Package com.irurueta.geometry

Class ProjectiveTransformation2D

java.lang.Object
com.irurueta.geometry.Transformation2D
com.irurueta.geometry.ProjectiveTransformation2D
All Implemented Interfaces:
Serializable
public class ProjectiveTransformation2D extends Transformation2D implements Serializable
This class performs projective transformations on 2D space. Projective transformations include any possible transformation that can be applied to 2D points.
See Also:

  • Field Details

    • NUM_TRANSLATION_COORDS

      public static final int NUM_TRANSLATION_COORDS
      Constant indicating number of coordinates required in translation arrays.
      See Also:

    • NUM_PROJECTIVE_PARAMS

      public static final int NUM_PROJECTIVE_PARAMS
      Constant indicating the number of projective parameters that can be set in projective parameters array.
      See Also:

    • INHOM_COORDS

      public static final int INHOM_COORDS
      Constant defining number of inhomogeneous coordinates in 2D space.
      See Also:

    • HOM_COORDS

      public static final int HOM_COORDS
      Constant defining number of homogeneous coordinates in 2D space.
      See Also:

    • EPS

      public static final double EPS
      Machine precision.
      See Also:

    • LARGE_ROTATION_MATRIX_THRESHOLD

      private static final double LARGE_ROTATION_MATRIX_THRESHOLD
      Constant defining a large threshold to consider a matrix valid as rotation.
      See Also:

    • t

      private com.irurueta.algebra.Matrix t
      Internal 3x3 matrix containing transformation.

    • normalized

      private boolean normalized
      Indicates whether internal matrix is normalized.

  • Constructor Details

    • ProjectiveTransformation2D

      public ProjectiveTransformation2D()
      Empty constructor. Creates transformation that has no effect.

    • ProjectiveTransformation2D

      public ProjectiveTransformation2D(com.irurueta.algebra.Matrix t)
      Creates transformation with provided internal matrix. Notice that provided matrix should usually be invertible, otherwise the transformation will be degenerate and its inverse will not be available.
      Parameters:
      t - Internal 3x3 matrix.
      Throws:
      NullPointerException - raised if provided matrix is null.
      IllegalArgumentException - raised if provided matrix is not 3x3

    • ProjectiveTransformation2D

      public ProjectiveTransformation2D(double scale)
      Creates transformation with provided scale value.
      Parameters:
      scale - scale value. Values between 0.0 and 1.0 reduce objects, values greater than 1.0 enlarge objects and negative values reverse objects.

    • ProjectiveTransformation2D

      public ProjectiveTransformation2D(Rotation2D rotation)
      Creates transformation with provided rotation.
      Parameters:
      rotation - a 2D rotation.
      Throws:
      NullPointerException - raised if provided rotation is null.

    • ProjectiveTransformation2D

      public ProjectiveTransformation2D(double scale, Rotation2D rotation)
      Creates transformation with provided scale and rotation.
      Parameters:
      scale - Scale value. Values between 0.0 and 1.0 reduce objects, values greater than 1.0 enlarge objects and negative values reverse objects.
      rotation - a 2D rotation.
      Throws:
      NullPointerException - raised if provided rotation is null.

    • ProjectiveTransformation2D

      public ProjectiveTransformation2D(AffineParameters2D params, Rotation2D rotation)
      Creates transformation with provided affine parameters and rotation.
      Parameters:
      params - affine parameters including horizontal scaling, vertical scaling and skewness.
      rotation - a 2D rotation.
      Throws:
      NullPointerException - raised if provided parameters are null or if provided rotation is null.

    • ProjectiveTransformation2D

      public ProjectiveTransformation2D(double[] translation)
      Creates transformation with provided 2D translation.
      Parameters:
      translation - array indicating 2D translation using inhomogeneous coordinates.
      Throws:
      NullPointerException - raised if provided array is null.
      IllegalArgumentException - raised if length of array is not equal to NUM_TRANSLATION_COORDS.

    • ProjectiveTransformation2D

      public ProjectiveTransformation2D(com.irurueta.algebra.Matrix a, double[] translation)
      Creates transformation with provided affine linear mapping and translation.
      Parameters:
      a - affine linear mapping.
      translation - array indicating 2D translation using inhomogeneous coordinates.
      Throws:
      NullPointerException - raised if provided array is null or if affine linear mapping is null.
      IllegalArgumentException - raised if length of array is not equal to NUM_TRANSLATION_COORDS.

