Interpolate
Create raster data in the specified Result destination and specified data type by interpolation using values in vector objects in a drawing. Parameter boxes will automatically appear as required by different interpolation options.
- gravity (IDW) - Compute pixel values in tiles from Z values in objects using gravity formulae with inverse distance weighting (IDW) for interpolation and optional specification of interpolation order.
- Kriging - Compute pixel values in tiles from Z values in objects using Kriging for interpolation.
- Kriging with median polish - The same as Kriging, but with the application of median-polish, an extra processing step, to improve the interpolation.
- Kriging with regression - The same as Kriging, but using a regression model as well. See notes below.
- natural neighbors - Use natural neighbors interpolation with Sibson weights for interpolation. Limited to interpolation within the convex hull of the source data.
- thin-plate spline - Use thin-plate spline (TPS) interpolation, which works both inside and outside the convex hull of the source data.
- triangulation - Compute pixel values in tiles from Z values in objects using triangulation for interpolation.
- triangulation with segments - Compute pixel values in tiles from Z values in objects using constrained triangulation for interpolation, and providing a Remove flat areas (DEST) option. The option improves triangulation of contours using a DEST (Determination of Earth Surface Structures) algorithm, which helps to remove or reduce terracing effects when contouring from contour lines or other regular data.
Typical interpolation parameters, depending on the operation:
Z - Field to use for interpolation value.
Margin - Additional distance, in the specified unit of measure, to create the image beyond the bounding rectangle of vector data in the drawing.
Resolution - Size of resulting pixels, in the specified unit of measure.
Radius - Radius, in the specified unit of measure, for neighbor searches. 0 or negative = Auto.
Neighbors - Number of neighbors to use. 0 or negative = Use Voronoi neighbors.
Model - Interpolation model. Default is to autoselect the model. Click to choose a specific model.
Regression - Regression model. Default is to autoselect the model. Click to choose a specific model.
Do not use a Resolution of 1 with a Unit of Degree when drawings are in an angular coordinate system, like Latitude / Longitude. That creates pixels which are 1 degree in size, many kilometers in size in most parts of the world. If drawings are in a linear coordinate system and the Unit chosen is Meter, a Resolution of 30 creates pixels that are 30 meters by 30 meters in size. To keep units straight, it is best to do interpolations using drawings that have been projected into linear coordinate systems, and not radial coordinate systems like Latitude / Longitude.
Interpreting various combinations of specified (positive value) or zero or negative value for Radius and Neighbors:
Specified Radius and Neighbors = Use all neighbors within the specified radius.
Radius auto-computed and Voronoi Neighbors = Use all Voronoi neighbors out to the Radius set by the system.
Specified number of Neighbors, but Radius auto-computed = Radius set by the system according to the global interpolation picture.
Specified number of Neighbors, and specified Radius = Use up to the specified number of neighbors within the specified radius.
Using a larger radius with a specified number of Neighbors, can dramatically increase the time required for computations. When interpolating closely packed points that are confined to a specific region of a drawing, measure a distance that is slightly beyond the group of packed points, and use that distance for the Radius when using a specified number of Neighbors.
See the Notes at the end of the Example: Create Terrain Elevation Raster from a NASA PDS Table topic.
Interpolation Model options:
auto
circular
exponential
gaussian
linear
power
rational
spherical
Regression model options:
auto
linear
quadratic
The SQL function used within interpolation transform templates operate on objects that have Z values within their geoms. The transform automatically takes Z values from the designated field and temporarily adds them as Z values within the geom for each object so the function used can operate. The starting data is not changed, so after running this transform objects will not end up with Z values in their geoms.
Kriging operations produce a report of the parameters used, including resolved values for autocomputed parameters, and save the report into the description property of the new image component.
In Kriging, geoms without Z values are ignored. All geoms are converted to coordinates. Duplicate XY coordinates are ignored: if duplicate XY coordinates have different Z values, the operation uses one of these values and ignores any other Z values. If there is too little data to set up the model, Kriging degrades to Gravity interpolation.
