TY - JOUR
T1 - An involute spiral that matches G2 Hermite data in the plane
AU - Goodman, T.N.T.
AU - Meek, D.S.
AU - Walton, D.J.
N1 - Copyright 2009 Elsevier B.V., All rights reserved.
PY - 2009/10
Y1 - 2009/10
N2 - A construction is given for a planar rational Pythagorean hodograph spiral, which interpolates any two-point G 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.
AB - A construction is given for a planar rational Pythagorean hodograph spiral, which interpolates any two-point G 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.
UR - http://www.scopus.com/inward/record.url?scp=68949099397&partnerID=8YFLogxK
U2 - 10.1016/j.cagd.2009.03.009
DO - 10.1016/j.cagd.2009.03.009
M3 - Article
AN - SCOPUS:68949099397
SN - 0167-8396
VL - 26
SP - 733
EP - 756
JO - Computer Aided Geometric Design
JF - Computer Aided Geometric Design
IS - 7
ER -