Design and shape adjustment of developable surfaces

This paper presents two direct explicit methods of computer-aided design for developable surfaces. The developable surfaces are designed by using control planes with C-Bézier basis functions. The shape of developable surfaces can be adjusted by using a control parameter. When the parameter takes on...

Full description

Saved in:
Bibliographic Details
Published in:Applied mathematical modelling 2013-03, Vol.37 (6), p.3789-3801
Main Authors: Zhou, Min, Yang, Junqing, Zheng, Hongchan, Song, Weijie
Format: Article
Language:English
Subjects:
Algorithms
Beta
Bezier
C-Bézier basis function
Computer aided design
Construction
Continuity
Control parameter
Control plane
Control surfaces
Developable surface
Duality
Geometric construction algorithm
Mathematical models
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:This paper presents two direct explicit methods of computer-aided design for developable surfaces. The developable surfaces are designed by using control planes with C-Bézier basis functions. The shape of developable surfaces can be adjusted by using a control parameter. When the parameter takes on different values, a family of developable surfaces can be constructed and they keep the characteristics of Bézier surfaces. The thesis also discusses the properties of designed developable surfaces and presents geometric construction algorithms, including the de Casteljau algorithm, the Farin–Boehm construction for G2 continuity, and the G2 Beta restricted condition algorithm. The techniques for the geometric design of developable surfaces in this paper have all the characteristics of existing approaches for curves design, but go beyond the limitations of traditional approaches in designing developable surfaces and resolve problems frequently encountered in engineering by adjusting the position and shape of developable surfaces.
ISSN:0307-904X
DOI:10.1016/j.apm.2012.07.050