Functions to create new PointCloud objects by transforming their points. More...

Data Structures
struct	CVC3DTransformation
	Affine transformation matrix. More...

Typedefs
typedef double	CVC3DMatrix[3][3]
	Row-major 3x3 matrix. More...

typedef double	CVC3DMatrixH[4][4]
	Row-major 4x4 matrix. More...

typedef double	CVC3DVector[3]
	x, y, z vector. More...

Functions
cvbres_t	CVC3DAlignToXYPlane (const CVC3DPlane &Plane, CVC3DTransformation &Transformation)
	Calculates a rigid body transformation that maps a specified plane into the xy plane of the global coordinate system. More...

cvbres_t	CVC3DCreateConvertedPointCloud (CVCOMPOSITE PointCloudIn, cvbval_t Flags, CVCOMPOSITE &PointCloudOut)
	Creates a new point cloud which is a copy from PointCloudIn, but with possibly different cvbdatatype_t and number of components. More...

cvbres_t	CVC3DCreateScaledPointCloud (CVCOMPOSITE PointCloudIn, CVC3DFactors Factors, CVCOMPOSITE &PointCloudOut)
	Creates a new point cloud with all points being scaled by the given Factors. More...

cvbres_t	CVC3DCreateTransformedPointCloud (CVCOMPOSITE PointCloudIn, const CVC3DTransformation &AffineTransformation, CVCOMPOSITE &PointCloudOut)
	Creates a new point cloud with all points being transformed by the given AffineTransformation. More...

cvbres_t	CVC3DCreateTransformedPointCloudH (CVCOMPOSITE PointCloudIn, const CVC3DMatrixH Transformation, CVCOMPOSITE &PointCloudOut)
	Creates a new point cloud with all points being transformed by the given Transformation. More...

cvbres_t	CVC3DInvertMatrix (const CVC3DMatrix A, CVC3DMatrix AInv)
	Computes the inverse of matrix A, if possible. More...

cvbres_t	CVC3DInvertTransformation (const CVC3DTransformation &A, CVC3DTransformation &AInv)
	Computes the inverse of the transformation matrix A, if possible. More...

cvbres_t	CVC3DMatrixDeterminant (const CVC3DMatrix A, double &Determinant)
	Calculates the Determinant of the given matrix A. More...

cvbres_t	CVC3DMatrixFromRollPitchYawScale (double Roll, double Pitch, double Yaw, CVC3DFactors Scale, CVC3DMatrix TransformationMatrix)
	Computes the transformation matrix M from the given Euler angles Roll, Pitch, Yaw and scaling Scale in x, y, z. More...

cvbres_t	CVC3DMatrixFromRotationAnglesScale (double Alpha, double Beta, double Gamma, CVC3DFactors Scale, CVC3DMatrix TransformationMatrix)
	Computes the transformation matrix M from the given Euler angles Alpha, Beta, Gamma and scaling Scale in x, y, z. More...

cvbres_t	CVC3DMultiplyMatrices (const CVC3DMatrix A, const CVC3DMatrix B, CVC3DMatrix R)
	Multiplies two matrices A and B. More...

cvbres_t	CVC3DMultiplyTransformations (const CVC3DTransformation &A, const CVC3DTransformation &B, CVC3DTransformation &R)
	Multiplies two transformation matrices A and B. More...

cvbres_t	CVC3DRollPitchYawFromRotationMatrix (const CVC3DMatrix R, double &Roll, double &Pitch, double &Yaw)
	Computes the Euler angles Roll, Pitch and Yaw from the given rotation matrix R. More...

cvbres_t	CVC3DRollPitchYawScaleFromMatrix (const CVC3DMatrix TransformationMatrix, double &Roll, double &Pitch, double &Yaw, CVC3DFactors &Scale)
	Computes the Euler angles Roll, Pitch, Yaw and the scaling Scale in x, y and z from the given transformation matrix TransformationMatrix. More...

cvbres_t	CVC3DRollPitchYawScaleFromMatrixApproximation (const CVC3DMatrix TransformationMatrix, double &Roll, double &Pitch, double &Yaw, CVC3DFactors &Scale, double &PrecisionOfApproximation)
	Estimates the Euler angles Roll, Pitch, Yaw and the scaling Scale in x, y and z from the given transformation matrix TransformationMatrix. The transformation matrix may be noisy. More...

cvbres_t	CVC3DRotationAnglesFromRotationMatrix (const CVC3DMatrix R, double &Alpha, double &Beta, double &Gamma)
	Computes the Euler angles Alpha, Beta and Gamma from the given rotation matrix R. More...

