
Geometric modeling with conical meshes and developable surfaces

ACM SIGGRAPH 2006 Papers
Introduction to Global Optimization (Nonconvex Optimization and Its Applications)

Introduction to Global Optimization (Nonconvex Optimization and Its Applications)
A rational extension of Piegl's method for filling n-sided holes

Computer-Aided Design
Projection of curves on B-spline surfaces using quadratic reparameterization

Graphical Models
Optimal parameterizations of bézier surfaces

ISVC'06 Proceedings of the Second international conference on Advances in Visual Computing - Volume Part I
G1 continuous approximate curves on NURBS surfaces

Computer-Aided Design
Computation of optimal composite re-parameterizations

Computer Aided Geometric Design

Weak visibility polygons of NURBS curves inside simple polygons

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	0.00

Visualization

Abstract

The parameterization of rational Bezier surfaces greatly affects rendering and tessellation results. The uniformity and orthogonality of iso-parametric curves are two key properties of the optimal parameterization. The only rational Bezier surfaces with uniform iso-parametric curves are bilinear surfaces, and the only rational Bezier surfaces with uniform and orthogonal iso-parametric curves are rectangles. To improve the uniformity and orthogonality of iso-parametric curves for general rational Bezier surfaces, an optimization algorithm using the rational bilinear reparameterizations is presented, which can produce a better parameterization with the cost of degree elevation. Examples are given to show the performance of our algorithm for rendering and tessellation applications.