Planar cubic G1 and quintic G2 Hermite interpolations via curvature variation minimization

• Published in: Computers & graphics Vol. 70; pp. 92 - 98
• Main Authors: Lu, Lizheng, Jiang, Chengkai, Hu, Qianqian
• Format: Journal Article
• Language: English; Japanese
• Published: Elsevier Ltd 01.02.2018
• Subjects: Curvature variation; Fair curve; Geometric continuity; Hermite interpolation; Polynomial representation; Curvature variation; Fair curve; Polynomial representation; Geometric continuity; Hermite interpolation
• ISSN: 0097-8493; 1873-7684
• DOI: 10.1016/j.cag.2017.07.007

•A new method for cubic G1 and quintic G1 Hermite interpolations is presented.•Better interpolation results are obtained by minimizing curvature variation energy.•Shape-preserving interpolation is achieved for arbitrary input data. [Display omitted] Given two data points and the associated unit tangents, cubic G1 Hermite interpolation is a simple and efficient scheme to construct fair curves by optimizing certain energy functionals. In order to obtain shape-preserving interpolation desired for applications, this paper presents cubic G1 Hermite interpolation by minimizing curvature variation energy subject to a feasible region, with the advantage of handling arbitrary G1 data. As a result, the G1 interpolating curves can always maintain specified end tangent directions by restricting the two parameters provided by G1 constraint to be positive; and the numerical solution is obtained by an iterative algorithm using the block coordinate descend method. This approach can be further extended to quintic G2 Hermite interpolation for input G2 data. A number of comparative experiments are conducted to verify the applicability and effectiveness of the proposed method.