cvbres_t	CVC3DRotationAnglesScaleFromMatrix (const CVC3DMatrix TransformationMatrix, double &Alpha, double &Beta, double &Gamma, CVC3DFactors &Scale)
	Computes the Euler angles Alpha, Beta, Gamma and the scaling in x, y and z from the given transformation matrix TransformationMatrix. More...

cvbres_t	CVC3DRotationAnglesScaleFromMatrixApproximation (const CVC3DMatrix TransformationMatrix, double &Alpha, double &Beta, double &Gamma, CVC3DFactors &Scale, double &PrecisionOfApproximation)
	Estimates the Euler angles Alpha, Beta, Gamma and the scaling in x, y and z from the given transformation matrix TransformationMatrix. The transformation matrix may be noisy. More...

cvbres_t	CVC3DRotationMatrixFromRollPitchYaw (double Roll, double Pitch, double Yaw, CVC3DMatrix R)
	Computes the rotation matrix R from the given Euler angles Roll, Pitch and Yaw. More...

cvbres_t	CVC3DRotationMatrixFromRotationAngles (double Alpha, double Beta, double Gamma, CVC3DMatrix R)
	Computes the rotation matrix R from the given Euler angles Alpha, Beta and Gamma. More...

cvbres_t	CVC3DTransformationDeterminant (const CVC3DTransformation &A, double &Determinant)
	Calculates the Determinant of the given transformation matrix A. More...

cvbres_t	CVC3DTransformPointCloud (CVCOMPOSITE PointCloudIn, const CVC3DTransformation &AffineTransformation, CVCOMPOSITE PointCloudOut)
	Transforms all points in PointCloudIn by the given AffineTransformation and stores them in PointCloudOut. More...

cvbres_t	CVC3DTransformPointCloudH (CVCOMPOSITE PointCloudIn, const CVC3DMatrixH Transformation, CVCOMPOSITE PointCloudOut)
	Transforms all points in PointCloudIn by the given Transformation and stores them in PointCloudOut. More...

Detailed Description

Functions to create new PointCloud objects by transforming their points.

Typedef Documentation

◆ CVC3DMatrix

CVC3DMatrix

Row-major 3x3 matrix.

This matrix is used e.g. in CVC3DTransformation for e.g. scaling or rotation.

Example: Initialize a unit matrix:
CVC3DMatrix m;

for(int row = 0; row < 3; ++row)

{

for(int column = 0; column < 3; ++column)

{

if (row == column)

m[row][column] = 1.0;

else

m[row][column] = 0.0;

}

}

CVC3DMatrix
double CVC3DMatrix[3][3]
Row-major 3x3 matrix.
Definition: iCVCore3D.h:22

◆ CVC3DMatrixH

CVC3DMatrixH

Row-major 4x4 matrix.

This matrix is used e.g. in CVC3DTransformPointCloudH for general homography transformation including perspective (pinhole camera model).

Example: Initialize a unit matrix:
CVC3DMatrixH m;

for(int row = 0; row < 4; ++row)

{

for(int column = 0; column < 4; ++column)

{

if (row == column)

m[row][column] = 1.0;

else

m[row][column] = 0.0;

}

}

CVC3DMatrixH
double CVC3DMatrixH[4][4]
Row-major 4x4 matrix.
Definition: iCVCore3D.h:23

◆ CVC3DVector

CVC3DVector

x, y, z vector.

This vector is used e.g. in CVC3DTransformation for translations.

Function Documentation

◆ CVC3DAlignToXYPlane()

cvbres_t CVC3DAlignToXYPlane	(	const CVC3DPlane &	Plane,
		CVC3DTransformation &	Transformation
	)

Calculates a rigid body transformation that maps a specified plane into the xy plane of the global coordinate system.

If a point cloud contains a tilted plane (e.g. representing a conveyer belt), which is not aligned to the xy plane, the following steps should be taken:

Calulate a plane fit on the data using function CVC3DPointCloudCalculatePlaneFromCuboid.
Align the output plane to the xy plane with CVC3DAlignToXYPlane.

Please note the following:

The transformation includes only a rotation about x and y axis. The resulting transformation will not contain any rotation about the global Z-axis.
The translation to the origin of the global coordinate system is done along z axis.

Parameters

[in]	Plane	Plane to be aligned.
[out]	Transformation	Calculated transformation to move given plane to xy plane.

Returns

CVC_ERROR (CVC_E_OK) on success
CVC_ERROR (CVC_E_PARAMETER) Plane parallel to z axis

◆ CVC3DCreateConvertedPointCloud()

cvbres_t CVC3DCreateConvertedPointCloud	(	CVCOMPOSITE	PointCloudIn,
		cvbval_t	Flags,
		CVCOMPOSITE &	PointCloudOut
	)

Creates a new point cloud which is a copy from PointCloudIn, but with possibly different cvbdatatype_t and number of components.

