Indirect pythagorean hodograph curves (indirect PH curves) represent a class of Bézier curves whose arc length, after an appropriate reparameterization of the parameter, is a rational or polynomial function. In this work, we present a theorem that provides a necessary and sufficient condition for a curve to be an indirect PH curve. We focus on cubic curves, for which we derive and prove a theorem establishing geometric constraints on the control points of a Bézier curve. Furthermore, we address the problem of Hermite $G^1$ interpolation, where, based on the aforementioned theorem, we construct suitable indirect PH interpolants. In this context, we distinguish between the case where a single regular indirect PH curve can be constructed and the case requiring a spline of two curves.
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