About regression Kriging: Imagine an undulating surface that lies on the slope of a large hill, where if the surface were not bumpy we would have a smooth plane inclined at the overall angle of the hill. Suppose now we have many points that lie on the surface with each point providing the X,Y, and Z value of the surface at that point. Some regions of the surface have relatively few points or are lacking points.
The general task of Kriging is to take the collection of many points and to re-create the surface, filling in through computation some plausible interpolation in regions where sample points are sparse or missing. Ordinary Kriging simply takes the X,Y,Z values of the points and applies Kriging computations to interpolate a surface.
Regression Kriging first attempts to ascertain the overall inclined plane and to remove that as a bias, to allow considering the undulating surface as if it were arranged horizontally and not tilted on the overall slope of a hill. A Kriging calculation is performed on the adjusted, "as if level," coordinates of the points, and then the resulting interpolated surface is titled back to the original overall incline. The choice of linear or quadratic regression is a choice of how the original "overall" tilted-plane setting is determined.
Regression Kriging can identify and set aside more complex biases than the case of an undulating surface within a simple, overall incline in a hill. This non-mathematical description provides an analogy, not an exact phrasing of the math involved, to help non-mathematicians understand how Regression Kriging can provide better results than ordinary Kriging.
Launch the template by choosing a geometry field and then double-clicking the Interpolate template. When the template launches we can specify options.
Interpolate : gravity (IDW)
Given a drawing with objects that have Z values in some field or which have Z values in their geometry, create an image and table using gravity formulae with inverse distance weighting (IDW) to interpolate pixel values in tiles from Z values for each object. The Result destination is always a new table and image.
All geoms are converted to their constituent coordinates. Duplicate XY coordinates are ignored: if duplicate XY coordinates have different Z values, the function uses one of these values and ignores any other Z values.
Interpolation parameters:
Z - Field to use for interpolation value.
Margin - Additional distance, in the specified units, to create the image beyond the bounding rectangle of vector data in the drawing.
Resolution - Size of resulting pixels, in the specified units.
Radius - Radius, in the specified units, for neighbor searches. 0 or negative = Auto.
Neighbors - Number of neighbors to use. 0 or negative = Auto.
Order - The interpolation order, any positive number and possibly fractional, with the default value of 2 using quadratic terms being a good choice.
Unit - Unit of measure to use
Result - Destination for results, always (new table).
Channel type - Numeric type for pixel values.
New image - Name to use for the new image that is created.
New table - Name to use for the new table that is created to store the new image's tiles.
Resources - Options for allow full or no CPU and GPU parallelization.
Transform selection only - When checked, use only selected objects in the drawing for interpolation.
Transform - Apply the transform.
Edit Query - Pop open a Command Window loaded with an SQL query that accomplishes the transform with given parameters.
Interpreting various combinations of specified (positive value) or auto-computed (zero or negative value) for Radius and Neighbors:
Specified Radius and Neighbors auto-computed = Use all neighbors within the specified radius.
Both Radius and Neighbors auto-computed = Use all Voronoi neighbors.
Specified number of Neighbors, but Radius auto-computed = Radius set by the system according to the global interpolation picture.
Specified number of Neighbors, and specified Radius = Use up to the specified number of neighbors within the specified radius.
Do not use a Resolution of 1 and a Unit of Degree when drawings are in a Latitude / Longitude coordinate system that uses degrees. That creates pixels which are 1 degree in size, many kilometers in size in most parts of the world. If drawings are in a coordinate system that uses meters or other linear unit, a Resolution of 30 using Meter as the Unit will create pixels that are 30 meters by 30 meters in size. To allow the widest choice of units it is best to do interpolations using drawings that have been projected into coordinate systems which use linear units of measure such as meters or feet and not angular units such as degrees.
Interpolate : Kriging
Given a drawing with objects that have Z values in some field, create an image and table using Kriging to interpolate pixel values in tiles from Z values for each object. The Result destination is always a new table and image. Produces a report of the parameters used, including resolved values for autocomputed parameters, and saves the report into the description property of the new component.
