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ARC-LENGTH ESTIMATIONS FOR QUADRATIC RATIONAL B´ ezier CURVES COINCIDING WITH ARC-LENGTH OF SPECIAL SHAPES

Seon-Hong Kim, Young Joon Ahn

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Abstract

ABSTRACT. In this paper, we present arc-length estimations for quadratic rational Bézier curves using the length of polygon and distance between both end points. Our arc-length es-timations coincide with the arc-length of the quadratic rational Bézier curve exactly when the weight w is 0, 1 and1. We show that for all w> 0 our estimations are strictly increasing with respect to w. Moreover, we find the parameter which makes our estimation coincide with the arc-length of the quadratic rational Bézier curve when it is a circular arc too. We also show that has a special limit, which is used for optimal estimation. We present some numerical examples, and the numerical results illustrates that the estimation with the limit value of is an optimal estimation. 1.

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What this paper is about

ABSTRACT. In this paper, we present arc-length estimations for quadratic rational Bézier curves using the length of polygon and distance between both end points. Our arc-length es-timations coincide with the arc-length of the quadratic rational Bézier curve exactly when the weight w is 0, 1 and1. We show that for all w> 0 our estimations are strictly increasing with respect to w. Moreover, we find the parameter which makes our estimation coincide with the arc-length of the quadratic rational Bézier curve when it is a circular arc too. We also show that has a special limit, which is used for optimal estimation. We present some numerical examples, and the numerical results illustrates that the estimation with the limit value of is an optimal estimation. 1.

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Available abstract

ABSTRACT. In this paper, we present arc-length estimations for quadratic rational Bézier curves using the length of polygon and distance between both end points. Our arc-length es-timations coincide with the arc-length of the quadratic rational Bézier curve exactly when the weight w is 0, 1 and1. We show that for all w> 0 our estimations are strictly increasing with respect to w. Moreover, we find the parameter which makes our estimation coincide with the arc-length of the quadratic rational Bézier curve when it is a circular arc too. We also show that has a special limit, which is used for optimal estimation. We present some numerical examples, and the numerical results illustrates that the estimation with the limit value of is an optimal estimation. 1.

Key concepts: Bézier curve, Arc length, Arc (geometry), Mathematics, Quadratic equation, Limit (mathematics), Polygon (computer graphics), Applied mathematics

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ARC-LENGTH ESTIMATIONS FOR QUADRATIC RATIONAL B´ ezier CURVES COINCIDING WITH ARC-LENGTH OF SPECIAL SHAPES — Research Paper | ScholarLens