Constructing G¹ quadratic Bézier curves with arbitrary endpoint tangent vectors

Quadratic Bezier 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 Bezier 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 Bezier 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 Bezier cures and other curve schemes such as the composite geometric Hermite curves and the biarcs.