3x3 matrix commonly used for pure rotations, but in general may also have scales and non-perpendicular rows and columns. More...

#include <rotmatrix.h>

Public Member Functions
void	InitIdentity ()
	Initialize an identity matrix. More...

void	Zero ()
	returns a zero matrix. More...

void	InitFromScale (double scale)
	Initializes a uniform scaling matrix. More...

void	InitFromScaleFactors (double xscale, double yscale, double zscale)
	Returns a scaling matrix with respective x, y, and z scaling factors. More...

void	ScaleRows (RotMatrixCR inMatrix, double xScale, double yScale, double zScale)
	Applies scale factors to corresponding rows of the input matrix, and places the result in this instance matrix. More...

void	ScaleColumns (RotMatrixCR in, double xs, double ys, double zs)
	Applies scale factors to corresponding columns of the input matrix, and places the result in this instance matrix. More...

void	ScaleColumns (double xs, double ys, double zs)
	Applies scale factors to corresponding columns. More...

void	NormalizeRowsOf (RotMatrixCR inMatrix, DVec3dR scaleVector)
	Returns a matrix whose rows are unit vectors in the same drection as corresponding rows of the input matrix. More...

void	NormalizeColumnsOf (RotMatrixCR inMatrix, DVec3dR scaleVector)
	Returns a matrix whose rows are unit vectors in the same drection as corresponding columns of the input matrix. More...

void	Scale (RotMatrixCR leftMatrix, double xs, double ys, double zs, RotMatrixCR rightMatrix)
	Returns a matrix formed from a scaling matrix which is multiplied on the left and/or right with other matrices. More...

void	InitFromScaledOuterProduct (DVec3dCR vectorU, DVec3dCR vectorV, double scale)
	Returns a 'rank one' matrix defined as a scale factor times the 'vector outer product' of two vectors, i.e. More...

void	AddScaledOuterProductInPlace (DVec3dCR vectorU, DVec3dCR vectorV, double scale)
	Accumulates a 'rank one' matrix defined as a scale factor times the 'vector outer product' of two vectors, i.e. More...

void	ShuffleColumnsOf (RotMatrixCR inMatrix, int i0, int i1, int i2)
	Moves columns 0, 1, 2 of the input matrix into columns i0, i1, i2 of the instance. More...

void	InitFromRowValues (double x00, double x01, double x02, double x10, double x11, double x12, double x20, double x21, double x22)
	Initializes a matrix with the 9 specified coefficients given in "row major" order. More...

void	InitFromRowValuesXY (double x00, double x01, double x10, double x11)
	Initializes a matrix with the 4 specified coefficients in xx,xy,yx,yy positions, and 1 in zz in "row major" order. More...

void	InitFromRowValuesXY (double const data[4])
	Initializes a matrix with 4 coefficients in xx,xy,yx,yy positions, and 1 in zz in "row major" order. More...

void	InitFromColumnVectors (DVec3dCR vectorU, DVec3dCR vectorV, DVec3dCR vectorW)
	Returns a matrix with 3 points copied to respective columns. More...

void	InitFromRowVectors (DVec3dCR vectorU, DVec3dCR vectorV, DVec3dCR vectorW)
	Initializes a matrix with 3 points copied to respective rows. More...

void	InitFromVectorAndRotationAngle (DVec3dCR axis, double radians)
	Initializes a matrix representing rotation around a vector. More...

void	InitFromAxisAndRotationAngle (int axis, double radians)
	Returns a matrix of rotation about the x,y, or z axis (indicated by axis = 0,1, or 2) by an angle in radians. More...

bool	InitRotationFromVectorToVector (DVec3dCR startVector, DVec3dCR endVector)
	(conditionally) initialize the instance as the (smallest) rotation that moves startVector so it is in the direction of endVector. More...

void	InitFromDirectionAndScale (DVec3dCR vector, double scale)
	Initializes a matrix which scales along a vector direction. More...

void	InitFromPrincipleAxisRotations (RotMatrixCR inMatrix, double xrot, double yrot, double zrot)
	Returns the product {RXRYRZ*M} where RX, RY, and RZ are rotations (in radians) around X, Y, and Z axes, and M is the input matrix. More...

bool	InitFrom1Vector (DVec3dCR dir, int axis, bool normalize)
	Initializes this instance matrix so that the indicated axis (axis = 0,1,or 2) is aligned with the vector dir. More...

void	InitFrom2Vectors (DVec3dCR xVector, DVec3dCR yVector)
	Copies vectors into the x and y columns of this instance matrix and sets the z column to their cross product. More...

bool	InitRotationFromOriginXY (DPoint3dCR origin, DPoint3dCR xPoint, DPoint3dCR yPoint)
	Set this instance matrix to be an orthogonal (rotation) matrix with column 0 in the direction from the origin to the x point, column 1 in the plane of the 3 points, directed so the Y point on the positive side, and column 2 as their cross product. More...

bool	SquareAndNormalizeColumns (RotMatrixCR inMatrix, int primaryAxis, int secondaryAxis)
	Adjust the direction and length of columns of the input matrix to produce an instance matrix which has perpendicular, unit length columns. More...

bool	SquareAndNormalizeColumns (RotMatrixCR inMatrix, int primaryAxis, int secondaryAxis, int preferredOrientation)

bool	SquareAndNormalizeColumnsAnyOrder (RotMatrixCR inMatrix, int preferredOrientation)
	Returns an orthogonal matrix that preserves aligns with the columns of inMatrix. More...

bool	SquareAndNormalizeColumnsAnyOrder (RotMatrixCR inMatrix)
	Returns an orthogonal matrix that preserves aligns with the columns of inMatrix. More...

void	InitFrom (TransformCR transform)
	Sets this instance matrix by copying the matrix part of the trasnform. More...

void	Copy (RotMatrixCR in)
	Sets this instance matrix by copying from the matrix parameter. More...

void	InitProduct (RotMatrixCR rotMatrixA, RotMatrixCR rotMatrixB)
	Returns the product {A*B} of two matrices. More...

void	InitProduct (RotMatrixCR rotMatrixA, RotMatrixCR rotMatrixB, RotMatrixCR rotMatrixC)
	Returns the product of three matrices. More...

void	InitProduct (RotMatrixCR rotMatrixA, TransformCR transformB)
	Sets this instance to the product of matrix rotMatrixA times the matrix part of transform transformB. More...

void	InitProduct (TransformCR transformA, RotMatrixCR rotMatrixB)
	Returns to the product of the matrix part of transform transformA times matrix rotMatrixB. More...

void	InitProductRotMatrixTransposeRotMatrix (RotMatrixCR rotMatrixA, RotMatrixCR rotMatrixB)
	Returns the product of the transpose of rotMatrixA times rotMatrixB. More...

void	InitProductRotMatrixRotMatrixTranspose (RotMatrixCR rotMatrixA, RotMatrixCR rotMatrixB)
	Returns the product of rotMatrixA times the transpose of rotMatrixB. More...

void	TransposeOf (RotMatrixCR matrix)
	Initializes this instance as the transpose of a matrix. More...

void	Transpose ()
	Transposes a matrix in place. More...

void	SumOf (RotMatrixCR matrix0, RotMatrixCR matrix1, double scale1, RotMatrixCR matrix2, double scale2)
	Returns {Matrix0 + Matrix1s1+Matrix2s2}, i.e. More...

void	Add (RotMatrixCR delta)
	Add a matrix (componentwise, in place). More...

void	Subtract (RotMatrixCR delta)
	Subtract a matrix (componentwise, in place). More...

bool	InverseOf (RotMatrixCR forward)
	Returns the inverse of the a matrix. More...

bool	Invert ()
	Inverts this instance matrix in place. More...

void	Multiply (DPoint4dP result, DPoint4dCP point, int numPoint) const
	Computes {M*P[i]} where M is this instance matrix and each P[i] is a point in the input array point. More...

