Multilevel B-Spline (3D)

Author: O.Conrad (c) 2019
Menu: Grid | Gridding | Interpolation (3D)

Description

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. doi:10.1109/2945.620490.

Parameters

	Name	Type	Identifier	Description	Constraints
Input	Points	shapes, input	`POINTS`	-	-
Input	Target System	grid, input, optional	`TARGET_TEMPLATE`	use this grid's system for output grids	-
Output	Grid Collection	grid collection, output	`GRIDS`	-	-
Options	Z	table field	`Z_FIELD`	-	-
	Z Factor	floating point number	`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 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`	-	-
	Cellsize	floating point number	`TARGET_USER_ZSIZE`	-	Minimum: 0.000000 Default: 1.000000
	Bottom	floating point number	`TARGET_USER_ZMIN`	-	Default: 0.000000
	Top	floating point number	`TARGET_USER_ZMAX`	-	Default: 100.000000
	Levels	integer number	`TARGET_USER_ZNUM`	-	Minimum: 1 Default: 101
	Threshold Error	floating point number	`EPSILON`	-	Minimum: 0.000000 Default: 0.000100
	Maximum Level	integer number	`LEVEL_MAX`	-	Minimum: 1 Maximum: 14 Default: 11

Command Line


Usage: saga_cmd grid_spline 8 [-POINTS ] [-Z_FIELD ] [-Z_SCALE ] [-V_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 ] [-GRIDS ] [-TARGET_USER_ZSIZE ] [-TARGET_USER_ZMIN ] [-TARGET_USER_ZMAX ] [-TARGET_USER_ZNUM ] [-EPSILON ] [-LEVEL_MAX ]
  -POINTS:                 Points
	shapes, input
  -Z_FIELD:                Z
	table field
  -Z_SCALE:             Z Factor
	floating point number
	Minimum: 0.000000
	Default: 1.000000
  -V_FIELD:                Value
	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
  -GRIDS:                  Grid Collection
	grid collection, output
  -TARGET_USER_ZSIZE:   Cellsize
	floating point number
	Minimum: 0.000000
	Default: 1.000000
  -TARGET_USER_ZMIN:    Bottom
	floating point number
	Default: 0.000000
  -TARGET_USER_ZMAX:    Top
	floating point number
	Default: 100.000000
  -TARGET_USER_ZNUM:       Levels
	integer number
	Minimum: 1
	Default: 101
  -EPSILON:             Threshold Error
	floating point number
	Minimum: 0.000000
	Default: 0.000100
  -LEVEL_MAX:              Maximum Level
	integer number
	Minimum: 1
	Maximum: 14
	Default: 11