    • ProjectiveTransformation2D

      public ProjectiveTransformation2D(double scale, double[] translation)
      Creates transformation with provided scale and translation.
      Parameters:
      scale - scale value. Values between 0.0 and 1.0 reduce objects, values greater than 1.0 enlarge objects and negative values reverse objects.
      translation - array indicating 2D translation using inhomogeneous coordinates.
      Throws:
      NullPointerException - raised if provided translation is null
      IllegalArgumentException - raised if provided translation does not have length 2.

    • ProjectiveTransformation2D

      public ProjectiveTransformation2D(Rotation2D rotation, double[] translation)
      Creates transformation with provided rotation and translation.
      Parameters:
      rotation - a 2D rotation.
      translation - array indicating 2D translation using inhomogeneous coordinates.
      Throws:
      NullPointerException - raised if provided rotation or translation is null.
      IllegalArgumentException - raised if provided translation does not have length 2.

    • ProjectiveTransformation2D

      public ProjectiveTransformation2D(double scale, Rotation2D rotation, double[] translation)
      Creates transformation with provided scale, rotation and translation.
      Parameters:
      scale - Scale value. Values between 0.0 and 1.0 reduce objects, values greater than 1.0 enlarge objects and negative values reverse objects.
      rotation - a 2D rotation.
      translation - array indicating 2D translation using inhomogeneous coordinates.
      Throws:
      NullPointerException - raised if provided rotation or translation is null.
      IllegalArgumentException - raised if provided translation does not have length 2.

    • ProjectiveTransformation2D

      public ProjectiveTransformation2D(double scale, Rotation2D rotation, double[] translation, double[] projectiveParameters)
      Creates transformation with provided scale, rotation and translation.
      Parameters:
      scale - scale value. Values between 0.0 and 1.0 reduce objects, values greater than 1.0 enlarge objects and negative values reverse objects.
      rotation - a 2D rotation.
      translation - array indicating 2D translation using inhomogeneous coordinates.
      projectiveParameters - array of length 3 containing projective parameters.
      Throws:
      NullPointerException - raised if provided rotation or translation is null.
      IllegalArgumentException - raised if provided translation does not have length 2 or if projective parameters array doesn't have length 3.

    • ProjectiveTransformation2D

      public ProjectiveTransformation2D(AffineParameters2D params, Rotation2D rotation, double[] translation)
      Creates transformation with provided parameters, rotation and translation.
      Parameters:
      params - Affine parameters including horizontal scaling, vertical scaling and skewness.
      rotation - a 2D rotation.
      translation - array indicating 2D translation using inhomogeneous coordinates.
      Throws:
      NullPointerException - raised if provided parameters, rotation or translation is null.
      IllegalArgumentException - raised if provided translation does not have length 2.

    • ProjectiveTransformation2D

      public ProjectiveTransformation2D(AffineParameters2D params, Rotation2D rotation, double[] translation, double[] projectiveParameters)
      Creates transformation with provided parameters, rotation and translation.
      Parameters:
      params - affine parameters including horizontal scaling, vertical scaling and skewness.
      rotation - a 2D rotation.
      translation - array indicating 2D translation using inhomogeneous coordinates.
      projectiveParameters - array of length 3 containing projective parameters.
      Throws:
      NullPointerException - raised if provided parameters, rotation or translation is null.
      IllegalArgumentException - raised if provided translation does not have length 2 or if projective parameters array doesn't have length 3.

    • ProjectiveTransformation2D

      public ProjectiveTransformation2D(Point2D inputPoint1, Point2D inputPoint2, Point2D inputPoint3, Point2D inputPoint4, Point2D outputPoint1, Point2D outputPoint2, Point2D outputPoint3, Point2D outputPoint4) throws CoincidentPointsException
      Creates transformation by estimating its internal matrix by providing 4 corresponding original and transformed points.
      Parameters:
      inputPoint1 - 1st input point.
      inputPoint2 - 2nd input point.
      inputPoint3 - 3rd input point.
      inputPoint4 - 4th input point.
      outputPoint1 - 1st transformed point corresponding to 1st input point.
      outputPoint2 - 2nd transformed point corresponding to 2nd input point.
      outputPoint3 - 3rd transformed point corresponding to 3rd input point.
      outputPoint4 - 4th transformed point corresponding to 4th input point.
      Throws:
      CoincidentPointsException - raised if transformation cannot be estimated for some reason (point configuration degeneracy, duplicate points or numerical instabilities).