All geoms are converted to their constituent coordinates. Duplicate XY coordinates are ignored: if duplicate XY coordinates have different Z values, the function uses one of these values and ignores any other Z values. If there is too little data to set up the model, Kriging degrades to Gravity interpolation.
Interpolation parameters:
Z - Field to use for interpolation value.
Margin - Additional distance, in the specified units, to create the image beyond the bounding rectangle of vector data in the drawing.
Resolution - Size of resulting pixels, in the specified units.
Radius - Radius, in the specified units, for neighbor searches. 0 or negative = Auto.
Neighbors - Number of neighbors to use. 0 or negative = Auto.
Model - Interpolation model. Default is to autoselect the model. Click to choose a specific model.
Unit - Unit of measure to use
Result - Destination for results, always (new table).
Channel type - Numeric type for pixel values.
New image - Name to use for the new image that is created.
New table - Name to use for the new table that is created to store the new image's tiles.
Resources - Options for allow full or no CPU and GPU parallelization.
Transform selection only - When checked, use only selected objects in the drawing for interpolation.
Transform - Apply the transform.
Edit Query - Pop open a Command Window loaded with an SQL query that accomplishes the transform with given parameters.
Interpreting various combinations of specified (positive value) or auto-computed (zero or negative value) for Radius and Neighbors:
Specified Radius and Neighbors auto-computed = Use all neighbors within the specified radius.
Both Radius and Neighbors auto-computed = Use all Voronoi neighbors.
Specified number of Neighbors, but Radius auto-computed = Radius set by the system according to the global interpolation picture.
Specified number of Neighbors, and specified Radius = Use up to the specified number of neighbors within the specified radius.
Interpolation Model options:
- auto
- circular
- exponential
- gaussian
- linear
- power
- rational
- spherical
Do not use a Resolution of 1 and a Unit of Degree when drawings are in a Latitude / Longitude coordinate system that uses degrees. That creates pixels which are 1 degree in size, many kilometers in size in most parts of the world. If drawings are in a coordinate system that uses meters or other linear unit, a Resolution of 30 using Meter as the Unit will create pixels that are 30 meters by 30 meters in size. To allow the widest choice of units it is best to do interpolations using drawings that have been projected into coordinate systems which use linear units of measure such as meters or feet and not angular units such as degrees.
Interpolate : Kriging with median polish
Given a drawing with objects that have Z values in some field, create an image and table using Kriging to interpolate pixel values in tiles from Z values for each object. Apply median-polish, an extra processing step, to improve the interpolation. The Result destination is always a new table and image. Produces a report of the parameters used, including resolved values for autocomputed parameters, and saves the report into the description property of the new component.
All geoms are converted to their constituent coordinates. Duplicate XY coordinates are ignored: if duplicate XY coordinates have different Z values, the function uses one of these values and ignores any other Z values. If there is too little data to set up the model, Kriging degrades to Gravity interpolation.
Interpolation parameters:
Z - Field to use for interpolation value.
Margin - Additional distance, in the specified units, to create the image beyond the bounding rectangle of vector data in the drawing.
Resolution - Size of resulting pixels, in the specified units.
Radius - Radius, in the specified units, for neighbor searches. 0 or negative = Auto.
Neighbors - Number of neighbors to use. 0 or negative = Auto.
Model - Interpolation model. Default is to autoselect the model. Click to choose a specific model.
Unit - Unit of measure to use
Result - Destination for results, always (new table).
Channel type - Numeric type for pixel values.
New image - Name to use for the new image that is created.
New table - Name to use for the new table that is created to store the new image's tiles.
Resources - Options for allow full or no CPU and GPU parallelization.
Transform selection only - When checked, use only selected objects in the drawing for interpolation.
Transform - Apply the transform.
Edit Query - Pop open a Command Window loaded with an SQL query that accomplishes the transform with given parameters.
