Relation among C-curve characterization diagrams

As three control points are fixed and the fourth control point varies, the planar cubic C-curve may take on a loop, a cusp, or zero to two inflection points, depending on the position of the moving point. The plane can, therefore, be partitioned into regions labelled according to the characterizatio...

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Bibliographic Details
Published in:Journal of Zhejiang University. A. Science 2007-10, Vol.8 (10), p.1663-1670
Main Authors: Cao, Juan, Wang, Guo-zhao
Format: Article
Language:English
Subjects:
C曲线
特征图表
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Summary:As three control points are fixed and the fourth control point varies, the planar cubic C-curve may take on a loop, a cusp, or zero to two inflection points, depending on the position of the moving point. The plane can, therefore, be partitioned into regions labelled according to the characterization of the curve when the fourth point is in each region. This partitioned plane is called a ＂characterization diagram＂. By moving one of the control points but fixing the rest, one can induce different characterization diagrams. In this paper, we investigate the relation among all different characterization diagrams of cubic C-curves based on the singularity conditions proposed by Yang and Wang （2004）. We conclude that, no matter what the C-curve type is or which control point varies, the characterization diagrams can be obtained by cutting a common 3D characterization space with a corresponding plane.
ISSN:1673-565X
1862-1775
DOI:10.1631/jzus.2007.A1663