void	Multiply (DPoint2dP result, DPoint2dCP point, int numPoint) const
	Computes {M*P[i]} where M is this instance matrix and each P[i] is a point in the input array point. More...

void	Multiply (DRange3dR outRange, DRange3dCR inRange) const
	computes the 8 corner points of the range cube defined by the two points of pRange, multiplies matrix times each point, and computes the twopoint range limits (min max) of the resulting rotated box. More...

void	Multiply (DPoint3dR point) const
	Computes the product {M*P} where M is this instance matrix and P the input point. More...

void	Multiply (DPoint3dR result, DPoint3dCR point) const
	Returns the product of a matrix times a point. More...

void	MultiplyTranspose (DPoint3dR result, DPoint3dCR point) const
	Returns the product of a matrix transpose times a point. More...

void	MultiplyComponents (DPoint3dR result, double x, double y, double z) const
	Returns the product of a matrix times a point, with the point given as separate components. More...

void	MultiplyTranspose (DPoint3dR point) const
	Computes the product {P*M} where M is this instance matrix and P is the input point The result overwrites the previous coordinates in the point. More...

void	MultiplyTransposeComponents (DPoint3dR result, double x, double y, double z) const
	Returns the product P = [x,y,z]*M where M is the input matrix and P is the product point. More...

void	Multiply (DPoint3dP result, DPoint3dCP point, int numPoint) const
	Computes {M*P[i]} where M is this instance matrix and each P[i] is a point in the input array point. More...

void	MultiplyTranspose (DPoint3dP result, DPoint3dCP point, int numPoint) const
	Computes {P[i]*M} where M is this instance matrix and each P[i] is a point in the input array point, transposed into row form. More...

void	Multiply (bvector< DPoint3d > &outXYZ, bvector< DPoint3d > const &inXYZ) const
	Description Multiply points. (Matrix on left, point on right as column vector) More...

void	MultiplyTranspose (bvector< DPoint3d > &outXYZ, bvector< DPoint3d > const &inXYZ) const
	Multiply the transposed matrix times points. (Tranposed matrix on left, point on right as column vector. Or (equivalent) point on left as row vector, matrix on right) More...

void	Multiply (bvector< DPoint2d > &out, bvector< DPoint2d > const &in) const
	Description Multiply 2D points. (Matrix on left, point on right as column vector) More...

void	Multiply (bvector< DPoint4d > &xyzwOut, bvector< DPoint4d > const &xyzwIn) const
	Multiply xyzw, with matrix w row and column 0001. More...

bool	SolveArray (bvector< DPoint3d > &xyzOut, bvector< DPoint3d > const &xyzIn) const
	Solve M*xyzOut[i] = xyzIn[i] for array of points. More...

bool	Solve (DPoint3dR result, DPoint3dCR point) const
	Return the product of a matrix inverse and a point. More...

bool	SolveTranspose (DPoint3dR result, DPoint3dCR point) const
	Return the product of a matrix inverse transpose and a point. More...

bool	SolveArray (DPoint3dP result, DPoint3dCP point, int numPoints) const
	Solves the matrix equation AX=B, where A is this instance, B is the matrix of numPoints input points and X is the matrix of numPoints output points. More...

void	GetColumns (DVec3dR vectorU, DVec3dR vectorV, DVec3dR vectorW) const
	Copies from columns of this instance matrix to corresponding points. More...

void	GetRows (DVec3dR vectorU, DVec3dR vectorV, DVec3dR vectorW) const
	Copies from rows of this instance matrix to corresponding points. More...

void	GetColumn (DVec3dR vector, int col) const
	Returns a point taken from a column of a matrix. More...

void	GetRow (DVec3dR vector, int row) const
	Returns a vector taken from a column of a matrix. More...

void	SetColumn (DVec3dCR vector, int col)
	Set the components in a column. More...

void	SetRow (DVec3dCR vector, int row)
	Set the components in a row. More...

double	GetComponentByRowAndColumn (int row, int col) const
	Returns a value from a specified row and column of the matrix. More...

void	GetRowValues (double &x00, double &x01, double &x02, double &x10, double &x11, double &x12, double &x20, double &x21, double &x22) const
	Get all contents as individual doubles, moving along rows. More...

void	GetRowValuesXY (double data[4]) const
	Copies 4 doubles from xx,xy,yx,yy positions into an array. More...

double	Determinant () const
	Returns the determinant of the matrix. More...

double	ConditionNumber () const
	Computes an estimate of the condition of this instance matrix. More...

bool	IsIdentity () const
	Tests if a matrix is the identity matrix. More...

bool	IsDiagonal () const
	Tests if a matrix has small offdiagonal entries compared to diagonals. More...

bool	IsUniformScale (double &maxScale) const
	Tests if a matrix has (nearly) equal diagaonal entries and (nearly) zero off diagonals. More...

void	DiagonalSignedRange (double &minValue, double &maxValue) const
	Return the (signed) range of entries on the diagonal. More...

void	DiagonalAbsRange (double &minValue, double &maxValue) const
	Return the (absolute value) range of entries on the diagonal. More...

void	OffDiagonalSignedRange (double &minValue, double &maxValue) const
	Return the (signed) range of entries off the diagonal. More...

void	OffDiagonalAbsRange (double &minValue, double &maxValue) const
	Return the (absolute value) range of entries off the diagonal. More...

DRange1d	LowerTriangleAbsRange ()
	return the range of absolute values strictly below the diagonal. More...

DRange1d	UpperTriangleAbsRange ()
	return the range of absolute values strictly above the diagonal. More...

DRange1d	DiagonalAbsRange ()
	return the range of absolute values on the diagonal. More...

double	LowerTriangleMaxAbs ()
	return the largest absolute value in the lower triangle. More...

double	UpperTriangleMaxAbs ()
	return the largest absolute value in the upper triangle. More...

double	DiagonalMaxAbs ()
	return the largest absolute value on the diagonal More...

double	SumSquares () const
	Return the sum of squares of coefficients in a matrix. More...

double	MaxAbs () const
	Find the largest absolute value of entries in the matrix. More...

double	MaxDiff (RotMatrixCR matrix2) const
	Returns the largest absolute value difference between corresponding coefficients in Matrix1 and Matrix2. More...

double	SumDiagonalSquares () const
	Computes the sum of the squares of the diagonal entries of this instance matrix. More...

double	SumOffDiagonalSquares () const
	Computes the sum of the squares of the off-diagonal entries of this instance matrix. More...

bool	IsSignedPermutation () const
	Test if this instance matrix does nothing more than exchange and possibly negate principle axes. More...

bool	IsNearSignedPermutation (RotMatrixR result, double tolerance) const
	Test if this instance matrix does nothing more than exchange and possibly negate principle axes, within a tolerance. More...

bool	IsRigid () const
	Test if a matrix is a rigid body rotation, i.e. More...

bool	IsOrthogonal () const
	Test if this instance matrix is orthogonal, i.e. More...

bool	IsOrthonormal (RotMatrixR columns, DVec3dR axisScales, double &axisRatio) const
	Test if this instance matrix has orthonormal columns, i.e. More...

bool	IsRigidScale (RotMatrixR columns, double &scale) const
	Test if this instance matrix is composed of only rigid rotation and scaling. More...

bool	IsNearRigidScale (RotMatrixR dest, int primaryAxis=0, double tolerance=1.0e-6) const
	Determine if a matrix is close to a pure rotate and scale. More...

bool	IsPlanar (DVec3dCR normal) const
	Tests if this instance matrix has no effects perpendicular to any plane with the given normal. More...

bool	IsEqual (RotMatrixCR matrix2) const
	Tests for equality between two matrices "Equality" means relative error less than 1.0e-12, in the sense that each component-wise difference is less than 1.0e-12 times the largest absolute value of the components of one matrix. More...

