Interpolation Tools

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Interpolation tools plugin

A plugin to interpolate points features to a raster DEM for OpenJUMP
(http://www.openjump.org/)

How to set up.

• Download and Instal OpenJUMP. Use one of the newer build available from this page: https://sourceforge.net/projects/jump-pilot/files/OpenJUMP_snapshots/
• Download the PlugIn InterpolatePlugIn_0.7.jar - https://sourceforge.net/projects/opensit/files/Openjump/PlugIn/Interpolate%20points%20to%20raster/
  ( in the same page you can download also the source code as ZIP file)
• Copy the file InterpolatePlugIn_0.7.jar into OpenJUMP/lib/ext folder.
• Start OpenJUMP.
• The plugin is available under Raster menu with the name: Interpolate a point layer. This plugin is activated only if a vector layer is loaded.

Algorithms available to interpolate points:

Linear regression.

This algorithm calculates, for each cell of the grid, a regression plane [z = ax + by +c] of the points quoted around the cell, with the method Ordinary Least Squares. User can define a kernel (max radius to search near points) and smoothing (higher smoothing>softned terrain.
The algorithm has been developed using a code available from AdBToolbox - AClim plugin (http://www.pcn.minambiente.it/mattm/adb-toolbox/)

Spline (Gaussian reduction)

This tool interpolates feature collection of points using a Gaussian elimination. This performs a sequence of row operations on a matrix of values to modify it until the lower left-hand corner of the matrix is filled with values (zero).
Due to memory usage of this algorithm, its limit of data analisys is set to max 1000 points. :

This method is named after Carl Friedrich Gauss (1777–1855).
Theory and code of Gaussian elimination can be found here: https://algs4.cs.princeton.edu/code/edu/princeton/cs/algs4/GaussianElimination.java

Triangulated irregular network (TIN)

This tool interpolates a regular grid raster from a point dataset using a Delaunay triangulation. It utilizes the points to constitute many nonoverlapping
triangles that cover the entire region of analysis. This method is quite fast and returns a relative good interpolation if the points are uniformely distributed and concentrated, like LIDAR data.
The algorithm has been developed using an ImageJ traingulation plugin from Martin Schlüter (http://ij.ms3d.de/xyz2dem-importer.php)

Nearest Neighbor

Nearest Neighbor is a simple method of numerical interpolation of a set of points. This interpolation method is particularly suited to situations where
the surface contains numerous discontinuities and the observations lie on a nearly complete grid with few missing holes. Radius option defines the circular
search neighbourhood used to identify nearby points.
The algorithm has been developed using Nearest Neighbor plugin form WhiteBox Gat (https://jblindsay.github.io/ghrg/Whitebox/)

Inverse Distance Weighting (IDW)

This algotithm interpolates using the Inverse Distance to a Weight (IDW) interpolation method (Shepard 1968). Each grid cell in the output raster surface
model (DEM) is assigned a value based on a distance-weighted combination of point value from the group of points contained within a circular area
encompassing the grid cell. Weight option determines how the distance among neighbouring points will contribute to their weighting. Max distance option
defines the radius of the circular search neighbourhood used to identify nearby points. An extra option tries to minimize bull's eye apparence using square
root of distance (John Lindsay - 2014).
The algorithm has been developed using IDW plugin form WhiteBox Gat (https://jblindsay.github.io/ghrg/Whitebox/)

Modified Inverse Distance Weighting (IDW)
This algotithm is a modified version of Shepard's one (IDW; each grid cell in the output raster surface model (DEM) is assigned a value based on a distance-weighted combination of point value from the group of points contained within a circular area encompassing the grid cell. User can choose the number of points to interpolate. This algorithm is faster than IDW and might partially reduce the bull's eye effects. The algorithm has been developed using Nearest Neighbor plugin form WhiteBox Gat (https://jblindsay.github.io/ghrg/Whitebox/)

 Copyright (C) <2020>  <Giuseppe Aruta>

This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.

This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
GNU General Public License for more details.

You should have received a copy of the GNU General Public License
along with this program.  If not, see <https://www.gnu.org/licenses/>.