Direction monotonicity for a rational Bézier curve

The monotonicity of a rational Bézier curve, usually related to an explicit function, is determined by the used coordinate system. However, the shape of the curve is independent of the coordinate system. To meet the affine invariant property, a kind of generalized monotonicity, called direction mono...

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Bibliographic Details
Published in:Applied Mathematics-A Journal of Chinese Universities 2016-03, Vol.31 (1), p.1-20
Main Authors: Shen, Wan-qiang, Wang, Guo-zhao, Huang, Fang
Format: Article
Language:English
Subjects:
Applications of Mathematics
Mathematics
Mathematics and Statistics
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Summary:The monotonicity of a rational Bézier curve, usually related to an explicit function, is determined by the used coordinate system. However, the shape of the curve is independent of the coordinate system. To meet the affine invariant property, a kind of generalized monotonicity, called direction monotonicity, is introduced for rational Bézier curves. The direction monotonicity is applied to both planar and space curves and to both Cartesian and affine coordinate systems, and it includes the traditional monotonicity as a subcase. By means of it, proper affine coordinate systems may be chosen to make some rational Bézier curves monotonic. Direction monotonic interpolation may be realized for some of the traditionally nonmonotonic data as well.
ISSN:1005-1031
1993-0445
DOI:10.1007/s11766-016-3399-7