A Pythagorean hodograph curve (PH curve) is a parametrically defined curve whose unit tangent vector has a rational representation. Such curves possess several useful properties, including straightforward arc length computation, rationally defined offset curves, and numerically simple reparametrization with respect to the arc-length parameter. Although the Bézier control polygon of a PH curve uniquely determines the curve, moving even a single control point typically destroys the Pythagorean property, which makes it unsuitable for describing such curves. To address this, we introduce the rectifying polygon, which has exactly the same number of free parameters as the PH curve itself. In particular, we examine the cases of PH curves of degrees 3, 5, and 7.
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