    • ProjectiveTransformation2D

      public ProjectiveTransformation2D(Line2D inputLine1, Line2D inputLine2, Line2D inputLine3, Line2D inputLine4, Line2D outputLine1, Line2D outputLine2, Line2D outputLine3, Line2D outputLine4) throws CoincidentLinesException
      Creates transformation by estimating its internal matrix by providing 4 corresponding original and transformed lines.
      Parameters:
      inputLine1 - 1st input line.
      inputLine2 - 2nd input line.
      inputLine3 - 3rd input line.
      inputLine4 - 4th input line.
      outputLine1 - 1st transformed line corresponding to 1st input line.
      outputLine2 - 2nd transformed line corresponding to 2nd input line.
      outputLine3 - 3rd transformed line corresponding to 3rd input line.
      outputLine4 - 4th transformed line corresponding to 4th input line.
      Throws:
      CoincidentLinesException - raised if transformation cannot be estimated for some reason (line configuration degeneracy, duplicate lines or numerical instabilities).

  • Method Details

    • getT

      public com.irurueta.algebra.Matrix getT()
      Returns internal matrix containing this transformation data. Point transformation is computed as t * x, where x is a 2D point expressed using homogeneous coordinates. Usually the internal transformation matrix will be invertible. When this is not the case, the transformation is considered degenerate and its inverse will not be available.
      Returns:
      internal transformation matrix.

    • setT

      public final void setT(com.irurueta.algebra.Matrix t)
      Sets internal matrix containing this transformation data. Point transformation is computed as t * x, where x is a 2D point expressed using homogeneous coordinates. Usually provided matrix will be invertible, when this is not the case this transformation will become degenerate and its inverse will not be available. This method does not check whether provided matrix is invertible or not.
      Parameters:
      t - transformation matrix.
      Throws:
      NullPointerException - raised if provided matrix is null.
      IllegalArgumentException - raised if provided matrix is not 3x3

    • isDegenerate

      public static boolean isDegenerate(com.irurueta.algebra.Matrix t)
      Returns boolean indicating whether provided matrix will produce a degenerate projective transformation or not.
      Parameters:
      t - a 3x3 matrix to be used as the internal matrix of a projective transformation.
      Returns:
      true if matrix will produce a degenerate transformation, false otherwise.
      Throws:
      IllegalArgumentException - raised if provided matrix is not 3x3.

    • isDegenerate

      public boolean isDegenerate()
      Indicates whether this transformation is degenerate. When a transformation is degenerate, its inverse cannot be computed.
      Returns:
      true if transformation is degenerate, false otherwise.

    • getA

      public com.irurueta.algebra.Matrix getA()
      Returns affine linear mapping matrix.
      Returns:
      linear mapping matrix.
      See Also:

    • setA

      public final void setA(com.irurueta.algebra.Matrix a)
      Sets affine linear mapping matrix.
      Parameters:
      a - linear mapping matrix.
      Throws:
      NullPointerException - raised if provided matrix is null.
      IllegalArgumentException - raised if provided matrix does not have size 2x2.
      See Also:

    • normalize

      public final void normalize()
      Normalizes current matrix instance.

    • getRotation

      public Rotation2D getRotation() throws com.irurueta.algebra.AlgebraException
      Returns the 2D rotation component associated to this transformation. Note: if this rotation instance is modified, its changes won't be reflected on this transformation until rotation is set again.
      Returns:
      2D rotation.
      Throws:
      com.irurueta.algebra.AlgebraException - if for some reason rotation cannot be estimated (usually because of numerical instability).

    • setRotation

      public void setRotation(Rotation2D rotation) throws com.irurueta.algebra.AlgebraException
      Sets 2D rotation for this transformation.
      Parameters:
      rotation - a 2D rotation.
      Throws:
      NullPointerException - raised if provided rotation is null.
      com.irurueta.algebra.AlgebraException - raised if for numerical reasons rotation cannot be set (usually because of numerical instability in parameters of this transformation).

    • addRotation

      public void addRotation(Rotation2D rotation) throws com.irurueta.algebra.AlgebraException
      Adds provided rotation to current rotation assigned to this transformation.
      Parameters:
      rotation - 2D rotation to be added.
      Throws:
      com.irurueta.algebra.AlgebraException - raised if for numerical reasons rotation cannot be set (usually because of numerical instability in parameters of this transformation).

