Package us.ihmc.euclid.tools

Class Matrix3DFeatures

java.lang.Object

us.ihmc.euclid.tools.Matrix3DFeatures

public abstract class Matrix3DFeatures
extends java.lang.Object

Tools for extracting or testing features for a matrix 3D, see Matrix3DTools for operations on a matrix 3D.

Author:

Sylvain Bertrand

Field Summary

Fields

Modifier and Type	Field	Description
static double	EPS_CHECK_2D	Default tolerance for determining whether a matrix 3D represents a 2D transformation or not.
static double	EPS_CHECK_IDENTITY	Default tolerance for determining whether a matrix 3D represents the identity matrix or not.
static double	EPS_CHECK_ROTATION	Default tolerance for determining whether a matrix 3D represents a 3D rotation matrix or not.
static double	EPS_CHECK_SKEW	Default tolerance for determining whether a matrix 3D is skew symmetric or not.

Constructor Summary

Constructors

Constructor	Description
Matrix3DFeatures()

Method Summary

Modifier and Type	Method	Description
static void	checkIfRotationMatrix(double[] matrixArray)	Asserts that the given matrix is a rotation matrix.
static void	checkIfRotationMatrix(double m00, double m01, double m02, double m10, double m11, double m12, double m20, double m21, double m22)	Asserts that the given coefficients describe a rotation matrix.
static void	checkIfRotationMatrix(org.ejml.data.DenseMatrix64F matrix)	Asserts that the given dense-matrix is a rotation matrix.
static void	checkMatrixSize(org.ejml.data.DenseMatrix64F matrix)	Asserts that the given matrix is a 3-by-3 matrix.
static double	determinant(double m00, double m01, double m02, double m10, double m11, double m12, double m20, double m21, double m22)	Computes the determinant of the matrix described by the given 9 coefficients.
static boolean	epsilonEquals(Matrix3DReadOnly m1, Matrix3DReadOnly m2, double epsilon)	Tests on a per component basis if the two given matrices are equal to an epsilon.
static boolean	equals(Matrix3DReadOnly m1, Matrix3DReadOnly m2)	Tests on a per coefficient basis if the two matrices m1 and m2 are exactly equal.
static boolean	isIdentity(double m00, double m01, double m02, double m10, double m11, double m12, double m20, double m21, double m22)	Tests if the matrix described by the given 9 coefficients is equal to the identity matrix.
static boolean	isIdentity(double m00, double m01, double m02, double m10, double m11, double m12, double m20, double m21, double m22, double epsilon)	Tests if the matrix described by the given 9 coefficients is equal to the identity matrix.
static boolean	isMatrix2D(double m00, double m01, double m02, double m10, double m11, double m12, double m20, double m21, double m22, double epsilon)	Verify the matrix described by the 9 given coefficients is a transformation in the XY plane.
static boolean	isMatrixSkewSymmetric(double m00, double m01, double m02, double m10, double m11, double m12, double m20, double m21, double m22)	Verify if the matrix described by the 9 given coefficients is skew symmetric:
static boolean	isMatrixSkewSymmetric(double m00, double m01, double m02, double m10, double m11, double m12, double m20, double m21, double m22, double epsilon)	Verify if the matrix described by the 9 given coefficients is skew symmetric:
static boolean	isRotationMatrix(double[] matrixArray)	Tests if the given matrix is a rotation matrix.
static boolean	isRotationMatrix(double m00, double m01, double m02, double m10, double m11, double m12, double m20, double m21, double m22)	Verify if the given coefficients describe a rotation matrix.
static boolean	isRotationMatrix(double m00, double m01, double m02, double m10, double m11, double m12, double m20, double m21, double m22, double epsilon)	Verify if the given coefficients describe a rotation matrix.
static boolean	isRotationMatrix(org.ejml.data.DenseMatrix64F matrix)	Tests if the given matrix is a rotation matrix.

Methods inherited from class java.lang.Object

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

Field Detail

EPS_CHECK_IDENTITY

public static final double EPS_CHECK_IDENTITY

Default tolerance for determining whether a matrix 3D represents the identity matrix or not.

See Also:

Constant Field Values

EPS_CHECK_ROTATION

public static final double EPS_CHECK_ROTATION

Default tolerance for determining whether a matrix 3D represents a 3D rotation matrix or not.

See Also:

Constant Field Values

EPS_CHECK_2D

public static final double EPS_CHECK_2D

Default tolerance for determining whether a matrix 3D represents a 2D transformation or not.

