Tool Name	Cubic Spline Approximation
Tool ID	6
Library ID	grid_spline
Version	1.0
Author(s)	O. Conrad (c) 2008

Description

This tool 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.

References

Haber, J., Zeilfelder, F., Davydov, O., Seidel, H.-P. (2001): Smooth approximation and rendering of large scattered data sets. In Ertl, T., Joy, K., Varshney, A. [Eds.]: Proceedings of IEEE Visualization. pp.341-347, 571, IEEE Computer Society.

Parameters

Name	Type	Identifier	Description	Constraints
Input
Points	shapes, input	SHAPES
Target System	grid, input, optional	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
Cellsize	floating point number	TARGET_USER_SIZE		Minimum: 0.000000 Default: 1.000000
West	floating point number	TARGET_USER_XMIN		Default: 0.000000
East	floating point number	TARGET_USER_XMAX		Default: 100.000000
South	floating point number	TARGET_USER_YMIN		Default: 0.000000
North	floating point number	TARGET_USER_YMAX		Default: 100.000000
Columns	integer number	TARGET_USER_COLS	Number of cells in East-West direction.	Minimum: 1 Default: 101
Rows	integer number	TARGET_USER_ROWS	Number of cells in North-South direction.	Minimum: 1 Default: 101
Rounding	boolean	TARGET_USER_FLAT	Round bounding coordinates to multiples of cell size. Ignored if cell size has decimal places.	Default: 1
Fit	choice	TARGET_USER_FITS		Available Choices: [0] nodes [1] cells Default: 0
Minimal Number of Points	integer number	NPMIN		Minimum: 0 Default: 3
Maximal Number of Points	integer number	NPMAX		Minimum: 11 Maximum: 59 Default: 20
Points per Square	floating point number	NPPC		Minimum: 1.000000 Default: 5.000000
Tolerance	integer number	K	Spline sensitivity, reduce to get smoother results, recommended: 80 < Tolerance < 200	Minimum: 0 Default: 140