Sparse Pythagorean hodograph curves

We introduce cubic-like sparse Pythagorean hodograph curves which are possibly of high degrees though they can be handled as cubic curves. They offer more flexibility than the classical Pythagorean hodograph cubic curves with which they share many properties. We give an elegant geometric characterization of their control polygons. This characterization leads to many interesting computational algorithms for curve design. We show how to extend such algorithms to quintic-like sparse PH curves.