Curvatures of the quadratic rational Bézier curves. (English) Zbl 0932.65015
Summary: We find necessary and sufficient conditions for the curvature of a quadratic rational Bézier curve to be monotone in \([0,1]\), to have a unique local minimum, to have a unique local maximum, and to have both extrema in \((0,1)\), and we also visualize them in figures. As an application, we present a necessary and sufficient condition for the offset curve to be regular and to have the same tangent direction with the given quadratic rational Bézier curve, and give a simple algorithm to find it.
MSC:
| 65D18 | Numerical aspects of computer graphics, image analysis, and computational geometry |
Keywords:
quadratic rational Bézier curves; monotone curvature; local extrema of curvature; fairing curves; offset curvesReferences:
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