org.geotools.referencing.operation.builder

Class ProjectiveTransformBuilder

• Direct Known Subclasses:
AffineTransformBuilder, SimilarTransformBuilder

public class ProjectiveTransformBuilder
extends MathTransformBuilder
Builds MathTransform setup as Projective transformation from a list of MappedPosition. The calculation uses least square method. The Projective transform equation: (2D). The calculation uses least square method. Projective transform equation:
[ x']   [  m00  m01  m02  ] [ x ]
[ y'] = [  m10  m11  m12  ] [ y ]
[ 1 ]   [  m20  m21    1  ] [ 1 ]                           x' = m * x

In the case that we have more identical points we can write it like this (in Matrix):
[ x'1 ]      [ x1 y1 1  0  0  0 -x'x  -x'y]   [ m00 ]
[ x'2 ]      [ x2 y2 1  0  0  0 -x'x  -x'y]   [ m01 ]
[  .  ]      [             .              ]   [ m02 ]
[  .  ]      [             .              ] * [ m10 ]
[ x'n ]   =  [ xn yn 1  0  0  0 -x'x  -x'y]   [ m11 ]
[ y'1 ]      [ 0  0  0  x1 y1 1 -y'x  -y'y]   [ m12 ]
[ y'2 ]      [ 0  0  0  x2 y2 1  -y'x  -y'y]   [ m20 ]
[  .  ]      [             .              ]   [ m21 ]
[  .  ]      [             .              ]
[ y'n ]      [ 0  0  0  xn yn 1  -y'x  -y'y]
x' = A*m
Using the least square method we get this result:
m = (ATPA)-1 ATPx'
Since:
2.4
Author:
Jan Jezek
• Method Detail

• getMinimumPointCount

public int getMinimumPointCount()
Returns the minimum number of points required by this builder, which is 4 by default. Subclasses like affine transform builders will reduce this minimum.
Specified by:
getMinimumPointCount in class MathTransformBuilder
Returns:
minimum number of points required by this builder, which is 4 by default.
• fillAMatrix

protected void fillAMatrix()
Fills A matrix for m = (ATPA)-1 ATPx' equation
• fillXMatrix

protected void fillXMatrix()
Fills x' matrix for m = (ATPA)-1 ATPx' equation
• includeWeights

public void includeWeights(boolean include)
throws MissingInfoException
Switch whether to include weights into the calculation. Weights are derived from each point accuracy. Weight p = 1 / accuracy2.
Parameters:
include - if true then the weights will be included onto the calculation. False is default.
Throws:
FactoryException - if all or some of the points does not have accuracy setup properly.
MissingInfoException
• calculateLSM

protected double[] calculateLSM()
Calculates the parameters using the least square method. The equation:
m = (ATA)-1 ATx'
Returns:
m matrix.
• getProjectiveMatrix

protected GeneralMatrix getProjectiveMatrix()
Returns the matrix of parameters for Projective transformation. This method should by override for the special cases like affine or similar transformation. The M matrix looks like this:
[  m00  m01  m02  ]
[  m10  m11  m12  ]
[  m20  m21   1   ]

Returns:
Matrix M