Planar cubic G~1 and quintic G2 Hermite interpolations via curvature variation minimization

摘要

Highlights•A new method for cubicG1and quinticG1Hermite interpolations is presented.•Better interpolation results are obtained by minimizing curvature variation energy.•Shape-preserving interpolation is achieved for arbitrary input data.Graphical abstractDisplay OmittedAbstractGiven two data points and the associated unit tangents, cubicG1Hermite 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 cubicG1Hermite interpolation by minimizing curvature variation energy subject to a feasible region, with the advantage of handling arbitraryG1data. As a result, theG1interpolating curves can always maintain specified end tangent directions by restricting the two parameters provided byG1constraint 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 quinticG2Hermite interpolation for inputG2data. A number of comparative experiments are conducted to verify the applicability and effectiveness of the proposed method.