Geometric construction of Pythagorean hodograph C-curves. (Chinese. English summary) Zbl 07828154
Summary: We study the geometric characteristics of C-Bézier curves that possess the Pythagorean Hodograph (PH) property. Based on the algebraic necessary and sufficient conditions for PH C-curves, we prove that a C-Bézier curve is a PH C-curve if and only if the interior angles of its control polygon are equal, and the second leg length of the control polygon is the geometric mean of the first and the last ones. Our main idea is to represent a planar parametric curve in complex form. We claim that the geometric characteristics of PH C-curves are quite similar to polynomial PH curves, which can be used to identify PH C-curves and their constructions. As an application, we give some examples of \(G^1\) Hermite interpolation using PH C-curves. We point out that there are no more than two PH C-curves for any given \(G^1\) Hermite conditions.
MSC:
| 65D17 | Computer-aided design (modeling of curves and surfaces) |
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