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TheG2andC2rational quadratic trigonometric Bézier curve with two shape parameters with applications

Authors
Journal
Applied Mathematics and Computation
0096-3003
Publisher
Elsevier
Publication Date
Volume
219
Issue
20
Identifiers
DOI: 10.1016/j.amc.2013.03.110
Keywords
  • Quadratic Trigonometric Polynomials
  • Rational Quadratic Trigonometric Bézier Curves
  • Shape Parameters
  • Parametric Continuity
  • Geometric Continuity
Disciplines
  • Mathematics

Abstract

Abstract The rational quadratic trigonometric Bézier curve with two shape parameters is presented in this paper, which is new in literature. The purposed curve inherits all the geometric properties of the traditional rational quadratic Bézier curve. The presence of shape parameters provides a control on the shape of the curve more than that of traditional Bézier curve. Moreover the weight offers an additional control on the curve. Simple constraints for shape parameters are derived using the end points curvature so that their values always fall within the defined range. The composition of two segments of curve using G2 and C2 continuity is given. The new curves can accurately represent some conics and best approximates the traditional rational quadratic Bézier curve.

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