Interpreting various combinations of specified (positive value) or auto-computed (zero or negative value) for Radius and Neighbors:
Specified Radius and Neighbors auto-computed = Use all neighbors within the specified radius.
Both Radius and Neighbors auto-computed = Use all Voronoi neighbors.
Specified number of Neighbors, but Radius auto-computed = Radius set by the system according to the global interpolation picture.
Specified number of Neighbors, and specified Radius = Use up to the specified number of neighbors within the specified radius.
Interpolation Model options:
- auto
- circular
- exponential
- gaussian
- linear
- power
- rational
- spherical
Do not use a Resolution of 1 and a Unit of Degree when drawings are in a Latitude / Longitude coordinate system that uses degrees. That creates pixels which are 1 degree in size, many kilometers in size in most parts of the world. If drawings are in a coordinate system that uses meters or other linear unit, a Resolution of 30 using Meter as the Unit will create pixels that are 30 meters by 30 meters in size. To allow the widest choice of units it is best to do interpolations using drawings that have been projected into coordinate systems which use linear units of measure such as meters or feet and not angular units such as degrees.
Interpolate : Kriging with regression
Given a drawing with objects that have Z values in some field, create an image and table using Kriging with regression to interpolate pixel values in tiles from Z values for each object. The Result destination is always a new table and image. Produces a report of the parameters used, including resolved values for autocomputed parameters, and saves the report into the description property of the new component.
All geoms are converted to their constituent coordinates. Duplicate XY coordinates are ignored: if duplicate XY coordinates have different Z values, the function uses one of these values and ignores any other Z values. If there is too little data to set up the model, Kriging degrades to Gravity interpolation.
Interpolation parameters:
Z - Field to use for interpolation value.
Margin - Additional distance, in the specified units, to create the image beyond the bounding rectangle of vector data in the drawing.
Resolution - Size of resulting pixels, in the specified units.
Radius - Radius, in the specified units, for neighbor searches. 0 or negative = Auto.
Neighbors - Number of neighbors to use. 0 or negative = Auto.
Model - Interpolation model. Default is to autoselect the model. Click to choose a specific model.
Regression - Regression model. Default is to autoselect the model. Click to choose a specific model.
Unit - Unit of measure to use
Result - Destination for results, always (new table).
Channel type - Numeric type for pixel values.
New image - Name to use for the new image that is created.
New table - Name to use for the new table that is created to store the new image's tiles.
Resources - Options for allow full or no CPU and GPU parallelization.
Transform selection only - When checked, use only selected objects in the drawing for interpolation.
Transform - Apply the transform.
Edit Query - Pop open a Command Window loaded with an SQL query that accomplishes the transform with given parameters.
Interpreting various combinations of specified (positive value) or auto-computed (zero or negative value) for Radius and Neighbors:
Specified Radius and Neighbors auto-computed = Use all neighbors within the specified radius.
Both Radius and Neighbors auto-computed = Use all Voronoi neighbors.
Specified number of Neighbors, but Radius auto-computed = Radius set by the system according to the global interpolation picture.
Specified number of Neighbors, and specified Radius = Use up to the specified number of neighbors within the specified radius.
Interpolation Model options:
- auto
- circular
- exponential
- gaussian
- linear
- power
- rational
- spherical
Regression model options:
- auto
- linear
- quadratic
Do not use a Resolution of 1 and a Unit of Degree when drawings are in a Latitude / Longitude coordinate system that uses degrees. That creates pixels which are 1 degree in size, many kilometers in size in most parts of the world. If drawings are in a coordinate system that uses meters or other linear unit, a Resolution of 30 using Meter as the Unit will create pixels that are 30 meters by 30 meters in size. To allow the widest choice of units it is best to do interpolations using drawings that have been projected into coordinate systems which use linear units of measure such as meters or feet and not angular units such as degrees.
About regression Kriging
Imagine an undulating surface that lies on the slope of a large hill, where if the surface were not bumpy we would have a smooth plane inclined at the overall angle of the hill. Suppose now we have many points that lie on the surface with each point providing the X,Y, and Z value of the surface at that point. Some regions of the surface have relatively few points or are lacking points.
