org.geotools.referencing.operation.builder

Class AffineTransformBuilder

Object

MathTransformBuilder

ProjectiveTransformBuilder

AffineTransformBuilder

public class AffineTransformBuilder
extends ProjectiveTransformBuilder

Builds MathTransform setup as Affine transformation from a list of MappedPosition. The calculation uses least square method. The Affine transform equation:

  [ x']   [  m00  m01  m02  ] [ x ]   [ m00x + m01y + m02 ]
  [ y'] = [  m10  m11  m12  ] [ y ] = [ m10x + m11y + m12 ]
  [ 1 ]   [   0    0    1   ] [ 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 ]   [ m00 ]
  [ x'2 ]      [ x2 y2 1  0  0  0 ]   [ m01 ]
  [  .  ]      [        .         ]   [ m02 ]
  [  .  ]      [        .         ] * [ m10 ]
  [ x'n ]   =  [ xn yn 1  0  0  0 ]   [ m11 ]
  [ y'1 ]      [ 0  0  0  x1 y1 1 ]   [ m12 ]
  [ y'2 ]      [ 0  0  0  x2 y2 1 ]
  [  .  ]      [        .         ]
  [  .  ]      [        .         ]
  [ y'n ]      [ 0  0  0  xn yn 1 ]
  x' = A*m 

Using the least square method we get this result:

  m = (ATA)-1 ATx'  
 

Since:

2.4

Author:

Jan Jezek

Field Summary

Fields inherited from class ProjectiveTransformBuilder

A, P, X

Fields inherited from class MathTransformBuilder

mtFactory

Constructor Summary

Constructors

Modifier	Constructor and Description
protected	AffineTransformBuilder()
	AffineTransformBuilder(List<MappedPosition> vectors) Creates AffineTransformBuilder for the set of properties.

Method Summary

Modifier and Type	Method and Description
protected void	fillAMatrix() Fills A matrix for m = (ATPA)-1 ATPx' equation
int	getMinimumPointCount() Returns the minimum number of points required by this builder, which is 3.
protected GeneralMatrix	getProjectiveMatrix() Returns the matrix for Projective transformation setup as Affine.

Methods inherited from class ProjectiveTransformBuilder

calculateLSM, computeMathTransform, fillPMatrix, fillXMatrix, getCoordinateSystemType, includeWeights

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

Constructor Detail

AffineTransformBuilder

protected AffineTransformBuilder()

AffineTransformBuilder

public AffineTransformBuilder(List<MappedPosition> vectors)
                       throws IllegalArgumentException,
                              MismatchedDimensionException,
                              MismatchedReferenceSystemException

Creates AffineTransformBuilder for the set of properties.

Parameters:

vectors - list of MappedPosition

Throws:

IllegalArgumentException

MismatchedDimensionException

MismatchedReferenceSystemException

Method Detail

getMinimumPointCount

public int getMinimumPointCount()

Returns the minimum number of points required by this builder, which is 3.

Overrides:

getMinimumPointCount in class ProjectiveTransformBuilder

Returns:

the minimum number of points required by this builder, which is 3.

getProjectiveMatrix

protected GeneralMatrix getProjectiveMatrix()

Returns the matrix for Projective transformation setup as Affine. The M matrix looks like this:

 [  m00  m01  m02  ]
 [  m10  m11  m12  ]
 [   0    0    1   ]
 

Overrides:

getProjectiveMatrix in class ProjectiveTransformBuilder

Returns:

Matrix M.

fillAMatrix

protected void fillAMatrix()

Description copied from class: ProjectiveTransformBuilder

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

Overrides:

fillAMatrix in class ProjectiveTransformBuilder