bool	IsEqual (RotMatrixCR matrix2, double tolerance) const
	Tests for equality between two matrices. More...

int	FactorRotateScaleRotate (RotMatrixR rotation1, DPoint3dR scalePoint, RotMatrixR rotation2) const
	Factor as {rotation1 * scale * rotation2}. More...

bool	RotateAndSkewFactors (RotMatrixR rotation, RotMatrixR skewFactor, int primaryAxis, int secondaryAxis) const
	Factor as {rotation*skewFactor} where the rotation favors indicated primary and secondary axes. More...

bool	FactorOrthogonalColumns (RotMatrixR matrixB, RotMatrixR matrixV) const
	Factor the instance as a product B*V^ where B has mutually perpendicular columns and V is orthogonal. More...

void	InitFromQuaternion (DPoint4dCR quat)

void	InitFromQuaternion (const double *pQuatAsDoubleArray)

void	InitTransposedFromQuaternionWXYZ (const double *pQuatAsDoubleArray)
	Initialization, compatible with mdlRMatrix_fromQuat. More...

void	GetQuaternion (DPoint4dR quat, bool transpose) const

void	GetQuaternion (double *pQuatAsDoubleArray, bool transpose) const

double	GetRotationAngleAndVector (DVec3dR axis) const
	Returns the angle of rotation of this instance and sets axis to be the normalized vector about which this instance rotates. More...

double	ColumnXAngleXY () const
	Returns the (0 or positive) angle from (1,0) to the XY vector in the first column. More...

void	GivensRowOp (double c, double s, int i0, int i1)
	Apply a Givens "row operation", i.e. More...

void	GivensColumnOp (double c, double s, int i0, int i1)
	Apply a Givens "column operation", i.e. More...

void	HyperbolicRowOp (double secant, double tangent, int i0, int i1)
	Apply a hyperbolic "row operation", i.e. More...

void	HyperbolicColumnOp (double secant, double tangent, int i0, int i1)
	Apply a hyperbolic "column operation", i.e. More...

Static Public Member Functions
static RotMatrix	FromIdentity ()
	Returns an identity matrix. More...

static RotMatrix	FromScale (double scale)
	Returns a uniform scaling matrix. More...

static RotMatrix	FromScaleFactors (double xscale, double yscale, double zscale)
	Returns a scaling matrix with respective x, y, and z scaling factors. More...

static RotMatrix	FromScaledOuterProduct (DVec3dCR vectorU, DVec3dCR vectorV, double scale)
	Returns a 'rank one' matrix defined as a scale factor times the 'vector outer product' of two vectors, i.e. More...

static RotMatrix	FromRowValues (double x00, double x01, double x02, double x10, double x11, double x12, double x20, double x21, double x22)
	Returns a matrix with the 9 specified coefficients given in "row major" order. More...

static RotMatrix	FromColumnVectors (DVec3dCR vectorU, DVec3dCR vectorV, DVec3dCR vectorW)
	Returns a matrix with 3 vectors copied to respective columns. More...

static RotMatrix	FromRowVectors (DVec3dCR vectorU, DVec3dCR vectorV, DVec3dCR vectorW)
	Returns a matrix with 3 vectors copied to respective rows. More...

static RotMatrix	FromVectorAndRotationAngle (DVec3dCR axis, double radians)
	Returns a matrix representing rotation around a vector. More...

static RotMatrix	FromVectorAndRotationAngle (DVec3dCR axis, double radians, RotMatrixR derivativeMatrix)
	Returns a matrix representing rotation around a vector. More...

static RotMatrix	FromAxisAndRotationAngle (int axis, double radians)
	Returns a matrix of rotation about the x,y, or z axis (indicated by axis = 0,1, or 2) by an angle in radians. More...

static RotMatrix	FromRotate90 (DVec3dCR axis)
	Return a matrix for retation of 90 degrees about a vector. More...

static RotMatrix	FromDirectionAndScale (DVec3dCR vector, double scale)
	Returns a matrix which scales along a vector direction. More...

static RotMatrix	FromPrincipleAxisRotations (RotMatrixCR inMatrix, double xrot, double yrot, double zrot)
	Returns the product {RXRYRZ*M} where RX, RY, and RZ are rotations (in radians) around X, Y, and Z axes, and M is the input matrix. More...

static RotMatrix	From1Vector (DVec3dCR dir, int axis, bool normalize)
	Initializes this instance matrix so that the indicated axis (axis = 0,1,or 2) is aligned with the vector dir. More...

static RotMatrix	From2Vectors (DVec3dCR xVector, DVec3dCR yVector)
	Returns a matrix copying vectors into the x and y columns of this instance matrix and sets the z column to their cross product. More...

static RotMatrix	RotationFromOriginXY (DPoint3dCR origin, DPoint3dCR xPoint, DPoint3dCR yPoint)
	Set this instance matrix to be an orthogonal (rotation) matrix with column 0 in the direction from the origin to the x point, column 1 in the plane of the 3 points, directed so the Y point on the positive side, and column 2 as their cross product. More...

static RotMatrix	From (TransformCR transform)
	Returns a matrix copying the matrix part of the trasnform. More...

static RotMatrix	FromTransposeOf (RotMatrixCR matrix)
	Return (as function value) the transpose of a matrix. More...

static RotMatrix	FromQuaternion (DPoint4dCR quat)

static RotMatrix	FromQuaternion (const double *pQuatAsDoubleArray)

Public Attributes
double	form3d [3][3]
	matrix coefficients. These are public, but direct use of the arrays is discouraged. More...

Detailed Description

3x3 matrix commonly used for pure rotations, but in general may also have scales and non-perpendicular rows and columns.

Member Function Documentation

void Add ( RotMatrixCR delta )

Add a matrix (componentwise, in place).

Parameters

[in] delta The matrix to add

void AddScaledOuterProductInPlace	(	DVec3dCR	vectorU,
		DVec3dCR	vectorV,
		double	scale
	)

Accumulates a 'rank one' matrix defined as a scale factor times the 'vector outer product' of two vectors, i.e.

as the matrix {s*U*V^T}

Parameters

[in]	vectorU	The column vector U
[in]	vectorV	The row vector V
[in]	scale	The scale factor

double ColumnXAngleXY ( ) const

Returns the (0 or positive) angle from (1,0) to the XY vector in the first column.

Returns: rotation angle (in radians) between 0 and 2Pi

double ConditionNumber ( ) const

Computes an estimate of the condition of this instance matrix.

Values near 0 are bad.

Returns: estimated condition number.

void Copy ( RotMatrixCR in )

Sets this instance matrix by copying from the matrix parameter.

Parameters

[in] in The source matrix

double Determinant ( ) const

Returns the determinant of the matrix.

Returns: determinant of the matrix.

void DiagonalAbsRange	(	double &	minValue,
		double &	maxValue
	)		const

Return the (absolute value) range of entries on the diagonal.

Parameters

[out]	minValue	smallest absolute value
[out]	maxValue	largest absolute value

DRange1d DiagonalAbsRange ( )

return the range of absolute values on the diagonal.

double DiagonalMaxAbs ( )

return the largest absolute value on the diagonal

void DiagonalSignedRange	(	double &	minValue,
		double &	maxValue
	)		const

Return the (signed) range of entries on the diagonal.

Parameters

[out]	minValue	smallest signed value
[out]	maxValue	largest signed value

bool FactorOrthogonalColumns	(	RotMatrixR	matrixB,
		RotMatrixR	matrixV
	)		const

Factor the instance as a product B*V^ where B has mutually perpendicular columns and V is orthogonal.