The general task of Kriging is to take the collection of many points and to re-create the surface, filling in through computation some plausible interpolation in regions where sample points are sparse or missing. Ordinary Kriging simply takes the X,Y,Z values of the points and applies Kriging computations to interpolate a surface.
Regression Kriging first attempts to ascertain the overall inclined plane and to remove that as a bias, to allow considering the undulating surface as if it were arranged horizontally and not tilted on the overall slope of a hill. A Kriging calculation is performed on the adjusted, "as if level," coordinates of the points, and then the resulting interpolated surface is titled back to the original overall incline. The choice of linear or quadratic regression is a choice of how the original "overall" tilted-plane setting is determined.
Regression Kriging can identify and set aside more complex biases than the case of an undulating surface within a simple, overall incline in a hill. This non-mathematical description provides an analogy, not an exact phrasing of the math involved, to help non-mathematicians understand how Regression Kriging can provide better results than ordinary Kriging.
Interpolate : natural neighbors
Given a drawing with objects that have Z values in some field or which have Z values in their geometry, create an image and table using natural neighbors interpolation with Sibson weights to interpolate pixel values in tiles from Z values for each object. Natural neighbors interpolation is limited to interpolations within the convex hull of the source data. The Result destination is always a new table and image.
All geoms are converted to their constituent coordinates. Duplicate XY coordinates are ignored: if duplicate XY coordinates have different Z values, the function uses one of these values and ignores any other Z values.
Interpolation parameters:
Z - Field to use for interpolation value.
Resolution - Size of resulting pixels, in the specified units.
Unit - Unit of measure to use
Result - Destination for results, always (new table).
Channel type - Numeric type for pixel values.
New image - Name to use for the new image that is created.
New table - Name to use for the new table that is created to store the new image's tiles.
Resources - Options for allow full or no CPU and GPU parallelization.
Transform selection only - When checked, use only selected objects in the drawing for interpolation.
Transform - Apply the transform.
Edit Query - Pop open a Command Window loaded with an SQL query that accomplishes the transform with given parameters.
See the Wikipedia article on natural neighbor interpolation for the mathematics behind the method.
Do not use a Resolution of 1 and a Unit of Degree when drawings are in a Latitude / Longitude coordinate system that uses degrees. That creates pixels which are 1 degree in size, many kilometers in size in most parts of the world. If drawings are in a coordinate system that uses meters or other linear unit, a Resolution of 30 using Meter as the Unit will create pixels that are 30 meters by 30 meters in size. To allow the widest choice of units it is best to do interpolations using drawings that have been projected into coordinate systems which use linear units of measure such as meters or feet and not angular units such as degrees.
Interpolate : thin-plate spline
Given a drawing with objects that have Z values in some field or which have Z values in their geometry, create an image and table using thin-plate spline (TPS) interpolation to interpolate pixel values in tiles from Z values for each object. Thin-plate spline interpolation works both inside and outside the convex hull of the source data. The Result destination is always a new table and image.
All geoms are converted to their constituent coordinates. Duplicate XY coordinates are ignored: if duplicate XY coordinates have different Z values, the function uses one of these values and ignores any other Z values.
Interpolation parameters:
Z - Field to use for interpolation value.
Margin - Additional distance, in the specified units, to create the image beyond the bounding rectangle of vector data in the drawing.
Resolution - Size of resulting pixels, in the specified units.
Radius - Radius, in the specified units, for neighbor searches. 0 or negative = Auto.
Neighbors - Number of neighbors to use. 0 or negative = Auto.
Unit - Unit of measure to use
Result - Destination for results, always (new table).
Channel type - Numeric type for pixel values.
New image - Name to use for the new image that is created.
New table - Name to use for the new table that is created to store the new image's tiles.
Resources - Options for allow full or no CPU and GPU parallelization.
Transform selection only - When checked, use only selected objects in the drawing for interpolation.
Transform - Apply the transform.
