Language:   Search:   Contact
Zentralblatt MATH has released its new interface!
For an improved author identification, see the new author database of ZBMATH.

Advanced Search

Query:
Fill in the form and click »Search«...
Format:
Display: entries per page entries
Zbl 0847.68125
Farouki, R.T.; Neff, C.A.
Hermite interpolation by Pythagorean hodograph quintics.
(English)
[J] Math. Comput. 64, No.212, 1589-1609 (1995). ISSN 0025-5718; ISSN 1088-6842/e

Summary: The Pythagorean hodograph (PH) curves are polynomial parametric curves $\{x(t), y(t)\}$ whose hodograph (derivative) components satisfy the Pythagorean condition $x^{\prime 2}(t)+ y^{\prime 2}(t)\equiv \sigma^2(t)$ for some polynomial $\sigma(t)$. Thus, unlike polynomial curves in general, PH curves have arc lengths and offset curves that admit exact rational representations. The lowest-order PH curves that are sufficiently flexible for general interpolation/approximation problems are the quintics. While the PH quintics are capable of matching arbitrary first-order Hermite data, the solution procedure is not straightforward and furthermore does not yield a unique result -- there are always four distinct interpolants (of which only one, in general, has acceptable shape'' characteristics). We show that formulating PH quintics as complex-valued functions of a real parameter leads to a compact Hermite interpolation algorithm and facilitates an identification of the good'' interpolant (in terms of minimizing the absolute rotation number). This algorithm establishes the PH quintics as a viable medium for the design or approximation of free-form curves, and allows a one-for-one substitution of PH quintics in lieu of the widely-used ordinary'' cubics.
MSC 2000:
*68U07 Computer aided design
53A04 Curves in Euclidean space
68U05 Computational geometry, etc.
41A05 Interpolation

Keywords: Pythagorean hodograph

Login Username: Password:

Highlights
Master Server

Zentralblatt MATH Berlin [Germany]

© FIZ Karlsruhe GmbH

Zentralblatt MATH master server is maintained by the Editorial Office in Berlin, Section Mathematics and Computer Science of FIZ Karlsruhe and is updated daily.

Other Mirror Sites

Copyright © 2013 Zentralblatt MATH | European Mathematical Society | FIZ Karlsruhe | Heidelberg Academy of Sciences
Published by Springer-Verlag | Webmaster