    • setScale

      public void setScale(double scale) throws com.irurueta.algebra.AlgebraException
      Sets scale of this transformation.
      Parameters:
      scale - scale value to be set. A value between 0.0 and 1.0 indicates that objects will be reduced, a value greater than 1.0 indicates that objects will be enlarged, and a negative value indicates that objects will be reversed.
      Throws:
      com.irurueta.algebra.AlgebraException - raised if for numerical reasons scale cannot be set (usually because of numerical instability in parameters of this transformation).

    • getAffineParameters

      public AffineParameters2D getAffineParameters() throws com.irurueta.algebra.AlgebraException
      Gets affine parameters of associated to this instance. Affine parameters contain horizontal scale, vertical scale and skewness of axes.
      Returns:
      affine parameters.
      Throws:
      com.irurueta.algebra.AlgebraException - raised if for numerical reasons affine parameters cannot be retrieved (usually because of numerical instability of the internal matrix of this instance).

    • getAffineParameters

      public void getAffineParameters(AffineParameters2D result) throws com.irurueta.algebra.AlgebraException
      Computes affine parameters associated to this instance and stores the result in provided instance. Affine parameters contain horizontal scale, vertical scale and skewness of axes.
      Parameters:
      result - instance where affine parameters will be stored.
      Throws:
      com.irurueta.algebra.AlgebraException - raised if for numerical reasons affine parameters cannot be retrieved (usually because of numerical instability of the internal matrix of this instance).

    • setAffineParameters

      public void setAffineParameters(AffineParameters2D parameters) throws com.irurueta.algebra.AlgebraException
      Sets affine parameters associated to this instance. Affine parameters contain horizontal scale, vertical scale and skewness of axes.
      Parameters:
      parameters - affine parameters to be set.
      Throws:
      com.irurueta.algebra.AlgebraException - raised if for numerical reasons affine parameters cannot be set (usually because of numerical instability of the internal matrix of this instance).

    • getProjectiveParameters

      public double[] getProjectiveParameters()
      Returns the projective parameters associated to this instance. These parameters are the located in the last row of the internal transformation matrix. For affine, metric or Euclidean transformations this last row is always [0, 0, 1] (taking into account that transformation matrix is defined up to scale).
      Returns:
      Projective parameters returned as the array containing the values of the last row of the internal transformation matrix.

    • setProjectiveParameters

      public final void setProjectiveParameters(double[] params)
      Sets the projective parameters associated to this instance. These parameters will be set in the last row of the internal transformation matrix. For affine, matrix or Euclidean transformations parameters are always [0, 0, 1] (taking into account that transformation matrix is defined up to scale).
      Parameters:
      params - projective parameters to be set. It must be an array of length 3.
      Throws:
      IllegalArgumentException - raised if provided array does not have length 3.

    • getTranslation

      public double[] getTranslation()
      Returns 2D translation assigned to this transformation as an array expressed in inhomogeneous coordinates. Note: Updating the values of the returned array will not update the translation of this instance. To do so, translation needs to be set again.
      Returns:
      2D translation array.

    • getTranslation

      public void getTranslation(double[] out) throws com.irurueta.algebra.WrongSizeException
      Obtains 2D translation assigned to this transformation and stores result into provided array. Note: updating the values of the returned array will not update the translation of this instance. To do so, translation needs to be set.
      Parameters:
      out - array where translation values will be stored.
      Throws:
      com.irurueta.algebra.WrongSizeException - if provided array does not have length 2.

    • setTranslation

      public void setTranslation(double[] translation)
      Sets 2D translation assigned to this transformation as an array expressed in inhomogeneous coordinates.
      Parameters:
      translation - 2D translation array.
      Throws:
      IllegalArgumentException - raised if provided array does not have length equal to NUM_TRANSLATION_COORDS.

    • addTranslation

      public void addTranslation(double[] translation)
      Adds provided translation to current translation on this transformation. Provided translation must be expressed as an array of inhomogeneous coordinates.
      Parameters:
      translation - 2D translation array.
      Throws:
      IllegalArgumentException - raised if provided array does not have length equal to NUM_TRANSLATION_COORDS.

    • getTranslationX

      public double getTranslationX()
      Returns current x coordinate translation assigned to this transformation.
      Returns:
      X coordinate translation.

    • setTranslationX

      public void setTranslationX(double translationX)
      Sets x coordinate translation to be made by this transformation.
      Parameters:
      translationX - X coordinate translation to be set.

