Planar PH quintics offer sufficient shape flexibility for most practical design and manufacturing applications — they can inflect, and are in many respects similar in behavior to “ordinary” plane cubics (see §19.7). To construct planar PH quintics, a scheme that provides control over basic geometrical properties of a curve segment is required. Selecting numerical values for the coefficients u0, u1, u2 and v0, v1, v2 in (17.6) by “guesswork” clearly does not satisfy this need: we must develop algorithms that determine appropriate values for these coefficients, consistent with the specified geometrical constraints. Because the control points (17.6) have a non—linear dependence on u0, u1, u2 and v0, v1, v2 such algorithms incur non—linear equations with a multiplicity of solutions.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
(2008). Planar Hermite Interpolants. 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_25
Download citation
DOI: https://doi.org/10.1007/978-3-540-73398-0_25
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-73397-3
Online ISBN: 978-3-540-73398-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)