Module Cubic Spline Approximation

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

Author: O. Conrad (c) 2008
Specification: grid
Menu: Grid|Gridding|Spline Interpolation

Parameters

	Name	Type	Identifier	Description	Constraints
Input	Points	Shapes (input)	`SHAPES`	-	-
Input	Target System (*)	Grid (optional input)	`TARGET_TEMPLATE`	use this grid's system for output grids	-
Output	Target Grid	Grid (output)	`TARGET_OUT_GRID`	-	-
Options	Attribute	Table field	`FIELD`	-	-
	Target Grid System	Choice	`TARGET_DEFINITION`	-	Available Choices: [0] user defined [1] grid or grid system Default: 0
	Left	Floating point	`TARGET_USER_XMIN`	-	Default: 0.000000
	Right	Floating point	`TARGET_USER_XMAX`	-	Default: 100.000000
	Bottom	Floating point	`TARGET_USER_YMIN`	-	Default: 0.000000
	Top	Floating point	`TARGET_USER_YMAX`	-	Default: 100.000000
	Cellsize	Floating point	`TARGET_USER_SIZE`	-	Minimum: 0.000000 Default: 1.000000
	Fit	Choice	`TARGET_USER_FITS`	-	Available Choices: [0] nodes [1] cells Default: 0
	Minimal Number of Points	Integer	`NPMIN`	-	Minimum: 0 Default: 3
	Maximal Number of Points	Integer	`NPMAX`	-	Minimum: 11 Maximum: 59 Default: 20
	Points per Square	Floating point	`NPPC`	-	Minimum: 1.000000 Default: 5.000000
	Tolerance	Integer	`K`	Spline sensitivity, reduce to get smoother results, recommended: 80 < Tolerance < 200	Minimum: 0 Default: 140
(*) optional

Command-line

Usage: saga_cmd grid_spline 6 [-SHAPES <str>] [-FIELD <str>] [-TARGET_DEFINITION <str>] [-TARGET_USER_XMIN <str>] [-TARGET_USER_XMAX <str>] [-TARGET_USER_YMIN <str>] [-TARGET_USER_YMAX <str>] [-TARGET_USER_SIZE <str>] [-TARGET_USER_FITS <str>] [-TARGET_TEMPLATE <str>] [-TARGET_OUT_GRID <str>] [-NPMIN <num>] [-NPMAX <num>] [-NPPC <str>] [-K <num>]
  -SHAPES:<str>           	Points
	Shapes (input)
  -FIELD:<str>            	Attribute
	Table field
  -TARGET_DEFINITION:<str>	Target Grid System
	Choice
	Available Choices:
	[0] user defined
	[1] grid or grid system
	Default: 0
  -TARGET_USER_XMIN:<str> 	Left
	Floating point
	Default: 0.000000
  -TARGET_USER_XMAX:<str> 	Right
	Floating point
	Default: 100.000000
  -TARGET_USER_YMIN:<str> 	Bottom
	Floating point
	Default: 0.000000
  -TARGET_USER_YMAX:<str> 	Top
	Floating point
	Default: 100.000000
  -TARGET_USER_SIZE:<str> 	Cellsize
	Floating point
	Minimum: 0.000000
	Default: 1.000000
  -TARGET_USER_FITS:<str> 	Fit
	Choice
	Available Choices:
	[0] nodes
	[1] cells
	Default: 0
  -TARGET_TEMPLATE:<str>  	Target System
	Grid (optional input)
  -TARGET_OUT_GRID:<str>  	Target Grid
	Grid (output)
  -NPMIN:<num>            	Minimal Number of Points
	Integer
	Minimum: 0
	Default: 3
  -NPMAX:<num>            	Maximal Number of Points
	Integer
	Minimum: 11
	Maximum: 59
	Default: 20
  -NPPC:<str>             	Points per Square
	Floating point
	Minimum: 1.000000
	Default: 5.000000
  -K:<num>                	Tolerance
	Integer
	Minimum: 0
	Default: 140