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 | - | - |
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