Spherical Bézier curve based on corner cutting

The classical de Casteljau algorithm for constructing Bézier curves can be generalized to sphere of arbitrary dimension by replacing line segments with shortest great circle arcs. The resulting spherical Bézier curve is C ∞ and interpolates the endpoints of its control polygons. In this paper, a n...

Full description

Saved in:
Bibliographic Details
Main Authors: Yunping Li, Yuehong Tang, Laishui Zhou
Format: Conference Proceeding
Language:English
Subjects:
Bézier curve
CAD/CAM
Computers
corner cutting
de Casteljau method
geodesics
IP networks
sphere
Online Access:Request full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The classical de Casteljau algorithm for constructing Bézier curves can be generalized to sphere of arbitrary dimension by replacing line segments with shortest great circle arcs. The resulting spherical Bézier curve is C ∞ and interpolates the endpoints of its control polygons. In this paper, a new method is proposed to construct spherical Bézier curves, which extends corner cutting method, introduced by Lane-Riesenfeld to sphere. The final curve created by this method converges to spherical Bézier curves named corner cutting spherical Bézier curves. The necessary and sufficient condition of G1 continuity for two spherical Bézier curves is presented. Finally, as a by-product geodesic can be created on free-form surfaces with presented approach.
DOI:10.1109/CAIDCD.2010.5681925