See Also:

Constant Field Values

EPS_CHECK_SKEW

public static final double EPS_CHECK_SKEW

Default tolerance for determining whether a matrix 3D is skew symmetric or not.

See Also:

Constant Field Values

Constructor Detail

Matrix3DFeatures

public Matrix3DFeatures()

Method Detail

determinant

public static double determinant(double m00,
                                 double m01,
                                 double m02,
                                 double m10,
                                 double m11,
                                 double m12,
                                 double m20,
                                 double m21,
                                 double m22)

Computes the determinant of the matrix described by the given 9 coefficients.

Parameters:

m00 - first matrix element in the first row.

m01 - second matrix element in the first row.

m02 - third matrix element in the first row.

m10 - first matrix element in the second row.

m11 - second matrix element in the second row.

m12 - third matrix element in the second row.

m20 - first matrix element in the third row.

m21 - second matrix element in the third row.

m22 - third matrix element in the third row.

Returns:

the determinant of the matrix.

checkIfRotationMatrix

public static void checkIfRotationMatrix(org.ejml.data.DenseMatrix64F matrix)

Asserts that the given dense-matrix is a rotation matrix.

The given matrix is a rotation matrix if:

• the length of each row vector is equal to 1.0 +/- EPS_CHECK_ROTATION,
• the dot product of each pair of row vectors is equal to 0.0 +/- EPS_CHECK_ROTATION,
• the determinant of the matrix is equal to 1.0 +/- EPS_CHECK_ROTATION.

Parameters:

matrix - the matrix to verify. Not modified.

Throws:

NotARotationMatrixException - if the matrix is not a rotation matrix.

checkIfRotationMatrix

public static void checkIfRotationMatrix(double[] matrixArray)

Asserts that the given matrix is a rotation matrix.

The given matrix is a rotation matrix if:

• the length of each row vector is equal to 1.0 +/- EPS_CHECK_ROTATION,
• the dot product of each pair of row vectors is equal to 0.0 +/- EPS_CHECK_ROTATION,
• the determinant of the matrix is equal to 1.0 +/- EPS_CHECK_ROTATION.

Parameters:

matrixArray - the matrix to verify, not null, not modified. The array is expected to be encoded in a row-major format.

Throws:

NotARotationMatrixException - if the matrix is not a rotation matrix.

checkIfRotationMatrix

public static void checkIfRotationMatrix(double m00,
                                         double m01,
                                         double m02,
                                         double m10,
                                         double m11,
                                         double m12,
                                         double m20,
                                         double m21,
                                         double m22)

Asserts that the given coefficients describe a rotation matrix.

This method is meant for internal use only.

The given matrix is a rotation matrix if:

• the length of each row vector is equal to 1.0 +/- EPS_CHECK_ROTATION,
• the dot product of each pair of row vectors is equal to 0.0 +/- EPS_CHECK_ROTATION,
• the determinant of the matrix is equal to 1.0 +/- EPS_CHECK_ROTATION.

Parameters:

m00 - first matrix element in the first row.

m01 - second matrix element in the first row.

m02 - third matrix element in the first row.

m10 - first matrix element in the second row.

m11 - second matrix element in the second row.

m12 - third matrix element in the second row.

m20 - first matrix element in the third row.

m21 - second matrix element in the third row.

m22 - third matrix element in the third row.

Throws:

NotARotationMatrixException - if the matrix is not a rotation matrix.

checkMatrixSize

public static void checkMatrixSize(org.ejml.data.DenseMatrix64F matrix)

Asserts that the given matrix is a 3-by-3 matrix.

Parameters:

matrix - the matrix to verify. Not modified.

Throws:

java.lang.RuntimeException - if the matrix is not a 3-by-3 matrix.

isIdentity

public static boolean isIdentity(double m00,
                                 double m01,
                                 double m02,
                                 double m10,
                                 double m11,
                                 double m12,
                                 double m20,
                                 double m21,
                                 double m22)

Tests if the matrix described by the given 9 coefficients is equal to the identity matrix.

The assertion is done on a per coefficient basis using EPS_CHECK_IDENTITY as the tolerance.

Parameters:

m00 - first matrix element in the first row.

m01 - second matrix element in the first row.

m02 - third matrix element in the first row.

m10 - first matrix element in the second row.

m11 - second matrix element in the second row.

m12 - third matrix element in the second row.

m20 - first matrix element in the third row.

m21 - second matrix element in the third row.

m22 - third matrix element in the third row.

