Curvature continuous piecewise Pythagorean hodograph curves

Abstract

This report develops constructions for cubic, quartic, and quintic Pythagorean hodograph curves (PHC). The cubic construction is a rederivation of an earlier cubic PHC construction, but in the real plane rather than the imaginary plane. The quartic construction is also a rederivation of an earlier construction, again in the real plane rather than the imaginary plane. In addition, the free parameter in this quartic construction is used to interpolate curvature at one end of the curve. The quintic construction builds a quintic PHC cure that interpolates the position, tangent, and curvature at two points.