An involute spiral that matches G2 Hermite data in the plane

被引：14
|
作者：
Goodman, T. N. T. [2 ]
Meek, D. S. [1 ]
Walton, D. J. [3 ]
机构：
[1] Univ Manitoba, Dept Comp Sci, Winnipeg, MB R3T 2N2, Canada
[2] Univ Dundee, Dept Math, Dundee DD1 4HN, Scotland
[3] Univ Manitoba, St Pauls Coll, Winnipeg, MB R3T 2M6, Canada
来源：
COMPUTER AIDED GEOMETRIC DESIGN | 2009年 / 26卷 / 07期
基金：
加拿大自然科学与工程研究理事会;
关键词：
Rational spirals; G(2) Hermite interpolation; HODOGRAPH QUINTIC TRANSITION; 2; CIRCLES; CURVES; LENGTH; PAIR;
D O I：
10.1016/j.cagd.2009.03.009
中图分类号：
TP31 [计算机软件];
学科分类号：
081202 ; 0835 ;
摘要：
A construction is given for a planar rational Pythagorean hodograph spiral, which interpolates any two-point G(2) Hermite data that a spiral can match. When the Curvature at one of the points is zero, the construction gives the unique interpolant that is an involute of a rational Pythagorean hodograph curve of the form cubic over linear. Otherwise, the spiral comprises an involute of a Tschirnhausen cubic together with at most two circular arcs. The construction is by explicit formulas in the first case, and requires the Solution of a quadratic equation in the second case. (C) 2009 Elsevier B.V. All rights reserved.
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页码：733 / 756
页数：24
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