# Cubic Spline Approximation

O. Conrad (c) 2008
This module approximates irregular scalar 2D data in specified points using C1-continuous bivariate cubic spline.
Minimal Number of Points: minimal number of points locally involved in spline calculation (normally = 3)
Maximal Number of Points:npmax: maximal number of points locally involved in spline calculation (required > 10, recommended 20 < npmax < 60)
Tolerance: relative tolerance multiple in fitting spline coefficients: the higher this value, the higher degree of the locally fitted spline (recommended 80 < k < 200)
Points per square: average number of points per square (increase if the point distribution is strongly non-uniform to get larger cells)
Author: Pavel Sakov, CSIRO Marine Research
Purpose: 2D data approximation with bivariate C1 cubic spline. A set of library functions + standalone utility.
Description: See J. Haber, F. Zeilfelder, O.Davydov and H.-P. Seidel, Smooth approximation and rendering of large scattered data sets, in 'Proceedings of IEEE Visualization 2001' (Th.Ertl, K.Joy and A.Varshney, Eds.), pp.341-347, 571, IEEE Computer Society, 2001.
www.uni-giessen.de/www-Numerische-Mathematik/davydov/VIS2001.ps.gz
www.math.uni-mannheim.de/~lsmath4/paper/VIS2001.pdf.gz

## Parameters

Points
Input Shapes
Attribute
Table field
Target Grid
Choice
  Available choices: user defined, grid
Minimal Number of Points
Integer
Maximal Number of Points
Integer
  Minimum: 11.0; Maximum: 59.0
Points per Square
Floating point
  Minimum: 1.0
Tolerance
Integer
  Spline sensitivity, reduce to get smoother results, recommended: 80 < Tolerance < 200
Left
Floating point
Right
Floating point
Bottom
Floating point
Top
Floating point
Cellsize
Floating point
Columns
Integer
Rows
Integer
Grid
Output Data Object
Grid system
Grid system
Grid
Output Grid