Tool Multilevel B-Spline (3D)

Multilevel B-spline algorithm for spatial interpolation of scattered data as proposed by Lee, Wolberg and Shin (1997) modified for 3D data.
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) 2019
Menu: Grid|Gridding|Interpolation (3D)

Parameters

	Name	Type	Identifier	Description	Constraints
Input	Points	Shapes, input	`POINTS`	-	-
Input	Target System (*)	Grid, input, optional, CMD	`TARGET_TEMPLATE`	use this grid's system for output grids	-
Output	Grid Collection	Grids, output	`GRIDS`	-	-
Options	Z	Table field	`Z_FIELD`	-	-
	Z Factor	Floating point	`Z_SCALE`	-	Minimum: 0.000000 Default: 1.000000
	Value	Table field	`V_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`	-	-
	Cellsize	Floating point	`TARGET_USER_ZSIZE`	-	Minimum: 0.000000 Default: 1.000000
	Bottom	Floating point	`TARGET_USER_ZMIN`	-	Default: 0.000000
	Top	Floating point	`TARGET_USER_ZMAX`	-	Default: 100.000000
	Levels	Integer	`TARGET_USER_ZNUM`	-	Minimum: 1 Default: 100
	Threshold Error	Floating point	`EPSILON`	-	Minimum: 0.000000 Default: 0.000100
	Maximum Level	Integer	`LEVEL_MAX`	-	Minimum: 1 Maximum: 14 Default: 11
(*) optional

Command-line

Usage: saga_cmd grid_spline 8 [-POINTS <str>] [-Z_FIELD <str>] [-Z_SCALE <double>] [-V_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>] [-GRIDS <str>] [-TARGET_USER_ZSIZE <double>] [-TARGET_USER_ZMIN <double>] [-TARGET_USER_ZMAX <double>] [-TARGET_USER_ZNUM <num>] [-EPSILON <double>] [-LEVEL_MAX <num>]
  -POINTS:<str>              	Points
	Shapes, input
  -Z_FIELD:<str>             	Z
	Table field
  -Z_SCALE:<double>          	Z Factor
	Floating point
	Minimum: 0.000000
	Default: 1.000000
  -V_FIELD:<str>             	Value
	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
  -GRIDS:<str>               	Grid Collection
	Grids, output
  -TARGET_USER_ZSIZE:<double>	Cellsize
	Floating point
	Minimum: 0.000000
	Default: 1.000000
  -TARGET_USER_ZMIN:<double> 	Bottom
	Floating point
	Default: 0.000000
  -TARGET_USER_ZMAX:<double> 	Top
	Floating point
	Default: 100.000000
  -TARGET_USER_ZNUM:<num>    	Levels
	Integer
	Minimum: 1
	Default: 100
  -EPSILON:<double>          	Threshold Error
	Floating point
	Minimum: 0.000000
	Default: 0.000100
  -LEVEL_MAX:<num>           	Maximum Level
	Integer
	Minimum: 1
	Maximum: 14
	Default: 11