Abstract
The Tschirnhausen cubic represents all non-degenerate Pythagorean Hododgraph cubics. We determine its support function and represent it as a convolution of a centrally symmetrical curve and a curve with linear normals. We use the support function to parametrize the Tschirnhausen cubic by normals. This parametrization is then used to an elegant and complete solution of the G 1 Hermite interpolation by Pythagorean Hodograph cubics. We apply the resulting algorithm to various examples and extend it to the interpolation by offsets of PH cubics.
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Černohorská, E., Šír, Z. (2010). Support Function of Pythagorean Hodograph Cubics and G 1 Hermite Interpolation. In: Mourrain, B., Schaefer, S., Xu, G. (eds) Advances in Geometric Modeling and Processing. GMP 2010. Lecture Notes in Computer Science, vol 6130. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13411-1_3
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DOI: https://doi.org/10.1007/978-3-642-13411-1_3
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