An involute spiral that matches G2 Hermite data in the plane

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 - https://www.scopus.com/pages/publications/68949099397

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 -