Trigonometric Bézier-like curves and transition curves

Abstract

. In this paper, planar cubic trigonometric Bézier curves with two shape parameters are considered. Appropriate conditions for these curves to be spiral are obtained and transition curves from the straight line to the straight line, from the straight line to the circle, from the circle to the circle with a C-shaped transition curve, from the circle to the circle with an S-shaped transition curve, from a circle to a circle where one of the circles lies inside of another circle are considered with the help of this spiral. Many numerical examples are also provided.