Returns:

true if the matrix is considered to be equal to the identity matrix, false otherwise.

isIdentity

public static boolean isIdentity(double m00,
                                 double m01,
                                 double m02,
                                 double m10,
                                 double m11,
                                 double m12,
                                 double m20,
                                 double m21,
                                 double m22,
                                 double epsilon)

Tests if the matrix described by the given 9 coefficients is equal to the identity matrix.

The assertion is done on a per coefficient basis using epsilon as the tolerance.

Parameters:

m00 - first matrix element in the first row.

m01 - second matrix element in the first row.

m02 - third matrix element in the first row.

m10 - first matrix element in the second row.

m11 - second matrix element in the second row.

m12 - third matrix element in the second row.

m20 - first matrix element in the third row.

m21 - second matrix element in the third row.

m22 - third matrix element in the third row.

epsilon - the tolerance as shown above.

Returns:

true if the matrix is considered to be equal to the identity matrix, false otherwise.

isRotationMatrix

public static boolean isRotationMatrix(org.ejml.data.DenseMatrix64F matrix)

Tests if the given matrix is a rotation matrix.

The given matrix is a rotation matrix if:

• the length of each row vector is equal to 1.0 +/- EPS_CHECK_ROTATION,
• the dot product of each pair of row vectors is equal to 0.0 +/- EPS_CHECK_ROTATION,
• the determinant of the matrix is equal to 1.0 +/- EPS_CHECK_ROTATION.

Parameters:

matrix - the matrix to verify, not null, not modified.

Returns:

true if the given matrix is a rotation matrix, false otherwise.

isRotationMatrix

public static boolean isRotationMatrix(double[] matrixArray)

Tests if the given matrix is a rotation matrix.

The given matrix is a rotation matrix if:

• the length of each row vector is equal to 1.0 +/- EPS_CHECK_ROTATION,
• the dot product of each pair of row vectors is equal to 0.0 +/- EPS_CHECK_ROTATION,
• the determinant of the matrix is equal to 1.0 +/- EPS_CHECK_ROTATION.

Parameters:

matrixArray - the matrix to verify, not null, not modified. The array is expected to be encoded in a row-major format.

Returns:

true if the given matrix is a rotation matrix, false otherwise.

isRotationMatrix

public static boolean isRotationMatrix(double m00,
                                       double m01,
                                       double m02,
                                       double m10,
                                       double m11,
                                       double m12,
                                       double m20,
                                       double m21,
                                       double m22)

Verify if the given coefficients describe a rotation matrix.

The given matrix is a rotation matrix if:

• the length of each row vector is equal to 1.0 +/- EPS_CHECK_ROTATION,
• the dot product of each pair of row vectors is equal to 0.0 +/- EPS_CHECK_ROTATION,
• the determinant of the matrix is equal to 1.0 +/- EPS_CHECK_ROTATION.

Parameters:

m00 - first matrix element in the first row.

m01 - second matrix element in the first row.

m02 - third matrix element in the first row.

m10 - first matrix element in the second row.

m11 - second matrix element in the second row.

m12 - third matrix element in the second row.

m20 - first matrix element in the third row.

m21 - second matrix element in the third row.

m22 - third matrix element in the third row.

Returns:

true if the given matrix is a rotation matrix, false otherwise.

isRotationMatrix

public static boolean isRotationMatrix(double m00,
                                       double m01,
                                       double m02,
                                       double m10,
                                       double m11,
                                       double m12,
                                       double m20,
                                       double m21,
                                       double m22,
                                       double epsilon)

Verify if the given coefficients describe a rotation matrix.

The given matrix is a rotation matrix if:

• the length of each row vector is equal to 1.0 +/- EPS_CHECK_ROTATION,
• the dot product of each pair of row vectors is equal to 0.0 +/- EPS_CHECK_ROTATION,
• the determinant of the matrix is equal to 1.0 +/- EPS_CHECK_ROTATION.

Parameters:

m00 - first matrix element in the first row.

m01 - second matrix element in the first row.

m02 - third matrix element in the first row.

m10 - first matrix element in the second row.

m11 - second matrix element in the second row.

m12 - third matrix element in the second row.

m20 - first matrix element in the third row.

m21 - second matrix element in the third row.

m22 - third matrix element in the third row.

epsilon - the tolerance as shown above.

