Self-intersections of rational Bézier curves

• Published in: Graphical models Vol. 76; no. 5; pp. 312 - 320
• Main Authors: Zhu, Chun-Gang, Zhao, Xuan-Yi
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Inc 01.09.2014; Elsevier
• Subjects: Applied sciences; Computer aided design; Computer science; control theory; systems; Control polygon; Curve fitting; Curves (geometry); Equivalence; Exact sciences and technology; Injectivity; Mathematical analysis; Mathematical models; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; Numerical approximation; Polygons; Rational Bézier curve; Sciences and techniques of general use; Self-intersection; Software; Control polygon; Injectivity; Self-intersection; Rational Bézier curve; Intersection; Geometrical model; Bézier curve; Rational interpolation; Polynomial interpolation; Degeneration; Polygon; Curve fitting; Computer aided design

[Display omitted] •We define the well-posedness of control polygon of the rational Bezier curve.•The Bezier curve is injective if and only if its control polygon is well-posed.•We present a geometric method to determine the injectivity of the Bezier curve. Rational Bézier curves provide a curve fitt...