The given PointCloudIn must have a valid CVC3DPointCloudLayout.

Note: PointCloudOut has the same properties as if a new point cloud was created via CVC3DCreateDuplicatePointCloud. If the Flags result in the same cvbdatatype_t/number of components, this function behaves like CVC3DCreateDuplicatePointCloud.

: If this function returns successfully you need to release the returned PointCloudOut via ReleaseObject if not needed anymore.

Parameters

[in]	PointCloudIn	Handle to point cloud object to convert.
[in]	Flags	CVC3DPointCloudFlags specifying the kind of point cloud to be created.
[out]	PointCloudOut	Variable to receive the handle of the resulting point cloud.

Returns

CVC_ERROR (CVC_E_OK) on success
CVC_ERROR (CVC_E_WRONGOBJECT) if PointCloudIn is not a valid point cloud IComposite.
CVC_ERROR (CVC_E_PARAMETER) if Flags contain an unsupported combination.
CVC_ERROR (CVC_E_MEMORY) if not enough memory was available to create the point cloud.

See also: CVC3DCreateSparsePointCloud, CVC3DCreateDuplicatePointCloud.

◆ CVC3DCreateScaledPointCloud()

cvbres_t CVC3DCreateScaledPointCloud	(	CVCOMPOSITE	PointCloudIn,
		CVC3DFactors	Factors,
		CVCOMPOSITE &	PointCloudOut
	)

Creates a new point cloud with all points being scaled by the given Factors.

The given PointCloudIn must have a valid CVC3DPointCloudLayout.

Note: PointCloudOut has the same properties as if a new point cloud was created via CVC3DCreateDuplicatePointCloud.

: If this function returns successfully you need to release the returned PointCloudOut via ReleaseObject if not needed anymore.

Parameters

[in]	PointCloudIn	Handle to point cloud object to scale.
[in]	Factors	Scale factors to be applied to each point.
[out]	PointCloudOut	Variable to receive the scaled point cloud.

Returns

CVC_ERROR (CVC_E_OK) on success.
CVC_ERROR (CVC_E_PARAMETER) if Factors contain NaN.
CVC_ERROR (CVC_E_WRONGOBJECT) if PointCloudIn is not a valid point cloud.
CVC_ERROR (CVC_E_NOTENOUGHDATA) if PointCloudIn is empty.
CVC_ERROR (CVC_E_MEMORY) if not enough memory was available to create the point cloud.

◆ CVC3DCreateTransformedPointCloud()

cvbres_t CVC3DCreateTransformedPointCloud	(	CVCOMPOSITE	PointCloudIn,
		const CVC3DTransformation &	AffineTransformation,
		CVCOMPOSITE &	PointCloudOut
	)

Creates a new point cloud with all points being transformed by the given AffineTransformation.

The given PointCloudIn must have a valid CVC3DPointCloudLayout.

Note: PointCloudOut has the same properties as if a new point cloud was created via CVC3DCreateDuplicatePointCloud.

: If this function returns successfully you need to release the returned PointCloudOut via ReleaseObject if not needed anymore.

Parameters

[in]	PointCloudIn	Handle to point cloud object to be transformed.
[in]	AffineTransformation	Homogeneous transformation matrix.
[out]	PointCloudOut	Variable to receive the transformed point cloud.

Returns

CVC_ERROR (CVC_E_OK) on success
CVC_ERROR (CVC_E_PARAMETER) if AffineTransformation contains NaN.
CVC_ERROR (CVC_E_WRONGOBJECT) if PointCloudIn is not a valid point cloud.
CVC_ERROR (CVC_E_NOTENOUGHDATA) if PointCloudIn is empty.
CVC_ERROR (CVC_E_MEMORY) if not enough memory was available to create the point cloud.

See also: CVC3DTransformPointCloudH, CVC3DCreateTransformedPointCloudH, CVC3DTransformPointCloud

◆ CVC3DCreateTransformedPointCloudH()

cvbres_t CVC3DCreateTransformedPointCloudH	(	CVCOMPOSITE	PointCloudIn,
		const CVC3DMatrixH	Transformation,
		CVCOMPOSITE &	PointCloudOut
	)

Creates a new point cloud with all points being transformed by the given Transformation.

The given PointCloudIn must have a valid CVC3DPointCloudLayout.

Note: PointCloudOut has the same properties as if a new point cloud was created via CVC3DCreateDuplicatePointCloud.

: If this function returns successfully you need to release the returned PointCloudOut via ReleaseObject if not needed anymore.

Parameters

[in]	PointCloudIn	Handle to point cloud object to be transformed.
[in]	Transformation	Homogeneous transformation matrix.
[out]	PointCloudOut	Variable to receive the transformed point cloud.

