# Pythagorean-Hodograph Quintic Curves

Pythagorean-Hodograph Quintic Curves

A polynomial curve is a Pythagorean-hodograph (PH) curve if + is the square of another polynomial. The lowest degree curves satisfying this condition are PH cubics, but such a curve cannot inflect. Quintic PH curves are needed to get an inflexion point. The degrees of freedom of such a curve allow the choice of four of the six control polygon points. The PH property determines the two remaining points.

M(t)=(x(t),y(t))

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