A polynomial curve with a Pythagorean hodograph has the properties that its arc-length is a polynomial of its parameter. and its offset is a rational algebraic expression. A quintic is the lowest degree Pythagorean hodograph curve that may have an inflection point and that inflection point allows a
Pythagorean-hodograph preserving mappings
β Scribed by Gwang-Il Kim; Sunhong Lee
- Publisher
- Elsevier Science
- Year
- 2008
- Tongue
- English
- Weight
- 380 KB
- Volume
- 216
- Category
- Article
- ISSN
- 0377-0427
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β¦ Synopsis
We study the scaled Pythagorean-hodograph (PH) preserving mappings. These mappings make offset-rational isothermal surfaces and map PH curves to PH curves. We present a method to produce a great number of the scaled PH preserving mappings. For an application of the PH preserving mappings, we solve the Hermite interpolation problem for PH curves in the space.
π SIMILAR VOLUMES
The structural invariance of the four-polynomial characterization for three-dimensional Pythagorean hodographs introduced by Dietz et al. (1993), under arbitrary spatial rotations, is demonstrated. The proof relies on a factoredquaternion representation for Pythagorean hodographs in three-dimensiona
have recently advocated the use of Pythagorean-hodograph quintics of monotone curvature, or "PH spirals" for short, as transitional elements that give G' connections of linear and circular arcs in applications such as layout of highways and railways-in which context PH curves provide the important a
We investigate the properties of a special kind of frame, which we call the Euler-Rodrigues frame (ERF), defined on the spatial Pythagorean-hodograph (PH) curves. It is a frame that can be naturally constructed from the PH condition. It turns out that this ERF enjoys some nice properties. In particu