    • getTranslationY

      public double getTranslationY()
      Returns current y coordinate translation assigned to this transformation.
      Returns:
      Y coordinate translation.

    • setTranslationY

      public void setTranslationY(double translationY)
      Sets y coordinate translation to be made by this transformation.
      Parameters:
      translationY - Y coordinate translation to be set.

    • setTranslation

      public void setTranslation(double translationX, double translationY)
      Sets x, y coordinates of translation to be made by this transformation.
      Parameters:
      translationX - translation x coordinate to be set.
      translationY - translation y coordinate to be set.

    • setTranslation

      public void setTranslation(Point2D translation)
      Sets x, y coordinates of translation to be made by this transformation.
      Parameters:
      translation - translation to be set.

    • getTranslationPoint

      public Point2D getTranslationPoint()
      Gets x, y coordinates of translation to be made by this transformation as a new point.
      Returns:
      a new point containing translation coordinates.

    • getTranslationPoint

      public void getTranslationPoint(Point2D out)
      Gets x, y coordinates of translation to be made by this transformation and stores them into provided point.
      Parameters:
      out - point where translation coordinates will be stored.

    • addTranslationX

      public void addTranslationX(double translationX)
      Adds provided x coordinate to current translation assigned to this transformation.
      Parameters:
      translationX - X coordinate to be added to current translation.

    • addTranslationY

      public void addTranslationY(double translationY)
      Adds provided y coordinate to current translation assigned to this transformation.
      Parameters:
      translationY - Y coordinate to be added to current translation.

    • addTranslation

      public void addTranslation(double translationX, double translationY)
      Adds provided coordinates to current translation assigned ot this transformation.
      Parameters:
      translationX - x coordinate to be added to current translation.
      translationY - y coordinate to be added to current translation.

    • addTranslation

      public void addTranslation(Point2D translation)
      Adds provided coordinates to current translation assigned to this transformation.
      Parameters:
      translation - x, y coordinates to be added to current translation.

    • asMatrix

      public com.irurueta.algebra.Matrix asMatrix()
      Represents this transformation as a 3x3 matrix. A point can be transformed as t * p, where t is the transformation matrix and p is a point expressed as an homogeneous vector.
      Specified by:
      asMatrix in class Transformation2D
      Returns:
      This transformation in matrix form.

    • asMatrix

      public void asMatrix(com.irurueta.algebra.Matrix m)
      Represents this transformation as a 3x3 matrix and stores the result in provided instance.
      Specified by:
      asMatrix in class Transformation2D
      Parameters:
      m - Instance where transformation matrix will be stored.
      Throws:
      IllegalArgumentException - Raised if provided instance is not a 3x3 matrix.

    • transform

      public void transform(Point2D inputPoint, Point2D outputPoint)
      Transforms input point using this transformation and stores the result in provided output points.
      Specified by:
      transform in class Transformation2D
      Parameters:
      inputPoint - point to be transformed.
      outputPoint - instance where transformed point data will be stored.

    • transform

      public void transform(Conic inputConic, Conic outputConic) throws NonSymmetricMatrixException, com.irurueta.algebra.AlgebraException
      Transforms a conic using this transformation and stores the result into provided output conic.
      Specified by:
      transform in class Transformation2D
      Parameters:
      inputConic - conic to be transformed.
      outputConic - instance where data of transformed conic will be stored.
      Throws:
      NonSymmetricMatrixException - raised if due to numerical precision the resulting output conic matrix is not considered to be symmetric.
      com.irurueta.algebra.AlgebraException - raised if transform cannot be computed because of numerical instabilities.

    • transform

      public void transform(DualConic inputDualConic, DualConic outputDualConic) throws NonSymmetricMatrixException, com.irurueta.algebra.AlgebraException
      Transforms a dual conic using this transformation and stores the result into provided output dual conic.
      Specified by:
      transform in class Transformation2D
      Parameters:
      inputDualConic - Dual conic to be transformed.
      outputDualConic - Instance where data of transformed dual conic will be stored.
      Throws:
      NonSymmetricMatrixException - raised if due to numerical precision the resulting output dual conic matrix is not considered to be symmetric.
      com.irurueta.algebra.AlgebraException - Raised if transform cannot be computed because of numerical instabilities.