Returns:

true if the given matrix is a rotation matrix, false otherwise.

isMatrix2D

public static boolean isMatrix2D(double m00,
                                 double m01,
                                 double m02,
                                 double m10,
                                 double m11,
                                 double m12,
                                 double m20,
                                 double m21,
                                 double m22,
                                 double epsilon)

Verify the matrix described by the 9 given coefficients is a transformation in the XY plane.

The matrix is considered to be a 2D transformation in the XY plane if:

• the last diagonal coefficient m22 is equal to 1.0 +/- epsilon,
• the coefficients m20, m02, m21, and m12 are equal to 0.0 +/- epsilon.

Parameters:

m00 - first matrix element in the first row.

m01 - second matrix element in the first row.

m02 - third matrix element in the first row.

m10 - first matrix element in the second row.

m11 - second matrix element in the second row.

m12 - third matrix element in the second row.

m20 - first matrix element in the third row.

m21 - second matrix element in the third row.

m22 - third matrix element in the third row.

epsilon - the tolerance used as shown above.

Returns:

true if the given matrix describes a 2D transformation in the XY plane, false otherwise.

isMatrixSkewSymmetric

public static boolean isMatrixSkewSymmetric(double m00,
                                            double m01,
                                            double m02,
                                            double m10,
                                            double m11,
                                            double m12,
                                            double m20,
                                            double m21,
                                            double m22)

Verify if the matrix described by the 9 given coefficients is skew symmetric:

     |  0 -z  y |
 m = |  z  0 -x |
     | -y  x  0 |
 

The given matrix is considered to be skew symmetric if:

• each diagonal coefficient is equal to 0.0 +/- EPS_CHECK_SKEW,
• the sum of each pair of cross diagonal coefficients (m10, m01), (m12, m21), and (m20, m02) are equal to 0.0 +/- EPS_CHECK_SKEW.

Parameters:

m00 - first matrix element in the first row.

m01 - second matrix element in the first row.

m02 - third matrix element in the first row.

m10 - first matrix element in the second row.

m11 - second matrix element in the second row.

m12 - third matrix element in the second row.

m20 - first matrix element in the third row.

m21 - second matrix element in the third row.

m22 - third matrix element in the third row.

Returns:

true if the matrix is skew symmetric, false otherwise.

isMatrixSkewSymmetric

public static boolean isMatrixSkewSymmetric(double m00,
                                            double m01,
                                            double m02,
                                            double m10,
                                            double m11,
                                            double m12,
                                            double m20,
                                            double m21,
                                            double m22,
                                            double epsilon)

Verify if the matrix described by the 9 given coefficients is skew symmetric:

     |  0 -z  y |
 m = |  z  0 -x |
     | -y  x  0 |
 

The given matrix is considered to be skew symmetric if:

• each diagonal coefficient is equal to 0.0 +/- EPS_CHECK_SKEW,
• the sum of each pair of cross diagonal coefficients (m10, m01), (m12, m21), and (m20, m02) are equal to 0.0 +/- EPS_CHECK_SKEW.

Parameters:

m00 - first matrix element in the first row.

m01 - second matrix element in the first row.

m02 - third matrix element in the first row.

m10 - first matrix element in the second row.

m11 - second matrix element in the second row.

m12 - third matrix element in the second row.

m20 - first matrix element in the third row.

m21 - second matrix element in the third row.

m22 - third matrix element in the third row.

epsilon - the tolerance used as shown above.

Returns:

true if the matrix is skew symmetric, false otherwise.

epsilonEquals

public static boolean epsilonEquals(Matrix3DReadOnly m1,
                                    Matrix3DReadOnly m2,
                                    double epsilon)

Tests on a per component basis if the two given matrices are equal to an epsilon.

Parameters:

m1 - the first matrix. Not modified.

m2 - the second matrix. Not modified.

epsilon - the tolerance to use when comparing each component.

Returns:

true if the two matrices are equal, false otherwise.

equals

public static boolean equals(Matrix3DReadOnly m1,
                             Matrix3DReadOnly m2)

Tests on a per coefficient basis if the two matrices m1 and m2 are exactly equal.

If any of the two matrices is null, this methods returns false.

Parameters:

m1 - the first matrix. Not modified.

m2 - the second matrix. Not modified.

Returns:

true if the two matrices are exactly equal, false otherwise or if at least one of the two matrices is null.