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Involute of Cubic Pythagorean-Hodograph

Author: LiuYing
Tutor: WangGuoZhao
School: Zhejiang University
Course: Applied Mathematics
Keywords: PH curves Involute Control points Control polygon Steering angle
CLC: TP391.41
Type: Master's thesis
Year: 2008
Downloads: 41
Quote: 1
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The PH curve derivative mold long as the the polynomial vector form of polynomial parametric curves , thus showing a good practical value , for example, it arc length can be expressed as a polynomial function curve parameters . Below , we discuss three times PH involute curve . First, we expressed Cubic PH Curve Involute : It is five rational polynomial curve ; including rights and control points by Cubic PH Curve control polygon vertices , control the length of a side of the polygon and the control polygon relative constitute between adjacent sides of the steering angle . Second, we take advantage of the detailed analysis of plane cubic parametric curve shape controllability and proved Cubic PH Curve no sharp points and inflection ; Cubic PH Curve Involute six control points in the first two vertices coincide ; three the two edges and cubic PH Curve control two edges of the polygon are perpendicular to each other , to determine the length of the two sides cubic PH Curve involute control polygon PH curve control polygon of involute ; cubic PH Curve is given , we can determine its involute six control five vertices , so we give a vertex and remaining a point constitute a vector ; cubic PH Curve its two symmetrical curve involute axisymmetric curve , is not the case in the rest of the case . Concluded that the examples involute encounter in our day-to-day after birth .

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