Multilevel B-Spline

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

Description

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. doi:10.1109/2945.620490.

Parameters

	Name	Type	Identifier	Description	Constraints
Input	Points	shapes, input	`SHAPES`	-	-
Input	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
	Grid System	grid system	`TARGET_SYSTEM`	-	-
	Refinement	choice	`METHOD`	-	Available Choices: [0] no [1] yes Default: 0
	Threshold Error	floating point number	`EPSILON`	-	Minimum: 0.000000 Default: 0.000100
	Maximum Level	integer number	`LEVEL_MAX`	-	Minimum: 1 Maximum: 14 Default: 11
	Update View	boolean [GUI]	`UPDATE`	-	Default: 0

Command Line


Usage: saga_cmd grid_spline 4 [-SHAPES ] [-FIELD ] [-TARGET_DEFINITION ] [-TARGET_USER_SIZE ] [-TARGET_USER_XMIN ] [-TARGET_USER_XMAX ] [-TARGET_USER_YMIN ] [-TARGET_USER_YMAX ] [-TARGET_USER_COLS ] [-TARGET_USER_ROWS ] [-TARGET_USER_FLAT ] [-TARGET_USER_FITS ] [-TARGET_TEMPLATE ] [-TARGET_OUT_GRID ] [-METHOD ] [-EPSILON ] [-LEVEL_MAX ]
  -SHAPES:             	Points
	shapes, input
  -FIELD:              	Attribute
	table field
  -TARGET_DEFINITION:  	Target Grid System
	choice
	Available Choices:
	[0] user defined
	[1] grid or grid system
	Default: 0
  -TARGET_USER_SIZE:	Cellsize
	floating point number
	Minimum: 0.000000
	Default: 1.000000
  -TARGET_USER_XMIN:	West
	floating point number
	Default: 0.000000
  -TARGET_USER_XMAX:	East
	floating point number
	Default: 100.000000
  -TARGET_USER_YMIN:	South
	floating point number
	Default: 0.000000
  -TARGET_USER_YMAX:	North
	floating point number
	Default: 100.000000
  -TARGET_USER_COLS:   	Columns
	integer number
	Minimum: 1
	Default: 101
  -TARGET_USER_ROWS:   	Rows
	integer number
	Minimum: 1
	Default: 101
  -TARGET_USER_FLAT:   	Rounding
	boolean
	Default: 1
  -TARGET_USER_FITS:   	Fit
	choice
	Available Choices:
	[0] nodes
	[1] cells
	Default: 0
  -TARGET_TEMPLATE:    	Target System
	grid, input, optional
  -TARGET_OUT_GRID:    	Target Grid
	grid, output
  -METHOD:             	Refinement
	choice
	Available Choices:
	[0] no
	[1] yes
	Default: 0
  -EPSILON:         	Threshold Error
	floating point number
	Minimum: 0.000000
	Default: 0.000100
  -LEVEL_MAX:          	Maximum Level
	integer number
	Minimum: 1
	Maximum: 14
	Default: 11