Edit Query - Pop open a Command Window loaded with an SQL query that accomplishes the transform with given parameters.
See the Wolfram MathWorld article on thin-plate splines for the mathematics behind the method.
Do not use a Resolution of 1 and a Unit of Degree when drawings are in a Latitude / Longitude coordinate system that uses degrees. That creates pixels which are 1 degree in size, many kilometers in size in most parts of the world. If drawings are in a coordinate system that uses meters or other linear unit, a Resolution of 30 using Meter as the Unit will create pixels that are 30 meters by 30 meters in size. To allow the widest choice of units it is best to do interpolations using drawings that have been projected into coordinate systems which use linear units of measure such as meters or feet and not angular units such as degrees.
Interpolate : triangulation
Given a drawing with objects that have Z values in some field or which have Z values in their geometry, create an image and table using triangulation to interpolate pixel values in tiles from Z values for each object. The Result destination is always a new table and image.
All geoms are converted to their constituent coordinates. Duplicate XY coordinates are ignored: if duplicate XY coordinates have different Z values, the function uses one of these values and ignores any other Z values.
Interpolation parameters:
Z - Field to use for interpolation value.
Resolution - Size of resulting pixels, in the specified units.
Unit - Unit of measure to use
Result - Destination for results, always (new table).
Channel type - Numeric type for pixel values.
New image - Name to use for the new image that is created.
New table - Name to use for the new table that is created to store the new image's tiles.
Resources - Options for allow full or no CPU and GPU parallelization.
Transform selection only - When checked, use only selected objects in the drawing for interpolation.
Transform - Apply the transform.
Edit Query - Pop open a Command Window loaded with an SQL query that accomplishes the transform with given parameters.
Do not use a Resolution of 1 and a Unit of Degree when drawings are in a Latitude / Longitude coordinate system that uses degrees. That creates pixels which are 1 degree in size, many kilometers in size in most parts of the world. If drawings are in a coordinate system that uses meters or other linear unit, a Resolution of 30 using Meter as the Unit will create pixels that are 30 meters by 30 meters in size. To allow the widest choice of units it is best to do interpolations using drawings that have been projected into coordinate systems which use linear units of measure such as meters or feet and not angular units such as degrees.
Interpolate : triangulation with segments
Given a drawing with objects that have Z values in some field or which have Z values in their geometry, create an image and table using constrained triangulation to interpolate pixel values in tiles from Z values for each object. The Result destination is always a new table and image.
Areas are converted to boundary lines. The constrained triangulation keeps segments from lines and areas, which are converted to boundary lines. Duplicate XY coordinates are ignored: if duplicate XY coordinates have different Z values, the function uses one of these values and ignores any other Z values.
Interpolation parameters:
Z - Field to use for interpolation value.
Resolution - Size of resulting pixels, in the specified units.
Remove flat areas (DEST) - Improve triangulation of contours using a DEST (Determination of Earth Surface Structures) algorithm, which helps to remove or reduce terracing effects when contouring from contour lines or other regular data.
Unit - Unit of measure to use
Result - Destination for results, always (new table).
Channel type - Numeric type for pixel values.
New image - Name to use for the new image that is created.
New table - Name to use for the new table that is created to store the new image's tiles.
Resources - Options for allow full or no CPU and GPU parallelization.
Transform selection only - When checked, use only selected objects in the drawing for interpolation.
Transform - Apply the transform.
Edit Query - Pop open a Command Window loaded with an SQL query that accomplishes the transform with given parameters.
Do not use a Resolution of 1 and a Unit of Degree when drawings are in a Latitude / Longitude coordinate system that uses degrees. That creates pixels which are 1 degree in size, many kilometers in size in most parts of the world. If drawings are in a coordinate system that uses meters or other linear unit, a Resolution of 30 using Meter as the Unit will create pixels that are 30 meters by 30 meters in size. To allow the widest choice of units it is best to do interpolations using drawings that have been projected into coordinate systems which use linear units of measure such as meters or feet and not angular units such as degrees.
