ScienceDirect - Computer-Aided Design : A practical construction of G1 smooth biquintic B-spline surfaces over arbitrary topology

Computer-Aided Design
Volume 36, Issue 5, April 2004, Pages 413-424

Font Size:

Abstract - selected

E-mail Article

Add to my Quick Links

Bookmark and share in 2collab (opens in new window)

Request permission to reuse this article

Cited By in Scopus (9)

Related Articles in ScienceDirect

G1 continuous conditions of biquartic B-spline surfaces
Journal of Computational and Applied Mathematics

Efficient ray-tracing for free-form reflectors
Optik - International Journal for Light and Electron Op...

Surface construction by fitting unorganized curves
Graphical Models

Reconstruction of convergent G1 smooth B-spline surface...
Computer Aided Geometric Design

Adaptive patch-based mesh fitting for reverse engineeri...
Computer-Aided Design

View More Related Articles

View Record in Scopus

doi:10.1016/S0010-4485(03)00111-8

A practical construction of G¹ smooth biquintic B-spline surfaces over arbitrary topology

Xiquan Shi ^a^,^c, Tianjun Wang ^d^,^,^,^b and Piqiang Yu ^a

^a Department of Mathematics, Dalian University of Technology, Dalian 116024, People's Republic of China ^b Atlantis Components Inc., 270 Third Street, Cambridge, MA 02142, USA ^c Department of Mathematics, Delaware State University, DE 19901, USA ^d Department of Mathematics, Horbin Institute of Technology, Horbin 150001, China

Received 20 November 2002;

Revised 5 May 2003;

accepted 14 May 2003.

Available online 14 June 2003.

References and further reading may be available for this article. To view references and further reading you must purchase this article.

Abstract

The motivation of this paper is to develop a local scheme of constructing G¹ smooth B-spline surfaces with single interior knots over arbitrary topology. In this paper, we obtain the conditions of G¹ continuity between two adjacent biquintic B-spline surfaces with interior single knots. These conditions are directly represented by the relevant control points of the two B-spline surfaces. By utilizing these G¹ conditions, we develop the first local scheme of constructing G¹ smooth biquintic B-spline surfaces with interior single knots for arbitrary topological type. The high complexity of deriving the local G¹ scheme is well overwhelmed. The biquintic is the lowest degree for which there exists a local scheme of constructing G¹ smooth B-spline surfaces with interior single knots over arbitrary topology.