WOLFRAM|DEMONSTRATIONS PROJECT

Pythagorean-Hodograph (PH) Cubic Curves

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curve
speed: σ(t) = 5.845
2
t
-0.1455t+3.711
A polynomial curve
M(t)=(x(t),y(t))
is a Pythagorean-Hodograph (PH) curve if
2
dx
dt
+
2
dy
dt
is the square of another polynomial. The lowest-degree curves satisfying this condition are PH-cubics, here presented in Bézier form. The degrees of freedom of such a curve let you choose three of the four control polygon points. The remaining point is then determined.