Returns

CVC_ERROR (CVC_E_OK) on success
CVC_ERROR (CVC_E_PARAMETER) if Transformation contains NaN or is nullptr.
CVC_ERROR (CVC_E_WRONGOBJECT) if PointCloudIn is not a valid point cloud.
CVC_ERROR (CVC_E_NOTENOUGHDATA) if PointCloudIn is empty.
CVC_ERROR (CVC_E_MEMORY) if not enough memory was available to create the point cloud.

See also: CVC3DTransformPointCloudH, CVC3DCreateTransformedPointCloud, CVC3DTransformPointCloud

◆ CVC3DInvertMatrix()

cvbres_t CVC3DInvertMatrix	(	const CVC3DMatrix	A,
		CVC3DMatrix	AInv
	)

Computes the inverse of matrix A, if possible.

Inversion is possible if the determinant is not zero.

Parameters

[in]	A	Input matrix.
[out]	AInv	Matrix to be filled with the coefficients of the inverted matrix A.

Returns

CVC_ERROR (CVC_E_OK) on success
CVC_ERROR (CVC_E_PARAMETER) if A or AInv is nullptr.
CVC_ERROR (CVC_E_DIVISIONBYZERO) if determinant is zero.

◆ CVC3DInvertTransformation()

cvbres_t CVC3DInvertTransformation	(	const CVC3DTransformation &	A,
		CVC3DTransformation &	AInv
	)

Computes the inverse of the transformation matrix A, if possible.

Inversion is possible if the determinant is not zero.

Parameters

[in]	A	Input transformation.
[out]	AInv	Transformation matrix to be filled with the coefficients of the inverted A.

Returns

CVC_ERROR (CVC_E_OK) on success
CVC_ERROR (CVC_E_DIVISIONBYZERO) if determinant is zero.

◆ CVC3DMatrixDeterminant()

cvbres_t CVC3DMatrixDeterminant	(	const CVC3DMatrix	A,
		double &	Determinant
	)

Calculates the Determinant of the given matrix A.

Parameters

[in]	A	Matrix for which the Determinant is to be calculated.
[out]	Determinant	Variable to be filled with the determinant.

Returns

CVC_ERROR (CVC_E_OK) on success
CVC_ERROR (CVC_E_PARAMETER) if A is nullptr.

◆ CVC3DMatrixFromRollPitchYawScale()

cvbres_t CVC3DMatrixFromRollPitchYawScale	(	double	Roll,
		double	Pitch,
		double	Yaw,
		CVC3DFactors	Scale,
		CVC3DMatrix	TransformationMatrix
	)

Computes the transformation matrix M from the given Euler angles Roll, Pitch, Yaw and scaling Scale in x, y, z.

This function computes the transformation matrix after the z-y′-x″ convention (see https://en.wikipedia.org/wiki/Euler_angles).
The scaling is applied before rotation:
M = R_z*R_y*R_x*S*xyz
where R_x, R_y, R_z is the rotation around x, y, z
S is the scaling matrix

Parameters

[in]	Roll	Angle around _x_″ in degrees.
[in]	Pitch	Angle around _y_′ axis in degrees.
[in]	Yaw	Angle around z axis in degrees.
[in]	Scale	Scaling factors in x, y and z.
[out]	TransformationMatrix	Non-nullptr pointer to matrix to be filled with the rotation matrix elements.

Returns

CVC_ERROR (CVC_E_OK) on success
CVC_ERROR (CVC_E_PARAMETER) if Roll, Pitch, Yaw and/or Scale are NaN or TransformationMatrix is nullptr.

See also: CVC3DRotationMatrixFromRollPitchYaw, CVC3DRollPitchYawScaleFromMatrix

◆ CVC3DMatrixFromRotationAnglesScale()

cvbres_t CVC3DMatrixFromRotationAnglesScale	(	double	Alpha,
		double	Beta,
		double	Gamma,
		CVC3DFactors	Scale,
		CVC3DMatrix	TransformationMatrix
	)

Computes the transformation matrix M from the given Euler angles Alpha, Beta, Gamma and scaling Scale in x, y, z.

The scaling is applied before rotation:

where
Alpha, Beta, Gamma are the rotation angles around x, y, z
s_x, s_y, s_z are the scaling factors for x, y, z.

Parameters

[in]	Alpha	Angle around x axis in degrees.
[in]	Beta	Angle around y axis in degrees.
[in]	Gamma	Angle around z axis in degrees.
[in]	Scale	Scaling factors in x, y and z.
[out]	TransformationMatrix	Non-nullptr pointer to matrix to be filled with the rotation matrix elements.

Returns

CVC_ERROR (CVC_E_OK) on success
CVC_ERROR (CVC_E_PARAMETER) if Alpha, Beta, Gamma and/or Scale are NaN or TransformationMatrix is nullptr.

