Constructing G1 quadratic Bezier curves with arbitrary endpoint tangent vectors

International audienceQuadratic Bézier curves are important geometric entities in many applications. However, it was often ignored by the literature the fact that a single segment of a quadratic Bézier curve may fail to fit arbitrary endpoint unit tangent vectors. The purpose of this paper is to provide a solution to this problem, i.e., constructing G1 quadratic Bézier curves satisfying given endpoint (positions and arbitrary unit tangent vectors) conditions. Examples are given to illustrate the new solution and to perform comparison between the G1 quadratic Bézier cures and other curve schemes such as the composite geometric Hermite curves and the biarcs

Fairing arc spline and designing by using cubic bézier spiral segments

This paper considers how to smooth three kinds of G 1 biarc models, the C-, S-, and J-shaped transitions, by replacing their parts with spiral segments using a single cubic Bézier curve. Arc spline is smoothed to G 2continuity. Use of a single curve rather than two has the benefit because designers and implementers have fewer entities to be concerned. Arc spline is planar, tangent continuous, piecewise curves made of circular arcs and straight line segments. It is important in manufacturing industries because of its use in the cutting paths for numerically controlled cutting machinery. Main contribution of this paper is to minimize the number of curvature extrema in cubic transition curves for further use in industrial applications such as non-holonomic robot path planning, highways or railways, and spur gear tooth designing