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. ResearchGate.
Parameters
| | Name | Type | Identifier | Description | Constraints |
|---|
| Input | Points | shapes, input | SHAPES | - | - |
| 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 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 |
| 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_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_FITS: Fit
choice
Available Choices:
[0] nodes
[1] cells
Default: 0
-TARGET_TEMPLATE: Target System
grid, input, optional, CMD
-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