TY - JOUR
T1 - Rectifying control polygon for planar Pythagorean hodograph curves
AU - Kim, Soo Hyun
AU - Moon, Hwan Pyo
N1 - Publisher Copyright:
© 2017 Elsevier B.V.
PY - 2017/5/1
Y1 - 2017/5/1
N2 - A Bézier control polygon is not appropriate to control a Pythagorean hodograph curve since it has redundant degrees of freedom. So we propose an alternative, which is the rectifying control polygon. A rectifying control polygon of a PH curve has the same degrees of freedom as the PH curve. It interpolates the end points of the PH curve, but not the end tangents. Most of all, it has the same arc length as the PH curve. In this paper, we present the method to compute the rectifying control polygon from the Bézier control polygon of the PH curve. We also present the procedure to compute the PH curves from a given rectifying control polygon. For the development of these algorithms, we employ the Gauss–Legendre quadrature method and the Bernstein–Vandermonde linear system.
AB - A Bézier control polygon is not appropriate to control a Pythagorean hodograph curve since it has redundant degrees of freedom. So we propose an alternative, which is the rectifying control polygon. A rectifying control polygon of a PH curve has the same degrees of freedom as the PH curve. It interpolates the end points of the PH curve, but not the end tangents. Most of all, it has the same arc length as the PH curve. In this paper, we present the method to compute the rectifying control polygon from the Bézier control polygon of the PH curve. We also present the procedure to compute the PH curves from a given rectifying control polygon. For the development of these algorithms, we employ the Gauss–Legendre quadrature method and the Bernstein–Vandermonde linear system.
KW - Bernstein–Vandermonde matrix
KW - Bézier control polygon
KW - Gauss–Legendre quadrature
KW - Pythagorean-hodograph curve
KW - Rectifying control polygon
UR - http://www.scopus.com/inward/record.url?scp=85017452188&partnerID=8YFLogxK
U2 - 10.1016/j.cagd.2017.03.016
DO - 10.1016/j.cagd.2017.03.016
M3 - Article
AN - SCOPUS:85017452188
SN - 0167-8396
VL - 54
SP - 1
EP - 14
JO - Computer Aided Geometric Design
JF - Computer Aided Geometric Design
ER -