Tool Multilevel B-Spline

Multilevel B-spline algorithm for spatial interpolation of scattered data as proposed by Lee, Wolberg and Shin (1997).
The algorithm makes use of a coarse-to-fine hierarchy of control lattices to generate a sequence of bicubic B-spline functions, whose sum approaches the desired interpolation function. Performance gains are realized by using B-spline refinement to reduce the sum of these functions into one equivalent B-spline function.

The 'Maximum Level' determines the maximum size of the final B-spline matrix and increases exponential with each level. Where level=10 requires about 1mb level=12 needs about 16mb and level=14 about 256mb(!) of additional memory.

References

Lee, S., Wolberg, G., Shin, S.Y. (1997): Scattered Data Interpolation with Multilevel B-Splines. IEEE Transactions On Visualisation And Computer Graphics, Vol.3, No.3., p.228-244. ResearchGate.

Author: O.Conrad (c) 2006
Menu: Grid|Gridding|Spline Interpolation

Parameters

	Name	Type	Identifier	Description	Constraints
Input	Points	Shapes, input	`SHAPES`	-	-
Input	Target System (*)	Grid, input, optional, CMD	`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	`TARGET_USER_SIZE`	-	Minimum: 0.000000 Default: 1.000000
	West	Floating point	`TARGET_USER_XMIN`	-	Default: 0.000000
	East	Floating point	`TARGET_USER_XMAX`	-	Default: 100.000000
	South	Floating point	`TARGET_USER_YMIN`	-	Default: 0.000000
	North	Floating point	`TARGET_USER_YMAX`	-	Default: 100.000000
	Columns	Integer	`TARGET_USER_COLS`	Number of cells in East-West direction.	Minimum: 1 Default: 100
	Rows	Integer	`TARGET_USER_ROWS`	Number of cells in North-South direction.	Minimum: 1 Default: 100
	Fit	Choice	`TARGET_USER_FITS`	-	Available Choices: [0] nodes [1] cells Default: 0
	Grid System	Grid system	`TARGET_SYSTEM`	-	-
	Refinement	Choice	`METHOD`	-	Available Choices: [0] no [1] yes Default: 0
	Threshold Error	Floating point	`EPSILON`	-	Minimum: 0.000000 Default: 0.000100
	Maximum Level	Integer	`LEVEL_MAX`	-	Minimum: 1 Maximum: 14 Default: 11
	Update View	Boolean, GUI	`UPDATE`	-	Default: 0
(*) optional

Command-line

Usage: saga_cmd grid_spline 4 [-SHAPES <str>] [-FIELD <str>] [-TARGET_DEFINITION <str>] [-TARGET_USER_SIZE <double>] [-TARGET_USER_XMIN <double>] [-TARGET_USER_XMAX <double>] [-TARGET_USER_YMIN <double>] [-TARGET_USER_YMAX <double>] [-TARGET_USER_COLS <num>] [-TARGET_USER_ROWS <num>] [-TARGET_USER_FITS <str>] [-TARGET_TEMPLATE <str>] [-TARGET_OUT_GRID <str>] [-METHOD <str>] [-EPSILON <double>] [-LEVEL_MAX <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_SIZE:<double>	Cellsize
	Floating point
	Minimum: 0.000000
	Default: 1.000000
  -TARGET_USER_XMIN:<double>	West
	Floating point
	Default: 0.000000
  -TARGET_USER_XMAX:<double>	East
	Floating point
	Default: 100.000000
  -TARGET_USER_YMIN:<double>	South
	Floating point
	Default: 0.000000
  -TARGET_USER_YMAX:<double>	North
	Floating point
	Default: 100.000000
  -TARGET_USER_COLS:<num>   	Columns
	Integer
	Minimum: 1
	Default: 100
  -TARGET_USER_ROWS:<num>   	Rows
	Integer
	Minimum: 1
	Default: 100
  -TARGET_USER_FITS:<str>   	Fit
	Choice
	Available Choices:
	[0] nodes
	[1] cells
	Default: 0
  -TARGET_TEMPLATE:<str>    	Target System
	Grid, input, optional, CMD
  -TARGET_OUT_GRID:<str>    	Target Grid
	Grid, output
  -METHOD:<str>             	Refinement
	Choice
	Available Choices:
	[0] no
	[1] yes
	Default: 0
  -EPSILON:<double>         	Threshold Error
	Floating point
	Minimum: 0.000000
	Default: 0.000100
  -LEVEL_MAX:<num>          	Maximum Level
	Integer
	Minimum: 1
	Maximum: 14
	Default: 11