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Applied Mathematics-A Journal of Chinese Universities  2018, Vol. 33 Issue (2): 234-252    DOI: 10.1007/s11766-018-3465-4
    
A note on Pythagorean hodograph quartic spiral
ZHENG Zhi-hao ,  WANG Guo-zhao
School of Mathematical Sciences, Zhejiang University, Hangzhou 310027, China
A note on Pythagorean hodograph quartic spiral
ZHENG Zhi-hao ,  WANG Guo-zhao
School of Mathematical Sciences, Zhejiang University, Hangzhou 310027, China
 全文: PDF 
摘要： 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 $G^2$ 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.
关键词： Pythagorean hodograph quartic curve ;   ;  spiral ;   ;  curvature ;   transition curve    
Abstract: 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 $G^2$ 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.
Key words: Pythagorean hodograph quartic curve         spiral         curvature     transition curve
出版日期: 2018-07-16
CLC:  65D17  
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ZHENG Zhi-hao
WANG Guo-zhao

引用本文:

ZHENG Zhi-hao, WANG Guo-zhao. A note on Pythagorean hodograph quartic spiral[J]. Applied Mathematics-A Journal of Chinese Universities, 2018, 33(2): 234-252.

ZHENG Zhi-hao , WANG Guo-zhao. A note on Pythagorean hodograph quartic spiral. Applied Mathematics-A Journal of Chinese Universities, 2018, 33(2): 234-252.

链接本文:

http://www.zjujournals.com/amjcub/CN/10.1007/s11766-018-3465-4    或    http://www.zjujournals.com/amjcub/CN/Y2018/V33/I2/234

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