A helix — or “curve of constant slope” — is characterized by the property that its tangent maintains a constant inclination relative to a fixed direction — the axis of the helix. Equivalently, a helix exhibits a circular tangent indicatrix, and the ratio of curvature and torsion remains constant along its length [290, 307, 433]. Whereas all spatial PH cubics are helical (see §21.1), the helical PH quintics constitute a proper subset of the spatial PH quintics.
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© 2008 Springer-Verlag Berlin Heidelberg
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(2008). Helical Polynomial Curves. In: Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable. Geometry and Computing, vol 1. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73398-0_23
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DOI: https://doi.org/10.1007/978-3-540-73398-0_23
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