2021/08/30 by Carlotta Giannelli, Giannelli, Carlotta, Lorenzo Sacco +3
Computer Science · Engineering · #Advanced Numerical Analysis Techniques #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Image and Signal Denoising Methods #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2108.12948
openalex publication_date 2021/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
The construction of smooth spatial paths with Pythagorean-hodograph (PH) quintic spline biarcs is proposed. To facilitate real-time computations of C2 PH quintic splines, an efficient local data stream interpolation algorithm is introduced. Each spline segment interpolates second and first order Hermite data at the initial and final end-point, respectively. In the spline extension of the scheme a C2 smooth connection between successive spline segments is obtained by taking the locally required second-order derivative information from the previous segment. Consequently, the data stream spline interpolant is globally C2 continuous and can be constructed for arbitrary C1 Hermite data configurations. A simple and effective selection of the free parameters that arise in the interpolation problem is proposed. The developed theoretical analysis proves the fourth approximation order of the local scheme while a selection of numerical examples confirms the same accuracy of its spline extension. In addition, the performances of the algorithm are also validated by considering its application to point stream interpolation with automatically generated first-order derivative information.