See also: CVC3DRotationMatrixFromRotationAngles, CVC3DRotationAnglesScaleFromMatrix

◆ CVC3DMultiplyMatrices()

cvbres_t CVC3DMultiplyMatrices	(	const CVC3DMatrix	A,
		const CVC3DMatrix	B,
		CVC3DMatrix	R
	)

Multiplies two matrices A and B.

Parameters

[in]	A	Left hand side matrix.
[in]	B	Right hand side matrix.
[out]	R	Matrix to be filled with the result coefficients of the operation.

Returns

CVC_ERROR (CVC_E_OK) on success
CVC_ERROR (CVC_E_PARAMETER) if A, B or R is nullptr.

◆ CVC3DMultiplyTransformations()

cvbres_t CVC3DMultiplyTransformations	(	const CVC3DTransformation &	A,
		const CVC3DTransformation &	B,
		CVC3DTransformation &	R
	)

Multiplies two transformation matrices A and B.

Parameters

[in]	A	Left hand side transformation.
[in]	B	Right hand side transformation.
[out]	R	Transformation to be filled with the result coefficients of the operation.

◆ CVC3DRollPitchYawFromRotationMatrix()

cvbres_t CVC3DRollPitchYawFromRotationMatrix	(	const CVC3DMatrix	R,
		double &	Roll,
		double &	Pitch,
		double &	Yaw
	)

Computes the Euler angles Roll, Pitch and Yaw from the given rotation matrix R.

This function computes the rotation matrix after the z-y′-x″ convention (see https://en.wikipedia.org/wiki/Euler_angles).

Note: If the resulting Pitch is outside the range ]-90° .. 90°[ , the computation of the Euler angles is ambiguous (rotation direction may be inversed).

Parameters

[in]	R	Non-nullptr pointer to rotation matrix elements.
[out]	Roll	Variable to receive angle around _x_″ in degrees.
[out]	Pitch	Variable to receive angle around _y_′ axis in degrees.
[out]	Yaw	Variable to receive angle around z axis in degrees.

Returns

CVC_ERROR (CVC_E_OK) on success
CVC_ERROR (CVC_E_PARAMETER) if R is not a valid rotation matrix.

See also: CVC3DRotationMatrixFromRollPitchYaw, CVC3DRollPitchYawScaleFromMatrix

◆ CVC3DRollPitchYawScaleFromMatrix()

cvbres_t CVC3DRollPitchYawScaleFromMatrix	(	const CVC3DMatrix	TransformationMatrix,
		double &	Roll,
		double &	Pitch,
		double &	Yaw,
		CVC3DFactors &	Scale
	)

Computes the Euler angles Roll, Pitch, Yaw and the scaling Scale in x, y and z from the given transformation matrix TransformationMatrix.

This function computes the rotation matrix after the z-y′-x″ convention (see https://en.wikipedia.org/wiki/Euler_angles).
The scaling must be applied before rotation:
M = R_z*R_y*R_x*S
where R_x, R_y, R_z is the rotation around x, y, z
S is the scaling matrix

The scaling factors are computed from the normed matrix TransformationMatrix and threfore positive as a start. If the determinant of the normed matrix is -1, the scaling factor in z is set to a negative value.

Note: If one of the resulting angles is outside the range ]-90° .. 90°[ or one of the scaling factors is negative, the computation of the Euler angles and the scaling factors is ambiguous (rotation direction may be inversed, negative scaling is the same as rotation about 180 degree).

Parameters

[in]	TransformationMatrix	Non-nullptr pointer to transformation matrix elements.
[out]	Roll	Variable to receive angle around _x_″ in degrees.
[out]	Pitch	Variable to receive angle around _y_′ axis in degrees.
[out]	Yaw	Variable to receive angle around z axis in degrees.
[out]	Scale	Scaling factors in x, y and z.

Returns

CVC_ERROR (CVC_E_OK) on success
CVC_ERROR (CVC_E_PARAMETER) if TransformationMatrix is not a valid rotation matrix or a nullptr or one or more elements are NaN .

See also: CVC3DMatrixFromRollPitchYawScale, CVC3DRollPitchYawScaleFromMatrixApproximation, CVC3DRollPitchYawFromRotationMatrix

◆ CVC3DRollPitchYawScaleFromMatrixApproximation()

cvbres_t CVC3DRollPitchYawScaleFromMatrixApproximation	(	const CVC3DMatrix	TransformationMatrix,
		double &	Roll,
		double &	Pitch,
		double &	Yaw,
		CVC3DFactors &	Scale,
		double &	PrecisionOfApproximation
	)

Estimates the Euler angles Roll, Pitch, Yaw and the scaling Scale in x, y and z from the given transformation matrix TransformationMatrix. The transformation matrix may be noisy.

