The Triangulation method creates triangles by joining input data points to neighboring points.
The Triangulation method produces a regular gridded raster from a set of input data points by creating a Delaunay triangulation of the input points, from which the value at the raster cell centers is estimated by linear interpolation of the plane defined by the three nodes of the overlapping triangle. A Delaunay triangulation seeks to maximize the minimum angle in each of the triangles and will generate a mesh that entirely encompasses the convex hull of the input points. The triangulation method is most suited to data that is evenly distributed over the area of interest. It does not produce a smooth raster under normal conditions where the grid cell size is small compared to the triangle size (i.e., data point separation).
For a large input point dataset, the algorithm is not able to generate a single Delaunay triangulation from which to perform the interpolation. Instead, it divides the area of interest up into a collection of overlapping tiles and triangulates each of these individually. In general this performs exceedingly well, but it does not produce the same result that would be obtained from a single triangulation. Firstly, the triangulation will not encompass the convex hull of the dataset as a whole – it may become concave. Also, you may see edge effects or artifacts near to large voids.
The Triangulation method does not require you to modify algorithm parameters. The primary input is the raster cell size. If the cell size is small compared to the data point separation, the raster will display a triangulated character with triangular areas of constant slope. If the cell size is larger than, or comparable to, the data point separation then the raster may appear smooth. For large input dataset, you can adjust parameters that control tiling and the issues that can arise when tiling occurs.
If you are not sure about the distribution or range of the input data sets then leave the interpolation properties to their default settings. If you are familiar with the input dataset and have a good understanding of the range of values in the field(s) being interpolated then you can modify the interpolation properties to suite the input and output data requirements.
Triangulation Method Options
Parameter Unit
Specifies whether spatial parameters are defined in cell units or distance units. The units should be supported by MapInfo Pro, for example, the options for Distance unit include: US Survey feet, yards, rods, chains, miles, nautical miles, millimeters, centimeters, meters, inches, links and kilometers. If you choose Distance, you need to select a distance unit from the Distance Unit drop-down list.
Distance Units - This parameter is used to control the units of distance that the ‘Maximum Triangle Size’ property is measured in. By default this control is disabled and the maximum distance unit is expressed as a fraction of the tile size. If you wish to constrain the Maximum triangle side length to a fixed value that is measured in absolute data units (e.g., 100 meters) then enable this control and enter an appropriate value. If the entered value is large and exceeds the size of an individual tile of data then it may have no effect on the output grid. If the coordinate system of the input data is Longitude/Latitude then the distance units need to be specified in fractions of a degree.
Maximum Triangle Size
This parameter is used to eliminate long thin triangles that may be created across large voids in the data or between widely separated points that lie around the perimeter of the dataset. It can be used to generate a natural level of clipping. Triangles that are deemed too long will not be used to interpolate raster cell values. The parameter defines the maximum allowable side length.
This is a distance that is the longest triangle that will be accepted in the triangulation. It can be set in cells or in distance units. The default value to set to 100 cell units.
Click More Options to open the following advanced options.
Smoothing Method - You can apply smoothing on the gridded data to produce smoother surface. Smoothing is used to enhance the sharpness of an image or improve the appearance of the edges. Select a suitable Smoothing method and level for your data.
Smoothing Level - Move the smoothing slider to set the smoothing level for the output raster. You can set a value between 0 to 6. A value of zero applies no smoothing. A value of 6 applies maximum smoothing.
Clipping - The Clipping control provides options to limit the extents of the interpolated raster, so it more closely approximates the distribution of the input data. Enabling this option can improve the appearance of the output raster when interpolating irregularly spaced input data, where the interpolation methods (such as Triangulation, Minimum Curvature or Natural Neighbor) has interpolated across large gaps in the input data.
- None - No clipping is applied to the raster cells.
- Near Only - The Near value represents the maximum distance from a source input data point for which an interpolated raster cell will be created. Cells in the raster which lie at a distance greater than the Near distance will be assigned a null value. This method has the same effect as applying a distance buffer to the source data points equal to the near distance.
- Near/Far - Interpolated cells in the output raster will be clipped to the near distance if no other data point is found within the Far distance that meet the angular search constraints. Applying both Near and Far clipping can be useful to constrain the interpolated raster to a required distance from the source points, while also permitting larger gaps to be interpolated in irregularly spaced data.
- Polygon - You can provide a TAB file of polygon(s) to clip the output raster to the polygon boundaries. You can specify whether to clip a region outside or inside the raster bounds. However, it does not support polygons with holes.
Coincident Point Method - The gridding engine can pre-process the input source data to identify points that are spatially coincident. In general, two points are spatially coincident if they lie within a specified distance of each other. When the distance is set to zero, then the points are coincident if the X and Y coordinates are computationally indistinguishable from one another. For more information see, Coincident Point Method.
Raster Geometry
Cell Size
Specify the cell size for the output raster in the Cell Size box. The cell size defines the width and height of a raster cell in distance units. If the raster cells are square both width and height are specified with same value.
By default, Automatic is selected which means will calculate the output raster cell size based on source data points. Click Suggest, to see the calculated cell size value in the box before it is processed. You can modify the cell size value to produce output raster with the desired cell size. The Suggest button is active only when the input data source is in MapInfo native format.
Output Geometry
The Output Geometry allows you to limit the output data points according to specified region (bounds) and ignore all points that lie outside of the specified region. The data within the specified bounds will be written in the output file. To specify the Raster Bounds, enter coordinate values for raster origin and extent.
- Min X - X coordinate of the origin (lower left corner of the cell).
- Min Y - Y coordinate of the origin (lower left corner of the cell).
- Max X - The maximum coordinate value for X (upper right corner of the cell).
- Max Y - The maximum coordinate value for Y (upper right corner of the cell).
The output file will contain data for the specified region only.
If required, click More Options to specify the projection for the output raster. If the input file is a MapInfo .TAB file, projection values are read from the input file, which you can override here.
- Category - The Category drop-down list consists of all projection systems supported by MapInfo Pro. For example, Longitude/Latitude, Universal Transverse Mercator (ED 50), Universal Transverse Mercator (NAD 27 for Canada), etc.
- Sub Category - The Sub Category drop-down list consists of the type of projection based on the selected projection system.