A weighted extremal problem for the Bézier curves of degree n with jacobi densities

Authors:
Przemysław Rutka;Ryszard Smarzewski
Affiliations:
Institute of Mathematics and Computer Science, John Paul II Catholic University of Lublin, Konstantynów 1H, 20-708 Lublin, Poland;Institute of Mathematics and Computer Science, John Paul II Catholic University of Lublin, Konstantynów 1H, 20-708 Lublin, Poland
Venue:
Annales UMCS, Informatica
Year:
2008

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Abstract

An efficient algorithm in the field of the computer aided geometric design and computer graphics, which solves a restricted weighted isoperimetric type problem in the class of Bézier curves of degree n 2 with Jacobi densities is presented. It requires to compute the maximal eigenvalue and the corresponding eigenvector of an extended eigenproblem with block square matrices of 2n-2 dimension. The coordinates of this eigenvector determine the control points of the extremal Bézier curve, while the maximal eigenvalue gives the maximal area bounded by this curve.