Parameters

[out]	matrixB	orthogonal columns
[out]	matrixV	transpose of right factor. (I.e. B = A*V)

int FactorRotateScaleRotate	(	RotMatrixR	rotation1,
		DPoint3dR	scalePoint,
		RotMatrixR	rotation2
	)		const

Factor as {rotation1 * scale * rotation2}.

Returns: number of nonzero scales (independent columns).

Parameters

[out]	rotation1	pure rotation
[out]	scalePoint	scale factors, largest first.
[out]	rotation2	pure rotation

static RotMatrix From ( TransformCR transform )

static

Returns a matrix copying the matrix part of the trasnform.

Parameters

[in] transform The transformation whose matrix part is returned

static RotMatrix From1Vector	(	DVec3dCR	dir,
		int	axis,
		bool	normalize
	)

static

Initializes this instance matrix so that the indicated axis (axis = 0,1,or 2) is aligned with the vector dir.

The normalize flag selects between normalized axes (all matrix columns of unit length) and unnormalized axes (all matrix columns of same length as the dir vector).

Parameters

[in]	dir	The fixed direction vector
[in]	axis	The axis column to be aligned with direction
[in]	normalize	true to have normalized columns

Returns: true if the direction vector is nonzero.

static RotMatrix From2Vectors	(	DVec3dCR	xVector,
		DVec3dCR	yVector
	)

static

Returns a matrix copying vectors into the x and y columns of this instance matrix and sets the z column to their cross product.

Use squareAndNormalizeColumns to force these (possibly skewed and scaled) coordinate axes to be perpendicular

Parameters

[in]	xVector	The vector to place in column 0
[in]	yVector	The vector to place in column 1

static RotMatrix FromAxisAndRotationAngle	(	int	axis,
		double	radians
	)

static

Returns a matrix of rotation about the x,y, or z axis (indicated by axis = 0,1, or 2) by an angle in radians.

Parameters

[in]	axis	The axis index 0=x, 1=y, 2=z
[in]	radians	The rotation angle in radians

static RotMatrix FromColumnVectors	(	DVec3dCR	vectorU,
		DVec3dCR	vectorV,
		DVec3dCR	vectorW
	)

static

Returns a matrix with 3 vectors copied to respective columns.

Parameters

[in]	vectorU	The vector to insert in column 0
[in]	vectorV	The vector to insert in column 1
[in]	vectorW	The vector to insert in column 2

static RotMatrix FromDirectionAndScale	(	DVec3dCR	vector,
		double	scale
	)

static

Returns a matrix which scales along a vector direction.

Parameters

[in]	vector	The scaling direction
[in]	scale	The scale factor

static RotMatrix FromIdentity ( )

static

Returns an identity matrix.

static RotMatrix FromPrincipleAxisRotations	(	RotMatrixCR	inMatrix,
		double	xrot,
		double	yrot,
		double	zrot
	)

static

Returns the product {RX*RY*RZ*M} where RX, RY, and RZ are rotations (in radians) around X, Y, and Z axes, and M is the input matrix.

Parameters

[in]	inMatrix	The prior matrix
[in]	xrot	The x axis rotation
[in]	yrot	The y axis rotation
[in]	zrot	The z axis rotation

static RotMatrix FromQuaternion ( DPoint4dCR quat )

static

Parameters

[in] quat The quaternion, stored as (xyzw)

static RotMatrix FromQuaternion ( const double * pQuatAsDoubleArray )

static

Parameters

[in] pQuatAsDoubleArray The quaternion, stored as (w,x,y,z) in an array of doubles.

static RotMatrix FromRotate90 ( DVec3dCR axis )

static

Return a matrix for retation of 90 degrees about a vector.

static RotMatrix FromRowValues	(	double	x00,
		double	x01,
		double	x02,
		double	x10,
		double	x11,
		double	x12,
		double	x20,
		double	x21,
		double	x22
	)

static

Returns a matrix with the 9 specified coefficients given in "row major" order.

Parameters

[in]	x00	The 00 entry
[in]	x01	The 01 entry
[in]	x02	The 02 entry
[in]	x10	The 10 entry
[in]	x11	The 11 entry
[in]	x12	The 12 entry
[in]	x20	The 20 entry
[in]	x21	The 21 entry
[in]	x22	The 22 entry

static RotMatrix FromRowVectors	(	DVec3dCR	vectorU,
		DVec3dCR	vectorV,
		DVec3dCR	vectorW
	)

static

Returns a matrix with 3 vectors copied to respective rows.

Parameters

[in]	vectorU	The vector to insert in row 0
[in]	vectorV	The vector to insert in row 1
[in]	vectorW	The vector to insert in row 2

static RotMatrix FromScale ( double scale )

static

Returns a uniform scaling matrix.

Parameters

[in] scale The scale factor.

static RotMatrix FromScaledOuterProduct	(	DVec3dCR	vectorU,
		DVec3dCR	vectorV,
		double	scale
	)

static

Returns a 'rank one' matrix defined as a scale factor times the 'vector outer product' of two vectors, i.e.

as the matrix {s*U*V^T}

Parameters

[in]	vectorU	The column vector U
[in]	vectorV	The row vector V
[in]	scale	The scale factor

static RotMatrix FromScaleFactors	(	double	xscale,
		double	yscale,
		double	zscale
	)

static

Returns a scaling matrix with respective x, y, and z scaling factors.

Parameters

[in]	xscale	The x direction scale factor (00 diagonal)
[in]	yscale	The y direction scale factor (11 diagonal)
[in]	zscale	The z direction scale factor (22 diagonal)

static RotMatrix FromTransposeOf ( RotMatrixCR matrix )

static

Return (as function value) the transpose of a matrix.

Parameters

[in] matrix The input matrix

static RotMatrix FromVectorAndRotationAngle	(	DVec3dCR	axis,
		double	radians
	)

static

Returns a matrix representing rotation around a vector.

Parameters

[in]	axis	The axis of rotation
[in]	radians	The rotation angle

static RotMatrix FromVectorAndRotationAngle	(	DVec3dCR	axis,
		double	radians,
		RotMatrixR	derivativeMatrix
	)

static

Returns a matrix representing rotation around a vector.

Also returns its derivatives with respect to the angle.

Parameters

[in]	axis	The axis of rotation
[in]	radians	The rotation angle
[out]	derivativeMatrix	derivative of returned matrix.

void GetColumn	(	DVec3dR	vector,
		int	col
	)		const

Returns a point taken from a column of a matrix.

Parameters

[out]	vector	filled vector
[in]	col	The index of column to extract. Column indices are 0, 1, 2.

void GetColumns	(	DVec3dR	vectorU,
		DVec3dR	vectorV,
		DVec3dR	vectorW
	)		const

Copies from columns of this instance matrix to corresponding points.

Parameters

[out]	vectorU	first column
[out]	vectorV	second column
[out]	vectorW	third column

double GetComponentByRowAndColumn	(	int	row,
		int	col
	)		const

Returns a value from a specified row and column of the matrix.

Parameters

[in]	row	The index of row to read. Row indices are 0, 1, 2.
[in]	col	The index of column to read. Column indices are 0, 1, 2.

void GetQuaternion	(	DPoint4dR	quat,
		bool	transpose
	)		const

Parameters

[out]	quat	quaternion, stored as xyzw
[in]	transpose	true if matrix is stored transposed

void GetQuaternion	(	double *	pQuatAsDoubleArray,
		bool	transpose
	)		const

Parameters

[out]	pQuatAsDoubleArray	quaternion, stored as (w,x,y,z) in an array of doubles.
[in]	transpose	true if matrix is stored transposed

double GetRotationAngleAndVector ( DVec3dR axis ) const

Returns the angle of rotation of this instance and sets axis to be the normalized vector about which this instance rotates.

NOTE: this instance is assumed to be a (rigid body, i.e. orthogonal) rotation matrix. Since negating both angle and axis produces an identical rotation, calculations are simplified by assuming (and returning) the angle in [0,Pi].

