The full text of this article
Finding the point on Bezier curves with the normal vector passing an external point
by Xia Hong, W.S. Harwin
International Journal of Modelling, Identification and Control (IJMIC), Vol. 1, No. 4, 2006
Abstract: Two algorithms for finding the point on non-rational/rational Bezier curves of which the normal vector passes through a given external point are presented. The algorithms are based on Bezier curves generation algorithms of de Casteljau's algorithm for non-rational Bezier curve or Farin's recursion for rational Bezier curve, respectively. Orthogonal projections from the external point are used to guide the directional search used in the proposed iterative algorithms. Using Lyapunov's method, it is shown that each algorithm is able to converge to a local minimum for each case of non-rational/rational Bezier curves. It is also shown that on convergence the distance between the point on curves to the external point reaches a local minimum for both approaches. Illustrative examples are included to demonstrate the effectiveness of the proposed approaches.
Online publication date: Tue, 27-Feb-2007
is only available to individual subscribers or to users at subscribing institutions.
Go to Inderscience Online Journals to access the Full Text of this article.
Pay per view:
If you are not a subscriber and you just want to read the full contents of this article, buy online access here.
Complimentary Subscribers, Editors or Members of the Editorial Board of the International Journal of Modelling, Identification and Control (IJMIC):
Login with your Inderscience username and password:
Want to subscribe?
A subscription gives you complete access to all articles in the current issue, as well as to all articles in the previous three years (where applicable).
See our Orders page to subscribe.
If you still need assistance, please email firstname.lastname@example.org