This function computes the rotation matrix after the z-y′-x″ convention (see https://en.wikipedia.org/wiki/Euler_angles).
The scaling must be applied before rotation:
M = R_z*R_y*R_x*S
where R_x, R_y, R_z is the rotation around x, y, z
S is the scaling matrix

This function should be used, if the matrix is noisy or not a valid transformation matrix.

Rotation angles and scaling factors are estimated using the Nelder-Mead algorithm. Therefore a cost function is set up and minimized over several iterations. The minimum value after the iteration stopped is stored to PrecisionOfApproximation. If the given matrix is valid and not noisy, the PrecisionOfApproximation will be very low.

Attention: This function does not work for large scaling factors or if all scaling factors are negative. In this case the output PrecisionOfApproximation will be large (in general greater 1). Then please norm your matrix first by dividing all matrix elements by a matrix norm (e.g. the Frobenius norm or other).

Note: If one of the resulting angles is outside the range ]-90° .. 90°[ or one of the scaling factors is negative, the computation of the Euler angles and the scaling factors is ambiguous (rotation direction may be inversed, negative scaling is the same as rotation about 180 degree).

Parameters

[in]	TransformationMatrix	Non-nullptr pointer to transformation matrix elements.
[out]	Roll	Variable to receive angle around _x_″ in degrees.
[out]	Pitch	Variable to receive angle around _y_′ axis in degrees.
[out]	Yaw	Variable to receive angle around z axis in degrees.
[out]	Scale	Scaling factors in x, y and z.
[out]	PrecisionOfApproximation	Precision of the approximation.

Returns

CVC_ERROR (CVC_E_OK) on success
CVC_ERROR (CVC_E_PARAMETER) if TransformationMatrix is not a valid rotation matrix or a nullptr or one or more elements are NaN .

See also: CVC3DMatrixFromRollPitchYawScale, CVC3DRollPitchYawScaleFromMatrixApproximation, CVC3DRollPitchYawFromRotationMatrix

◆ CVC3DRotationAnglesFromRotationMatrix()

cvbres_t CVC3DRotationAnglesFromRotationMatrix	(	const CVC3DMatrix	R,
		double &	Alpha,
		double &	Beta,
		double &	Gamma
	)

Computes the Euler angles Alpha, Beta and Gamma from the given rotation matrix R.

The rotation matrix R is interpreted as:

where
Alpha, Beta, Gamma are the rotation angles around x, y, z.

Note: If the resulting Beta is outside the range ]-90° .. 90°[ , the computation of the Euler angles is ambiguous (rotation direction may be inversed).

Parameters

[in]	R	Non-nullptr pointer to rotation matrix elements.
[out]	Alpha	Variable to receive rotation angle around x axis in degrees.
[out]	Beta	Variable to receive rotation angle around y axis in degrees.
[out]	Gamma	Variable to receive rotation angle around z axis in degrees.

Returns

CVC_ERROR (CVC_E_OK) on success
CVC_ERROR (CVC_E_PARAMETER) if R is not a valid rotation matrix.

See also: CVC3DRotationMatrixFromRotationAngles, CVC3DRotationAnglesScaleFromMatrix

◆ CVC3DRotationAnglesScaleFromMatrix()

cvbres_t CVC3DRotationAnglesScaleFromMatrix	(	const CVC3DMatrix	TransformationMatrix,
		double &	Alpha,
		double &	Beta,
		double &	Gamma,
		CVC3DFactors &	Scale
	)

Computes the Euler angles Alpha, Beta, Gamma and the scaling in x, y and z from the given transformation matrix TransformationMatrix.

The transformation matrix M is interpreted as:

where
Alpha, Beta, Gamma are the rotation angles around x, y, z
s_x, s_y, s_z are the scaling factors for x, y, z.

The scaling factors are computed from the normed matrix TransformationMatrix and threfore positive as a start. If the determinant of the normed matrix is -1, the scaling factor in z is set to a negative value.

Note: If one of the resulting angles is outside the range ]-90° .. 90°[ or one of the scaling factors is negative, the computation of the Euler angles and the scaling factors is ambiguous (rotation direction may be inversed, negative scaling is the same as rotation about 180 degree).

Parameters

[in]	TransformationMatrix	Non-nullptr pointer to transformation matrix elements.
[out]	Alpha	Variable to receive rotation angle around x axis in degrees.
[out]	Beta	Variable to receive rotation angle around y axis in degrees.
[out]	Gamma	Variable to receive rotation angle around z axis in degrees.
[out]	Scale	Scaling factors in x, y and z.

Returns

CVC_ERROR (CVC_E_OK) on success
CVC_ERROR (CVC_E_PARAMETER) if TransformationMatrix is not a valid rotation matrix or a nullptr or one or more elements are NaN .