Parameters

[out] axis normalized axis of rotation

Returns: rotation angle (in radians) between 0 and Pi, inclusive

void GetRow	(	DVec3dR	vector,
		int	row
	)		const

Returns a vector taken from a column of a matrix.

Parameters

[out]	vector	filled vector
[in]	row	The index of row to extract. Row indices are 0, 1, and 2.

void GetRows	(	DVec3dR	vectorU,
		DVec3dR	vectorV,
		DVec3dR	vectorW
	)		const

Copies from rows of this instance matrix to corresponding points.

Parameters

[out]	vectorU	first row
[out]	vectorV	second row
[out]	vectorW	third row

void GetRowValues	(	double &	x00,
		double &	x01,
		double &	x02,
		double &	x10,
		double &	x11,
		double &	x12,
		double &	x20,
		double &	x21,
		double &	x22
	)		const

Get all contents as individual doubles, moving along rows.

void GetRowValuesXY ( double data[4] ) const

Copies 4 doubles from xx,xy,yx,yy positions into an array.

Parameters

[out] data returned data – first 2 entries in row 0, then first 2 in row 1.

void GivensColumnOp	(	double	c,
		double	s,
		int	i0,
		int	i1
	)

Apply a Givens "column operation", i.e.

post-multiply by a Givens rotation matrix. The Givens matrix is an identity except for the 4 rotational entries, viz R(i0,i0)=R(i1,i1)=c R(i0,i1)=-s R(i1,i0)=s

Parameters

[in]	c	The cosine of givens rotation.
[in]	s	The sine of givens rotation.
[in]	i0	The index of the first affected row.
[in]	i1	The index of the second affected row.

void GivensRowOp	(	double	c,
		double	s,
		int	i0,
		int	i1
	)

Apply a Givens "row operation", i.e.

pre-multiply by a Givens rotation matrix. The Givens matrix is an identity except for the 4 rotational entries, viz R(i0,i0)=R(i1,i1)=c R(i0,i1)=s R(i1,i0)=-s

Parameters

[in]	c	The cosine of givens rotation.
[in]	s	The sine of givens rotation.
[in]	i0	The index of the first affected row.
[in]	i1	The index of the second affected row.

void HyperbolicColumnOp	(	double	secant,
		double	tangent,
		int	i0,
		int	i1
	)

Apply a hyperbolic "column operation", i.e.

pre-multiply by a hyperbolic reflection matrix The matrix is an identity except for the 4 entries R(i0,i0)=R(i1,i1)=secant R(i0,i1)=R(i1,i0)=tangent

Parameters

[in]	secant	The cosine of reflection.
[in]	tangent	The sine of reflection.
[in]	i0	The index of the first affected row.
[in]	i1	The index of the second affected row.

void HyperbolicRowOp	(	double	secant,
		double	tangent,
		int	i0,
		int	i1
	)

Apply a hyperbolic "row operation", i.e.

pre-multiply by a hyperbolic reflection matrix The matrix is an identity except for the 4 entries R(i0,i0)=R(i1,i1)=secant R(i0,i1)=R(i1,i0)=tangent

Parameters

[in]	secant	The cosine of reflection.
[in]	tangent	The sine of reflection.
[in]	i0	The index of the first affected row.
[in]	i1	The index of the second affected row.

void InitFrom ( TransformCR transform )

Sets this instance matrix by copying the matrix part of the trasnform.

Parameters

[in] transform The transformation whose matrix part is returned

bool InitFrom1Vector	(	DVec3dCR	dir,
		int	axis,
		bool	normalize
	)

Initializes this instance matrix so that the indicated axis (axis = 0,1,or 2) is aligned with the vector dir.

The normalize flag selects between normalized axes (all matrix columns of unit length) and unnormalized axes (all matrix columns of same length as the dir vector).

Parameters

[in]	dir	The fixed direction vector
[in]	axis	The axis column to be aligned with direction
[in]	normalize	true to have normalized columns

Returns: true if the direction vector is nonzero.

void InitFrom2Vectors	(	DVec3dCR	xVector,
		DVec3dCR	yVector
	)

Copies vectors into the x and y columns of this instance matrix and sets the z column to their cross product.

Use squareAndNormalizeColumns to force these (possibly skewed and scaled) coordinate axes to be perpendicular

Parameters

[in]	xVector	The vector to place in column 0
[in]	yVector	The vector to place in column 1

void InitFromAxisAndRotationAngle	(	int	axis,
		double	radians
	)

Returns a matrix of rotation about the x,y, or z axis (indicated by axis = 0,1, or 2) by an angle in radians.

Parameters

[in]	axis	The axis index 0=x, 1=y, 2=z
[in]	radians	The rotation angle in radians

void InitFromColumnVectors	(	DVec3dCR	vectorU,
		DVec3dCR	vectorV,
		DVec3dCR	vectorW
	)

Returns a matrix with 3 points copied to respective columns.

Parameters

[in]	vectorU	The vector to insert in column 0
[in]	vectorV	The vector to insert in column 1
[in]	vectorW	The vector to insert in column 2

void InitFromDirectionAndScale	(	DVec3dCR	vector,
		double	scale
	)

Initializes a matrix which scales along a vector direction.

Parameters

[in]	vector	The scaling direction
[in]	scale	The scale factor

void InitFromPrincipleAxisRotations	(	RotMatrixCR	inMatrix,
		double	xrot,
		double	yrot,
		double	zrot
	)

Returns the product {RX*RY*RZ*M} where RX, RY, and RZ are rotations (in radians) around X, Y, and Z axes, and M is the input matrix.

Parameters

[in]	inMatrix	The prior matrix
[in]	xrot	The x axis rotation
[in]	yrot	The y axis rotation
[in]	zrot	The z axis rotation

void InitFromQuaternion ( DPoint4dCR quat )

Parameters

[in] quat The quaternion, stored as (xyzw)

void InitFromQuaternion ( const double * pQuatAsDoubleArray )

Parameters

[in] pQuatAsDoubleArray The quaternion, stored as (w,x,y,z) in an array of doubles.

void InitFromRowValues	(	double	x00,
		double	x01,
		double	x02,
		double	x10,
		double	x11,
		double	x12,
		double	x20,
		double	x21,
		double	x22
	)

Initializes a matrix with the 9 specified coefficients given in "row major" order.

Parameters

[in]	x00	The 00 entry
[in]	x01	The 01 entry
[in]	x02	The 02 entry
[in]	x10	The 10 entry
[in]	x11	The 11 entry
[in]	x12	The 12 entry
[in]	x20	The 20 entry
[in]	x21	The 21 entry
[in]	x22	The 22 entry

void InitFromRowValuesXY	(	double	x00,
		double	x01,
		double	x10,
		double	x11
	)

Initializes a matrix with the 4 specified coefficients in xx,xy,yx,yy positions, and 1 in zz in "row major" order.

Parameters

[in]	x00	The 00 entry
[in]	x01	The 01 entry
[in]	x10	The 10 entry
[in]	x11	The 11 entry

void InitFromRowValuesXY ( double const data[4] )

Initializes a matrix with 4 coefficients in xx,xy,yx,yy positions, and 1 in zz in "row major" order.

Parameters

[in] data matrix entries in order xx,xy,yx,yy

void InitFromRowVectors	(	DVec3dCR	vectorU,
		DVec3dCR	vectorV,
		DVec3dCR	vectorW
	)

Initializes a matrix with 3 points copied to respective rows.

Parameters

[in]	vectorU	The vector to insert in row 0
[in]	vectorV	The vector to insert in row 1
[in]	vectorW	The vector to insert in row 2

void InitFromScale ( double scale )

Initializes a uniform scaling matrix.

