Graphics Gems V (IBM Version)

IV.6

Sparse Smooth Connection between Bézier/B-Spline Curves

Chandrajit Bajaj and Guoliang Xu,     Purdue University West Lafayette, Indiana; Computing Center, Academia Sinica Beijing, China

Introduction

Often in interactive font design, free-form sketching, and input path specification for graphics animation, one is faced with the problem of connecting two Bézier or B-spline polynomial curves with a piecewise transition polynomial curve achieving prescribed continuity at the two endpoints. Furthermore, one desires the transition polynomial curve to have the fewest number of (sparse) pieces. This issue is addressed by first identifying the degrees of freedom ¹ needed to achieve the conditions for smoothness and sparseness, described below, ...