Natural spline interpolation and exponential parameterization for length estimation of curves

2017 ◽  
Author(s):  
R. Kozera ◽  
M. Wilkołazka
Keyword(s):  
Spline Interpolation ◽  
Length Estimation ◽  
Natural Spline ◽  
Exponential Parameterization

scholarly journals Elements of Bi-cubic Polynomial Natural Spline Interpolation for Scattered Data: Boundary Conditions Meet Partition of Unity Technique

2020 ◽  
Vol 8 (4) ◽  
pp. 994-1010
Author(s):  
Weizhi Xu
Keyword(s):  
Boundary Conditions ◽  
Spline Interpolation ◽  
Partition Of Unity ◽  
Scattered Data ◽  
Rectangular Domain ◽  
Natural Boundary ◽  
Natural Spline ◽  
Cubic Polynomial ◽  
Natural Boundary Conditions ◽  
Cubic Polynomials

This paper investigates one kind of interpolation for scattered data by bi-cubic polynomial natural spline, in which the integral of square of partial derivative of two orders to x and to y for the interpolating function is minimal (with natural boundary conditions). Firstly, bi-cubic polynomial natural spline interpolations with four kinds of boundary conditions are studied. By the spline function methods of Hilbert space, their solutions are constructed as the sum of bi-linear polynomials and piecewise bi-cubic polynomials. Some properties of the solutions are also studied. In fact, bi-cubic natural spline interpolation on a rectangular domain is a generalization of the cubic natural spline interpolation on an interval. Secondly, based on bi-cubic polynomial natural spline interpolations of four kinds of boundary conditions, and using partition of unity technique, a Partition of Unity Interpolation Element Method (PUIEM) for fitting scattered data is proposed. Numerical experiments show that the PUIEM is adaptive and outperforms state-of-the-art competitions, such as the thin plate spline interpolation and the bi-cubic polynomial natural spline interpolations for scattered data.

Algorithm 472: procedures for natural spline interpolation [E1]

1973 ◽  
Vol 16 (12) ◽  
pp. 763-768 ◽  
Author(s):  
John G. Herriot ◽  
Christian H. Reinsch
Keyword(s):  
Spline Interpolation ◽  
Natural Spline

Algorithm 507: Procedures for Quintic Natural Spline Interpolation [E1]

1976 ◽  
Vol 2 (3) ◽  
pp. 281-289 ◽  
Author(s):  
John G. Herriot ◽  
Christian H. Reinsch
Keyword(s):  
Spline Interpolation ◽  
Natural Spline

An algorithm for natural spline interpolation

1993 ◽  
Vol 5 (1) ◽  
pp. 63-70 ◽  
Author(s):  
Leonardo Traversoni
Keyword(s):  
Spline Interpolation ◽  
Natural Spline
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