Parameters

[in] scale The scale factor.

void InitFromScaledOuterProduct	(	DVec3dCR	vectorU,
		DVec3dCR	vectorV,
		double	scale
	)

Returns a 'rank one' matrix defined as a scale factor times the 'vector outer product' of two vectors, i.e.

as the matrix {s*U*V^T}

Parameters

[in]	vectorU	The column vector U
[in]	vectorV	The row vector V
[in]	scale	The scale factor

void InitFromScaleFactors	(	double	xscale,
		double	yscale,
		double	zscale
	)

Returns a scaling matrix with respective x, y, and z scaling factors.

Parameters

[in]	xscale	The x direction scale factor
[in]	yscale	The y direction scale factor
[in]	zscale	The z direction scale factor

void InitFromVectorAndRotationAngle	(	DVec3dCR	axis,
		double	radians
	)

Initializes a matrix representing rotation around a vector.

Parameters

[in]	axis	The axis of rotation
[in]	radians	The rotation angle

void InitIdentity ( )

Initialize an identity matrix.

void InitProduct	(	RotMatrixCR	rotMatrixA,
		RotMatrixCR	rotMatrixB
	)

Returns the product {A*B} of two matrices.

Parameters

[in]	rotMatrixA	The first factor
[in]	rotMatrixB	The second factor

void InitProduct	(	RotMatrixCR	rotMatrixA,
		RotMatrixCR	rotMatrixB,
		RotMatrixCR	rotMatrixC
	)

Returns the product of three matrices.

Parameters

[in]	rotMatrixA	The first factor
[in]	rotMatrixB	The second factor
[in]	rotMatrixC	The third factor

void InitProduct	(	RotMatrixCR	rotMatrixA,
		TransformCR	transformB
	)

Sets this instance to the product of matrix rotMatrixA times the matrix part of transform transformB.

In this 'post multiplication' the matrix part of transformB multiplies rotMatrixA ON THE RIGHT and the translation part of transformB is ignored.

Parameters

[in]	rotMatrixA	The first factor (matrix)
[in]	transformB	The second factor (transform)

void InitProduct	(	TransformCR	transformA,
		RotMatrixCR	rotMatrixB
	)

Returns to the product of the matrix part of transform transformA times matrix rotMatrixB.

In this 'pre multiplication' the matrix part of transformA multiplies rotMatrixB ON THE LEFT and the translation part of transformA is ignored.

Parameters

[in]	transformA	The first factor (transform)
[in]	rotMatrixB	The second factor (matrix)

void InitProductRotMatrixRotMatrixTranspose	(	RotMatrixCR	rotMatrixA,
		RotMatrixCR	rotMatrixB
	)

Returns the product of rotMatrixA times the transpose of rotMatrixB.

Parameters

[in]	rotMatrixA	The first factor
[in]	rotMatrixB	The second factor (to be transposed)

void InitProductRotMatrixTransposeRotMatrix	(	RotMatrixCR	rotMatrixA,
		RotMatrixCR	rotMatrixB
	)

Returns the product of the transpose of rotMatrixA times rotMatrixB.

Parameters

[in]	rotMatrixA	The first factor (to be transposed)
[in]	rotMatrixB	The second factor

bool InitRotationFromOriginXY	(	DPoint3dCR	origin,
		DPoint3dCR	xPoint,
		DPoint3dCR	yPoint
	)

Set this instance matrix to be an orthogonal (rotation) matrix with column 0 in the direction from the origin to the x point, column 1 in the plane of the 3 points, directed so the Y point on the positive side, and column 2 as their cross product.

Parameters

[in]	origin	The reference point
[in]	xPoint	The x axis target point
[in]	yPoint	The 3rd point defining xy plane.

bool InitRotationFromVectorToVector	(	DVec3dCR	startVector,
		DVec3dCR	endVector
	)

(conditionally) initialize the instance as the (smallest) rotation that moves startVector so it is in the direction of endVector.

In the normal case where the vectors are not parallel or antiparallel, this is a rotation around their cross product.

Returns: false if one or both are zero vectors.

Remarks: if the vectors are direction opposite, the rotation is around an arbitrarily

Parameters

[in]	startVector	starting vector
[in]	endVector	ending vector.

void InitTransposedFromQuaternionWXYZ ( const double * pQuatAsDoubleArray )

Initialization, compatible with mdlRMatrix_fromQuat.

Parameters

[in] pQuatAsDoubleArray The quaternion, stored as (w,x,y,z) in an array of doubles.

bool InverseOf ( RotMatrixCR forward )

Returns the inverse of the a matrix.

Parameters

[in] forward The input matrix

Returns: true if the matrix is invertible.

bool Invert ( )

Inverts this instance matrix in place.

Returns: true if the matrix is invertible.

bool IsDiagonal ( ) const

Tests if a matrix has small offdiagonal entries compared to diagonals.

The specific test condition is that the largest off diagonal absolute value is less than a tight tolerance fraction times the largest diagonal entry.

Returns: true if matrix is approximately diagonal

bool IsEqual ( RotMatrixCR matrix2 ) const

Tests for equality between two matrices "Equality" means relative error less than 1.0e-12, in the sense that each component-wise difference is less than 1.0e-12 times the largest absolute value of the components of one matrix.

Parameters

[in] matrix2 The second matrix

Returns: true if the matrices are identical.

bool IsEqual	(	RotMatrixCR	matrix2,
		double	tolerance
	)		const

Tests for equality between two matrices.

Parameters

[in]	matrix2	The second matrix
[in]	tolerance	The relative error tolerance. Absolute tolerance is this (relative) tolerance times the largest absolute value in Matrix1.

Returns: true if the matrices are identical within tolerance.

bool IsIdentity ( ) const

Tests if a matrix is the identity matrix.

Returns: true if matrix is approximately an identity.

bool IsNearRigidScale	(	RotMatrixR	dest,
		int	primaryAxis = `0`,
		double	tolerance = `1.0e-6`
	)		const

Determine if a matrix is close to a pure rotate and scale.

If source is not near rigid, return false and copy to the output. If near an identity return identity. If nearly perpendicular with scales other than 1, clean preserving the length and direction of the primary axis. This is intended to be used with a crude (e.g. 1.0e-6) reltol to identify old DGN file matrices that are "dirty" by modern standards but were meant to be identity, rotation, or scaled rotations in the UOR era.

Parameters

[in]	dest	result matrix
[in]	primaryAxis	axis whose orientation and direction is preserved.
[in]	tolerance	relative tolerance for recognizing near-perpendicular conditions.

bool IsNearSignedPermutation	(	RotMatrixR	result,
		double	tolerance
	)		const

Test if this instance matrix does nothing more than exchange and possibly negate principle axes, within a tolerance.

Parameters

[out]	result	the nearby permutation, or the orignal matrix if none near.
[in]	tolerance	tolerance for comparison to the permutation

Returns: true if the matrix is a near permutation of the principle axes.

bool IsOrthogonal ( ) const

Test if this instance matrix is orthogonal, i.e.

its transpose is its inverse. This class of matrices includes both rigid body rotations and reflections.

Returns: true if the matrix is orthogonal.

bool IsOrthonormal	(	RotMatrixR	columns,
		DVec3dR	axisScales,
		double &	axisRatio
	)		const

Test if this instance matrix has orthonormal columns, i.e.

its columns are all perpendicular to one another.

Parameters

[out]	columns	matrix containing the unit vectors along the columns.
[out]	axisScales	point whose x, y, and z components are the magnitudes of the original columns.
[out]	axisRatio	smallest axis length divided by largest.

Returns: true if the matrix is orthonormal.

bool IsPlanar ( DVec3dCR normal ) const

Tests if this instance matrix has no effects perpendicular to any plane with the given normal.

This will be true if the matrix represents a combination of (a) scaling perpencicular to the normal and (b) rotation around the normal.