See also: CVC3DMatrixFromRotationAnglesScale, CVC3DRotationAnglesScaleFromMatrixApproximation, CVC3DRotationAnglesFromRotationMatrix

◆ CVC3DRotationAnglesScaleFromMatrixApproximation()

cvbres_t CVC3DRotationAnglesScaleFromMatrixApproximation	(	const CVC3DMatrix	TransformationMatrix,
		double &	Alpha,
		double &	Beta,
		double &	Gamma,
		CVC3DFactors &	Scale,
		double &	PrecisionOfApproximation
	)

Estimates the Euler angles Alpha, Beta, Gamma and the scaling in x, y and z from the given transformation matrix TransformationMatrix. The transformation matrix may be noisy.

The transformation matrix M is interpreted as:

where
Alpha, Beta, Gamma are the rotation angles around x, y, z
s_x, s_y, s_z are the scaling factors for x, y, z.

This function should be used, if the matrix is noisy or not a valid transformation matrix.

Rotation angles and scaling factors are estimated using the Nelder-Mead algorithm. Therefore a cost function is set up and minimized over several iterations. The minimum value after the iteration stopped is stored to PrecisionOfApproximation. If the given matrix is valid and not noisy, the PrecisionOfApproximation will be very low.

Attention: This function does not work for large scaling factors or if all scaling factors are negative. In this case the output PrecisionOfApproximation will be large (in general greater 1). Then please norm your matrix first by dividing all matrix elements by a matrix norm (e.g. the Frobenius norm or other).

Note: If one of the resulting angles is outside the range ]-90° .. 90°[ or one of the scaling factors is negative, the computation of the Euler angles and the scaling factors is ambiguous (rotation direction may be inversed, negative scaling is the same as rotation about 180 degree).

Parameters

[in]	TransformationMatrix	Non-nullptr pointer to transformation matrix elements.
[out]	Alpha	Variable to receive rotation angle around x axis in degrees.
[out]	Beta	Variable to receive rotation angle around y axis in degrees.
[out]	Gamma	Variable to receive rotation angle around z axis in degrees.
[out]	Scale	Scaling factors in x, y and z.
[out]	PrecisionOfApproximation	Precision of the approximation.

Returns

CVC_ERROR (CVC_E_OK) on success
CVC_ERROR (CVC_E_PARAMETER) if TransformationMatrix is not a valid rotation matrix or a nullptr or one or more elements are NaN .

See also: CVC3DMatrixFromRotationAnglesScale, CVC3DRotationAnglesScaleFromMatrixApproximation, CVC3DRotationAnglesFromRotationMatrix

◆ CVC3DRotationMatrixFromRollPitchYaw()

cvbres_t CVC3DRotationMatrixFromRollPitchYaw	(	double	Roll,
		double	Pitch,
		double	Yaw,
		CVC3DMatrix	R
	)

Computes the rotation matrix R from the given Euler angles Roll, Pitch and Yaw.

This function computes the rotation matrix after the z-y′-x″ convention (see https://en.wikipedia.org/wiki/Euler_angles).

Parameters

[in]	Roll	Angle around _x_″ in degrees.
[in]	Pitch	Angle around _y_′ axis in degrees.
[in]	Yaw	Angle around z axis in degrees.
[out]	R	Non-nullptr pointer to matrix to be filled with the rotation matrix elements.

Returns

CVC_ERROR (CVC_E_OK) on success
CVC_ERROR (CVC_E_PARAMETER) if Roll, Pitch and/or Yaw are NaN or R is nullptr.

See also: CVC3DRollPitchYawFromRotationMatrix, CVC3DMatrixFromRollPitchYawScale

◆ CVC3DRotationMatrixFromRotationAngles()

cvbres_t CVC3DRotationMatrixFromRotationAngles	(	double	Alpha,
		double	Beta,
		double	Gamma,
		CVC3DMatrix	R
	)

Computes the rotation matrix R from the given Euler angles Alpha, Beta and Gamma.

The rotation matrix R is computed via:

where
Alpha, Beta, Gamma are the rotation angles around x, y, z.

Parameters

[in]	Alpha	Angle around x axis in degrees.
[in]	Beta	Angle around y axis in degrees.
[in]	Gamma	Angle around z axis in degrees.
[out]	R	Non-nullptr pointer to matrix to be filled with the rotation matrix elements.

Returns

CVC_ERROR (CVC_E_OK) on success
CVC_ERROR (CVC_E_PARAMETER) if Alpha, Beta and/or Gamma are NaN or R is nullptr.

See also: CVC3DRotationAnglesFromRotationMatrix, CVC3DMatrixFromRotationAnglesScale

◆ CVC3DTransformationDeterminant()

cvbres_t CVC3DTransformationDeterminant	(	const CVC3DTransformation &	A,
		double &	Determinant
	)

Calculates the Determinant of the given transformation matrix A.

