2020•arXiv (Cornell University)Open access

Conversion of matrix weighted rational B\'{e}zier curves to rational B\'{e}zier curves

Xunnian Yang

Abstract

Matrix weighted rational Bezier curves can represent complex curve shapes using small numbers of control points and clear geometric definitions of matrix weights. Explicit formulae are derived to convert matrix weighted rational Bezier curves in 2D or 3D space to rational Bezier curves. A method for computing the convex hulls of matrix weighted rational Bezier curves is given as a conjecture.

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Key concepts: Bézier curve, Mathematics, Conjecture, Matrix (chemical analysis), Family of curves, Regular polygon, Pure mathematics, Mathematical analysis