Parameters

[in] normal The plane normal

Returns: true if the matrix has no effects perpendicular to any plane with the given normal.

bool IsRigid ( ) const

Test if a matrix is a rigid body rotation, i.e.

its transpose is its inverse and it has a positive determinant.

Returns: true if the matrix is a rigid body rotation.

bool IsRigidScale	(	RotMatrixR	columns,
		double &	scale
	)		const

Test if this instance matrix is composed of only rigid rotation and scaling.

Parameters

[out]	columns	matrix containing the unit vectors along the columns.
[out]	scale	largest axis scale factor. If function value is true, the min scale is the same. Use areColumnsOrthonormal to get separate column scales.

Returns: true if the matrix is orthonormal.

bool IsSignedPermutation ( ) const

Test if this instance matrix does nothing more than exchange and possibly negate principle axes.

Returns: true if the matrix is a permutation of the principle axes.

bool IsUniformScale ( double & maxScale ) const

Tests if a matrix has (nearly) equal diagaonal entries and (nearly) zero off diagonals.

Tests use a tight relative tolerance.

Parameters

[out] maxScale the largest diagaonal entry

Returns: true if matrix is approximately diagonal

DRange1d LowerTriangleAbsRange ( )

return the range of absolute values strictly below the diagonal.

double LowerTriangleMaxAbs ( )

return the largest absolute value in the lower triangle.

double MaxAbs ( ) const

Find the largest absolute value of entries in the matrix.

Returns: largest absolute value in matrix

double MaxDiff ( RotMatrixCR matrix2 ) const

Returns the largest absolute value difference between corresponding coefficients in Matrix1 and Matrix2.

Parameters

[in] matrix2 The matrix to compare to

Returns: largest absolute difference between the two matrices.

void Multiply	(	DPoint4dP	result,
		DPoint4dCP	point,
		int	numPoint
	)		const

Computes {M*P[i]} where M is this instance matrix and each P[i] is a point in the input array point.

Each result is placed in the corresponding entry in the output array result. The same array may be named for the input and output arrays.

Parameters

[out]	result	output points
[in]	point	The input points
[in]	numPoint	The number of points

void Multiply	(	DPoint2dP	result,
		DPoint2dCP	point,
		int	numPoint
	)		const

Computes {M*P[i]} where M is this instance matrix and each P[i] is a point in the input array point.

Each result is placed in the corresponding entry in the output array result. The same array may be named for the input and output arrays.

Parameters

[out]	result	output points
[in]	point	The input points
[in]	numPoint	The number of points

void Multiply	(	DRange3dR	outRange,
		DRange3dCR	inRange
	)		const

computes the 8 corner points of the range cube defined by the two points of pRange, multiplies matrix times each point, and computes the twopoint range limits (min max) of the resulting rotated box.

Note that the volume of the rotated box is generally larger than that of the input because the postrotation minmax operation expands the box. Ranges that are null as defined by inRange->isNull are left unchanged.

Parameters

[out]	outRange	range of transformed cube
[in]	inRange	Any two corners of original cube

void Multiply ( DPoint3dR point ) const

Computes the product {M*P} where M is this instance matrix and P the input point.

The result overwrites the previous coordinates in point.

Parameters

[in,out] point The point to be updated

void Multiply	(	DPoint3dR	result,
		DPoint3dCR	point
	)		const

Returns the product of a matrix times a point.

Parameters

[out]	result	result of the multiplication.
[in]	point	The known point.

void Multiply	(	DPoint3dP	result,
		DPoint3dCP	point,
		int	numPoint
	)		const

Computes {M*P[i]} where M is this instance matrix and each P[i] is a point in the input array point.

Each result is placed in the corresponding entry in the output array result. The same array may be named for the input and output arrays.

Parameters

[out]	result	output points
[in]	point	The input points
[in]	numPoint	The number of points

void Multiply	(	bvector< DPoint3d > &	outXYZ,
		bvector< DPoint3d > const &	inXYZ
	)		const

Description Multiply points. (Matrix on left, point on right as column vector)

Parameters

[in]	outXYZ	transformed coordinates.
[in]	inXYZ	input coordinates

void Multiply	(	bvector< DPoint2d > &	out,
		bvector< DPoint2d > const &	in
	)		const

Description Multiply 2D points. (Matrix on left, point on right as column vector)

Parameters

[in]	out	transformed coordinates. z row of matrix ignored.
[in]	in	input coordinates. z=0 implied for multiplication.

void Multiply	(	bvector< DPoint4d > &	xyzwOut,
		bvector< DPoint4d > const &	xyzwIn
	)		const

Multiply xyzw, with matrix w row and column 0001.

Parameters

[in]	xyzwOut	transformed coordinates.
[in]	xyzwIn	input coordinates.

void MultiplyComponents	(	DPoint3dR	result,
		double	x,
		double	y,
		double	z
	)		const

Returns the product of a matrix times a point, with the point given as separate components.

Parameters

[out]	result	result of multiplication
[in]	x	The x component of input point
[in]	y	The y component of input point
[in]	z	The z component of input point

void MultiplyTranspose	(	DPoint3dR	result,
		DPoint3dCR	point
	)		const

Returns the product of a matrix transpose times a point.

Parameters

[out]	result	result of the multiplication.
[in]	point	The known point.

void MultiplyTranspose ( DPoint3dR point ) const

Computes the product {P*M} where M is this instance matrix and P is the input point The result overwrites the previous coordinates in the point.

Parameters

[in,out] point The point to be multiplied

void MultiplyTranspose	(	DPoint3dP	result,
		DPoint3dCP	point,
		int	numPoint
	)		const

Computes {P[i]*M} where M is this instance matrix and each P[i] is a point in the input array point, transposed into row form.

(Equivalently, multiply M^*p[i], where M^ indicates transpose.) Each result is placed in the corresponding entry in the output array result. The same array may be named for the input and output arrays.

Parameters

[out]	result	output points
[in]	point	The input points
[in]	numPoint	The number of points

void MultiplyTranspose	(	bvector< DPoint3d > &	outXYZ,
		bvector< DPoint3d > const &	inXYZ
	)		const

Multiply the transposed matrix times points. (Tranposed matrix on left, point on right as column vector. Or (equivalent) point on left as row vector, matrix on right)

Parameters

[in]	outXYZ	transformed coordinates.
[in]	inXYZ	input coordinates

void MultiplyTransposeComponents	(	DPoint3dR	result,
		double	x,
		double	y,
		double	z
	)		const

Returns the product P = [x,y,z]*M where M is the input matrix and P is the product point.

Parameters

[out]	result	product point
[in]	x	The x component
[in]	y	The y component
[in]	z	The z component

void NormalizeColumnsOf	(	RotMatrixCR	inMatrix,
		DVec3dR	scaleVector
	)

Returns a matrix whose rows are unit vectors in the same drection as corresponding columns of the input matrix.

Also (optionally) stores the original column magnitudes as components of the point.

Parameters

[in]	inMatrix	The input matrix
[out]	scaleVector	length of original columns

void NormalizeRowsOf	(	RotMatrixCR	inMatrix,
		DVec3dR	scaleVector
	)

Returns a matrix whose rows are unit vectors in the same drection as corresponding rows of the input matrix.

Also (optionally) stores the original row magnitudes as components of the point.

Parameters

[in]	inMatrix	The input matrix
[out]	scaleVector	length of original rows

void OffDiagonalAbsRange	(	double &	minValue,
		double &	maxValue
	)		const

Return the (absolute value) range of entries off the diagonal.

Parameters

[out]	minValue	smallest absolute value
[out]	maxValue	largest absolute value

void OffDiagonalSignedRange	(	double &	minValue,
		double &	maxValue
	)		const

Return the (signed) range of entries off the diagonal.

