Area-preserving geometric Hermite interpolation

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:361

Article

McGregor, Geoffrey¹  Nave, Jean-Christophe¹ 

[1] McGill Univ, Dept Math, Montreal, PQ, Canada

关键词: Bezier curves;    Hermite interpolation;    Conservation;   

DOI  :  10.1016/j.cam.2019.03.005

来源: Elsevier

【 摘 要 】

In this paper we establish a framework for planar geometric interpolation with exact area preservation using cubic Bezier polynomials. We show there exists a family of such curves which are 5th order accurate, one order higher than standard geometric cubic Hermite interpolation. We prove this result is valid when the curvature at the endpoints does not vanish, and in the case of vanishing curvature, the interpolation is 4th order accurate. The method is computationally efficient and prescribes the parametrization speed at endpoints through an explicit formula based on the given data. Additional accuracy (i.e. same order but lower error constant) may be obtained through an iterative process to find optimal parametrization speeds which further reduces the error while still preserving the prescribed area exactly. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free