A note on Pythagorean hodograph quartic spiral
| Autor: | Zhi-hao Zheng, Guozhao Wang |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Applied Mathematics
Mathematical analysis 020207 software engineering 010103 numerical & computational mathematics 02 engineering and technology Curvature 01 natural sciences Pythagorean hodograph Quintic function Range (mathematics) Monotone polygon Quartic function Polygon 0202 electrical engineering electronic engineering information engineering 0101 mathematics Spiral Mathematics |
| Zdroj: | Applied Mathematics-A Journal of Chinese Universities. 33:234-252 |
| ISSN: | 1993-0445 1005-1031 |
| Popis: | By using the geometric constraints on the control polygon of a Pythagorean hodograph (PH) quartic curve, we propose a sufficient condition for this curve to have monotone curvature and provide the detailed proof. Based on the results, we discuss the construction of spiral PH quartic curves between two given points and formulate the transition curve of a G2 contact between two circles with one circle inside another circle. In particular, we deduce an attainable range of the distance between the centers of the two circles and summarize the algorithm for implementation. Compared with the construction of a PH quintic curve, the complexity of the solution of the equation for obtaining the transition curves is reduced. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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