Constructing G1 quadratic Bézier curves with arbitrary endpoint tangent vectors

Quadratic 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 G
¹
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 G
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quadratic Bézier cures and other curve schemes such as the composite geometric Hermite curves and the biarcs.