Cubic Bézier spiral segments for planar G2 curve design

Abstract

In curve design it is often desirable to match G2 Hermite data with a pair of spirals. An existing method addresses this problem using cubics by first requiring the joint to be placed, and then matching tangents at the joint. It is now shown that an alternative method of first matching tangents, which then determine an interval along a line for placement of the joint, is more convenient and requires less computation.