Algorithm 761: Scattered-data surface fitting that has the accuracy of a cubic polynomial

1996 ◽  
Vol 22 (3) ◽  
pp. 362-371 ◽  
Author(s):  
Hiroshi Akima
Keyword(s):  
Scattered Data ◽  
Surface Fitting ◽  
Cubic Polynomial ◽  
Data Surface

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.

scholarly journals Surface Fitting for Quasi Scattered Data from Coordinate Measuring Systems

Sensors ◽  
2018 ◽  
Vol 18 (2) ◽  
pp. 214 ◽  
Author(s):  
Qing Mao ◽  
Shugui Liu ◽  
Sen Wang ◽  
Xinhui Ma
Keyword(s):  
Scattered Data ◽  
Surface Fitting ◽  
Measuring Systems

Tri-cubic polynomial natural spline interpolation for scattered data

CALCOLO ◽  
2011 ◽  
Vol 49 (2) ◽  
pp. 127-148 ◽  
Author(s):  
Yingxiang Xu ◽  
Gaohang Yu ◽  
Lutai Guan
Keyword(s):  
Spline Interpolation ◽  
Scattered Data ◽  
Natural Spline ◽  
Cubic Polynomial

Surface fitting to scattered data by a sum of Gaussians

1993 ◽  
Vol 10 (2) ◽  
pp. 143-156 ◽  
Author(s):  
Ardeshir Goshtasby ◽  
William D. O'Neill
Keyword(s):  
Scattered Data ◽  
Surface Fitting
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