Parameters

[in]	A	Transformation for which the Determinant is to be calculated.
[out]	Determinant	Variable to be filled with the determinant.

Returns: Always CVC_ERROR (CVC_E_OK).

◆ CVC3DTransformPointCloud()

cvbres_t CVC3DTransformPointCloud	(	CVCOMPOSITE	PointCloudIn,
		const CVC3DTransformation &	AffineTransformation,
		CVCOMPOSITE	PointCloudOut
	)

Transforms all points in PointCloudIn by the given AffineTransformation and stores them in PointCloudOut.

The given PointCloudIn and PointCloudOut must have valid CVC3DPointCloudLayout.

Note: This operation also allows in-place transformation: PointCloudOut is PointCloudIn.

Parameters

[in]	PointCloudIn	Handle to point cloud object to be transformed.
[in]	AffineTransformation	Homogeneous transformation matrix.
[in]	PointCloudOut	Handle to sparse point cloud were the transformed points are stored in.

Returns

CVC_ERROR (CVC_E_OK) on success
CVC_ERROR (CVC_E_PARAMETER) if AffineTransformation contains NaN.
CVC_ERROR (CVC_E_WRONGOBJECT) if PointCloudIn or PointCloudOut are not valid point clouds or PointCloudOut is dense.
CVC_ERROR (CVC_E_NOTENOUGHDATA) if PointCloudIn is empty.
CVC_ERROR (CVC_E_INVALIDDIMENSION) if PointCloudOut has a different number of points than PointCloudIn.

See also: CVC3DTransformPointCloudH, CVC3DCreateTransformedPointCloud, CVC3DCreateTransformedPointCloudH

◆ CVC3DTransformPointCloudH()

cvbres_t CVC3DTransformPointCloudH	(	CVCOMPOSITE	PointCloudIn,
		const CVC3DMatrixH	Transformation,
		CVCOMPOSITE	PointCloudOut
	)

Transforms all points in PointCloudIn by the given Transformation and stores them in PointCloudOut.

The given PointCloudIn and PointCloudOut must have valid CVC3DPointCloudLayout.

Note: This operation also allows in-place transformation: PointCloudOut is PointCloudIn.

Parameters

[in]	PointCloudIn	Handle to point cloud object to be transformed.
[in]	Transformation	Homogeneous transformation matrix.
[in]	PointCloudOut	Handle to sparse point cloud were the transformed points are stored in.

Returns

CVC_ERROR (CVC_E_OK) on success
CVC_ERROR (CVC_E_PARAMETER) if Transformation contains NaN or is nullptr.
CVC_ERROR (CVC_E_WRONGOBJECT) if PointCloudIn or PointCloudOut are not valid point clouds or PointCloudOut is dense.
CVC_ERROR (CVC_E_NOTENOUGHDATA) if PointCloudIn is empty.
CVC_ERROR (CVC_E_INVALIDDIMENSION) if PointCloudOut has a different number of points than PointCloudIn.

See also: CVC3DTransformPointCloudH, CVC3DCreateTransformedPointCloud, CVC3DCreateTransformedPointCloudH

Data Structures

Typedefs

Functions

Detailed Description

Typedef Documentation

◆ CVC3DMatrix

◆ CVC3DMatrixH

◆ CVC3DVector

Function Documentation

◆ CVC3DAlignToXYPlane()

◆ CVC3DCreateConvertedPointCloud()

◆ CVC3DCreateScaledPointCloud()

◆ CVC3DCreateTransformedPointCloud()

◆ CVC3DCreateTransformedPointCloudH()

◆ CVC3DInvertMatrix()

◆ CVC3DInvertTransformation()

◆ CVC3DMatrixDeterminant()

◆ CVC3DMatrixFromRollPitchYawScale()

◆ CVC3DMatrixFromRotationAnglesScale()

◆ CVC3DMultiplyMatrices()

◆ CVC3DMultiplyTransformations()

◆ CVC3DRollPitchYawFromRotationMatrix()

◆ CVC3DRollPitchYawScaleFromMatrix()

◆ CVC3DRollPitchYawScaleFromMatrixApproximation()

◆ CVC3DRotationAnglesFromRotationMatrix()

◆ CVC3DRotationAnglesScaleFromMatrix()

◆ CVC3DRotationAnglesScaleFromMatrixApproximation()

◆ CVC3DRotationMatrixFromRollPitchYaw()

◆ CVC3DRotationMatrixFromRotationAngles()

◆ CVC3DTransformationDeterminant()

◆ CVC3DTransformPointCloud()

◆ CVC3DTransformPointCloudH()