Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 1172.65327
Han, Chang Yong
Nonexistence of rational rotation-minimizing frames on cubic curves. (English)
[J] Comput. Aided Geom. Des. 25, No. 4-5, 298-304 (2008). ISSN 0167-8396

Summary: We prove there is no rational rotation-minimizing frame (RMF) along any non-planar regular cubic polynomial curve. Although several schemes have been proposed to generate rational frames that approximate RMF's, exact rational RMF's have been only observed on certain Pythagorean-hodograph curves of degree seven. Using the Euler-Rodrigues frames naturally defined on Pythagorean-hodograph curves, we characterize the condition for the given curve to allow a rational RMF and rigorously prove its nonexistence in the case of cubic curves.

MSC 2000:: *65D17 Computer aided design (modeling of curves and surfaces)
53A04 Curves in Euclidean space

Keywords: Pythagorean-hodograph curve; rotation-minimizing frame; Euler-Rodrigues frame; rational frame; cubic curve

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]