    • transform

      public void transform(Line2D inputLine, Line2D outputLine) throws com.irurueta.algebra.AlgebraException
      Transforms provided input line using this transformation and stores the result into provided output line instance.
      Specified by:
      transform in class Transformation2D
      Parameters:
      inputLine - line to be transformed.
      outputLine - instance where data of transformed line will be stored
      Throws:
      com.irurueta.algebra.AlgebraException - Raised if transform cannot be computed because of numerical instabilities.

    • inverse

      public void inverse() throws com.irurueta.algebra.AlgebraException
      Inverses this transformation.
      Throws:
      com.irurueta.algebra.AlgebraException - if inverse transform cannot be computed because of numerical instabilities.

    • inverseAndReturnNew

      public Transformation2D inverseAndReturnNew() throws com.irurueta.algebra.AlgebraException
      Computes the inverse of this transformation and returns the result as a new transformation instance.
      Returns:
      inverse transformation.
      Throws:
      com.irurueta.algebra.AlgebraException - if inverse transform cannot be computed because of numerical instabilities.

    • inverse

      protected void inverse(ProjectiveTransformation2D result) throws com.irurueta.algebra.AlgebraException
      Computes the inverse of this transformation and stores the result in provided instance.
      Parameters:
      result - Instance where inverse transformation will be stored.
      Throws:
      com.irurueta.algebra.AlgebraException - if inverse transform cannot be computed because of numerical instabilities.

    • combine

      public void combine(ProjectiveTransformation2D transformation)
      Combines this transformation with provided transformation. The combination is equivalent to multiplying the matrix of this transformation with the matrix of provided transformation.
      Parameters:
      transformation - transformation to be combined with.

    • combineAndReturnNew

      public ProjectiveTransformation2D combineAndReturnNew(ProjectiveTransformation2D transformation)
      Combines this transformation with provided transformation and returns the result as a new transformation instance. The combination is equivalent to multiplying the matrix of this transformation with the matrix of provided transformation.
      Parameters:
      transformation - transformation to be combined with.
      Returns:
      a new transformation resulting of the combination with this transformation and provided transformation.

    • combine

      private void combine(ProjectiveTransformation2D inputTransformation, ProjectiveTransformation2D outputTransformation)
      Combines this transformation with provided input transformation and stores the result into provided output transformation. The combination is equivalent to multiplying the matrix of this transformation with the matrix of provided input transformation.
      Parameters:
      inputTransformation - transformation to be combined with.
      outputTransformation - transformation where result will be stored.

    • setTransformationFromPoints

      public final void setTransformationFromPoints(Point2D inputPoint1, Point2D inputPoint2, Point2D inputPoint3, Point2D inputPoint4, Point2D outputPoint1, Point2D outputPoint2, Point2D outputPoint3, Point2D outputPoint4) throws CoincidentPointsException
      Estimates this transformation internal matrix by providing 4 corresponding original and transformed points.
      Parameters:
      inputPoint1 - 1st input point.
      inputPoint2 - 2nd input point.
      inputPoint3 - 3rd input point.
      inputPoint4 - 4th input point.
      outputPoint1 - 1st transformed point corresponding to 1st input point.
      outputPoint2 - 2nd transformed point corresponding to 2nd input point.
      outputPoint3 - 3rd transformed point corresponding to 3rd input point.
      outputPoint4 - 4th transformed point corresponding to 4th input point.
      Throws:
      CoincidentPointsException - raised if transformation cannot be estimated for some reason (point configuration degeneracy, duplicate points or numerical instabilities).

    • setTransformationFromLines

      public final void setTransformationFromLines(Line2D inputLine1, Line2D inputLine2, Line2D inputLine3, Line2D inputLine4, Line2D outputLine1, Line2D outputLine2, Line2D outputLine3, Line2D outputLine4) throws CoincidentLinesException
      Estimates this transformation internal matrix by providing 4 corresponding original and transformed lines.
      Parameters:
      inputLine1 - 1st input line.
      inputLine2 - 2nd input line.
      inputLine3 - 3rd input line.
      inputLine4 - 4th input line.
      outputLine1 - 1st transformed line corresponding to 1st input line.
      outputLine2 - 2nd transformed line corresponding to 2nd input line.
      outputLine3 - 3rd transformed line corresponding to 3rd input line.
      outputLine4 - 4th transformed line corresponding to 4th input line.
      Throws:
      CoincidentLinesException - raised if transformation cannot be estimated for some reason (line configuration degeneracy, duplicate line or numerical instabilities).