The new characterization of ruled surfaces corresponding dual Bézier curves

Abstract

Abstract View references (64) Let (Formula presented.) be a Bézier curve in D3, that is, the control points of (Formula presented.) are the vectors in D3 = {u = (u1, u2, u3) : ui ∈ D,i = 1,2,3} which is the set of dual vectors whose each coordinate components are dual numbers defined as a+εa* : a,a* ∈ R,ε ≠ 0; ε2 = 0. So the spherical projection of (Formula presented.) is a spherical curve denoted by (Formula presented.) on the unit sphere in D3 and every point of (Formula presented.) corresponds to a directed line in real space R3 by Study transformation. In this study, the ruled surface X(t, ν) corresponding to this projection curve (Formula presented.) of dual Bézier curve (Formula presented.) is stated in terms of the parametric equation of the real and dual part of a given dual Bézier curve (Formula presented.). Also, in this study, some fundamental characteristics such as the striction curve, the Gaussian curvature, and the distribution parameter of the ruled surface X(t, ν) corresponding to this projection curve (Formula presented.) of the dual Bézier curve (Formula presented.) are investigated. These concepts at any point are stated in terms of the control points of the given dual Bézier curve (Formula presented.). © 2021 John Wiley & Sons, Ltd.