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Quartic C-curves with given tangent polygons. (Chinese. English summary) Zbl 1199.68455

Summary: Quartic C-curves, including quartic C-Bézier curves and quartic C-B spline curves, are yielded by the basis \(\{\sin t,\cos t,t^2,t,1\}\). They have a lot of good properties which Bézier curves and B spline curves also possess. This paper presents an approach of constructing planar piecewise quartic C-Bézier curves and quartic C-B spline curves with all edges tangent to a given control polygon. The C-Bézier curve segments are joined together with \(C^1\) continuity and the quartic C-B spline closed curves and open curves are \(C^3\) continuous. All curves are shape preserving to their tangent polygons. All control points of the curve segments can be calculated simply by the vertices of the given tangent polygon. Finally, some numerical examples illustrate that the method given in this paper is effective.

MSC:

68U05 Computer graphics; computational geometry (digital and algorithmic aspects)
65D18 Numerical aspects of computer graphics, image analysis, and computational geometry
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