org.geotools.referencing.operation.builder
Class ProjectiveTransformBuilder

Object
  MathTransformBuilder
      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

Field Summary

protected GeneralMatrix	A Matrix of derivations
protected GeneralMatrix	P Matrix of wights
protected GeneralMatrix	X Matrix of target values

Fields inherited from class MathTransformBuilder

mtFactory

Constructor Summary

protected	ProjectiveTransformBuilder()
	ProjectiveTransformBuilder(List<MappedPosition> vectors) Creates ProjectiveTransformBuilder for the set of properties.

Method Summary

protected double[]	calculateLSM() Calculates the parameters using the least square method.
protected MathTransform	computeMathTransform() Calculates the math transform immediately.
protected void	fillAMatrix() Fills A matrix for m = (ATPA)-1 ATPx' equation
protected void	fillPMatrix() Fills P matrix for m = (ATPA)-1 ATPx' equation
protected void	fillXMatrix() Fills x' matrix for m = (ATPA)-1 ATPx' equation
Class<? extends CartesianCS>	getCoordinateSystemType() Returns the required coordinate system type, which is cartesian CS.
int	getMinimumPointCount() Returns the minimum number of points required by this builder, which is 4 by default.
protected GeneralMatrix	getProjectiveMatrix() Returns the matrix of parameters for Projective transformation.
void	includeWeights(boolean include) Switch whether to include weights into the calculation.

Methods inherited from class MathTransformBuilder

getDimension, getErrorStatistics, getMappedPositions, getMathTransform, getName, getSourceCRS, getSourcePoints, getTargetCRS, getTargetPoints, getTransformation, printPoints, setMappedPositions, setSourcePoints, setTargetPoints, toString

Methods inherited from class Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

Field Detail

A

protected GeneralMatrix A

Matrix of derivations

P

protected GeneralMatrix P

Matrix of wights

X

protected GeneralMatrix X

Matrix of target values

Constructor Detail

ProjectiveTransformBuilder

protected ProjectiveTransformBuilder()

ProjectiveTransformBuilder

public ProjectiveTransformBuilder(List<MappedPosition> vectors)
                           throws MismatchedSizeException,
                                  MismatchedDimensionException,
                                  MismatchedReferenceSystemException

Creates ProjectiveTransformBuilder for the set of properties.

Parameters:

vectors - list of MappedPosition

Throws:

MismatchedSizeException - if the number of properties is not set properly.

MismatchedDimensionException - if the dimension of properties is not set properly.

MismatchedReferenceSystemException - -if there is mismatch in coordinate system in MappedPosition

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.

getCoordinateSystemType

public Class<? extends CartesianCS> getCoordinateSystemType()

Returns the required coordinate system type, which is cartesian CS.

Overrides:

getCoordinateSystemType in class MathTransformBuilder

Returns:

required coordinate system type

fillPMatrix

protected void fillPMatrix()
                    throws MissingInfoException

Fills P matrix for m = (A^TPA)^-1 A^TPx' equation

Throws:

MissingInfoException - if accuracy is not defined.

fillAMatrix

protected void fillAMatrix()

Fills A matrix for m = (A^TPA)^-1 A^TPx' equation

fillXMatrix

protected void fillXMatrix()

Fills x' matrix for m = (A^TPA)^-1 A^TPx' 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

computeMathTransform

protected MathTransform computeMathTransform()

Description copied from class: MathTransformBuilder

Calculates the math transform immediately.

Specified by:

computeMathTransform in class MathTransformBuilder

Returns:

Math transform from MappedPosition.