Finding the point on Bezier Curves with the normal vector passing an external point

Hong, X. ORCID: https://orcid.org/0000-0002-6832-2298 and Harwin, W.S. ORCID: https://orcid.org/0000-0002-3928-3381 (2006) Finding the point on Bezier Curves with the normal vector passing an external point. International Journal of Modelling Identification and Control, 1 (4). doi: 10.1504/IJMIC.2006.012620

Abstract/Summary

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.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/15283
Item Type	Article
Refereed	Yes
Divisions	Life Sciences > School of Biological Sciences > Department of Bio-Engineering Science > School of Mathematical, Physical and Computational Sciences > Department of Computer Science
Uncontrolled Keywords	Keywords: Bezier curves; de Casteljau algorithm; derivatives; haptics; Lyapunov method; normal vector; Farin recursion; haptic rendering.
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