Parameters

[out]	minValue	smallest signed value
[out]	maxValue	largest signed value

bool RotateAndSkewFactors	(	RotMatrixR	rotation,
		RotMatrixR	skewFactor,
		int	primaryAxis,
		int	secondaryAxis
	)		const

Factor as {rotation*skewFactor} where the rotation favors indicated primary and secondary axes.

Parameters

[out]	rotation	the (orthogonal, right handed) rotation.
[out]	skewFactor	the scale and skew parts.
[in]	primaryAxis	selects column whose direction is preserved.
[in]	secondaryAxis	selects columns that defines plane (with primaryAxis)

Returns: true if primary and secondary are independent.

static RotMatrix RotationFromOriginXY	(	DPoint3dCR	origin,
		DPoint3dCR	xPoint,
		DPoint3dCR	yPoint
	)

static

Set this instance matrix to be an orthogonal (rotation) matrix with column 0 in the direction from the origin to the x point, column 1 in the plane of the 3 points, directed so the Y point on the positive side, and column 2 as their cross product.

Parameters

[in]	origin	The reference point
[in]	xPoint	The x axis target point
[in]	yPoint	The 3rd point defining xy plane.

void Scale	(	RotMatrixCR	leftMatrix,
		double	xs,
		double	ys,
		double	zs,
		RotMatrixCR	rightMatrix
	)

Returns a matrix formed from a scaling matrix which is multiplied on the left and/or right with other matrices.

That is, form LeftMatrix * ScaleMatrix * RightMatrix where the ScaleMatrix is constructed from the given scale factors.

Parameters

[in]	leftMatrix	The matrix on left of product
[in]	xs	The x scale factor
[in]	ys	The y scale factor
[in]	zs	The z scale factor
[in]	rightMatrix	The matrix on right of product

void ScaleColumns	(	RotMatrixCR	in,
		double	xs,
		double	ys,
		double	zs
	)

Applies scale factors to corresponding columns of the input matrix, and places the result in this instance matrix.

Parameters

[in]	in	The initial matrix
[in]	xs	The scale factor for column 0
[in]	ys	The scale factor for column 1
[in]	zs	The scale factor for column 2

void ScaleColumns	(	double	xs,
		double	ys,
		double	zs
	)

Applies scale factors to corresponding columns.

Parameters

[in]	xs	The scale factor for column 0
[in]	ys	The scale factor for column 1
[in]	zs	The scale factor for column 2

void ScaleRows	(	RotMatrixCR	inMatrix,
		double	xScale,
		double	yScale,
		double	zScale
	)

Applies scale factors to corresponding rows of the input matrix, and places the result in this instance matrix.

Parameters

[in]	inMatrix	The initial matrix
[in]	xScale	The scale factor for row 0
[in]	yScale	The scale factor for row 1
[in]	zScale	The scale factor for row 2

void SetColumn	(	DVec3dCR	vector,
		int	col
	)

Set the components in a column.

Parameters

[in]	vector	new values
[in]	col	The index of column to change. Column indices are 0, 1, 2.

void SetRow	(	DVec3dCR	vector,
		int	row
	)

Set the components in a row.

Parameters

[in]	vector	new values
[in]	row	The index of row to change. Row indices are 0, 1, 2.

void ShuffleColumnsOf	(	RotMatrixCR	inMatrix,
		int	i0,
		int	i1,
		int	i2
	)

Moves columns 0, 1, 2 of the input matrix into columns i0, i1, i2 of the instance.

Parameters

[in]	inMatrix	The input matrix
[in]	i0	The column to receive input column 0
[in]	i1	The column to receive input column 1
[in]	i2	The column to receive input column 2

bool Solve	(	DPoint3dR	result,
		DPoint3dCR	point
	)		const

Return the product of a matrix inverse and a point.

Parameters

[out]	result	the unknown point
[in]	point	The The known point

Returns: false if this instance is singular.

bool SolveArray	(	bvector< DPoint3d > &	xyzOut,
		bvector< DPoint3d > const &	xyzIn
	)		const

Solve M*xyzOut[i] = xyzIn[i] for array of points.

(Equivalent to multiplying by the matrix inverse)

Parameters

[in]	xyzOut	solution coordinates
[in]	xyzIn	input coordinates.

bool SolveArray	(	DPoint3dP	result,
		DPoint3dCP	point,
		int	numPoints
	)		const

Solves the matrix equation AX=B, where A is this instance, B is the matrix of numPoints input points and X is the matrix of numPoints output points.

point and result may have identical addresses.

Parameters

[out]	result	column points of solution matrix to system
[in]	point	The column points of constant matrix of system
[in]	numPoints	The number of input/output points

Returns: false if this instance is singular.

bool SolveTranspose	(	DPoint3dR	result,
		DPoint3dCR	point
	)		const

Return the product of a matrix inverse transpose and a point.

Parameters

[out]	result	result of the multiplication
[in]	point	The known point multipled by the matrix inverse.

Returns: false if this instance is singular.

bool SquareAndNormalizeColumns	(	RotMatrixCR	inMatrix,
		int	primaryAxis,
		int	secondaryAxis
	)

Adjust the direction and length of columns of the input matrix to produce an instance matrix which has perpendicular, unit length columns.

The column whose index is primaryAxis (i.e. 0,1,2 for x,y,z axis of coordinate frame) is normalized to unit length in its current direction. The column whose index is secondaryAxis is unit length and perpendicular to the primaryAxis column, and lies in the same plane as that defined by the original primary and secondary columns. To preserve X axis and XY plane, call with axis id's 0 and 1. To preserve Z axis and ZX plane, call with axis id's 2 and 0. inMatrix and pMatrix may be the same address.

Parameters

[in]	inMatrix	The input matrix
[in]	primaryAxis	The axis id (0, 1, 2) which is to be normalized but left in its current direction
[in]	secondaryAxis	The axis id (0, 1, 2) which is to be kept within the plane of the primary and secondary axis.

Returns: false if primaryAxis and secondaryAxis are the same, or either axis has zero length

bool SquareAndNormalizeColumns	(	RotMatrixCR	inMatrix,
		int	primaryAxis,
		int	secondaryAxis,
		int	preferredOrientation
	)

bool SquareAndNormalizeColumnsAnyOrder	(	RotMatrixCR	inMatrix,
		int	preferredOrientation
	)

Returns an orthogonal matrix that preserves aligns with the columns of inMatrix.

This is done by trying various combinations of primary and secondary axes until one succeeds in squareAndNormalizeColumns.

Parameters

[in]	inMatrix	The input matrix
[in]	preferredOrientation	1 for right handed system -1 for left handed system 0 to match orientation of input (but default to right handed if input is singular)

bool SquareAndNormalizeColumnsAnyOrder ( RotMatrixCR inMatrix )

Returns an orthogonal matrix that preserves aligns with the columns of inMatrix.

This is done by trying various combinations of primary and secondary axes until one succeeds in squareAndNormalizeColumns.

Parameters

[in] inMatrix The input matrix

void Subtract ( RotMatrixCR delta )

Subtract a matrix (componentwise, in place).

Parameters

[in] delta The matrix to subtract

double SumDiagonalSquares ( ) const

Computes the sum of the squares of the diagonal entries of this instance matrix.

Returns: Sum of squares of diagonal entries

void SumOf	(	RotMatrixCR	matrix0,
		RotMatrixCR	matrix1,
		double	scale1,
		RotMatrixCR	matrix2,
		double	scale2
	)

Returns {Matrix0 + Matrix1*s1+Matrix2*s2}, i.e.

the sum of matrix M0, matrix M1 multiplied by scale s1, and matrix M2 multiplied by scale s2. Any combination of the matrix pointers may have identical addresses.

Parameters

[in]	matrix0	The matrix0 of formula
[in]	matrix1	The matrix1 of formula
[in]	scale1	The scale factor to apply to Matrix1
[in]	matrix2	The matrix2 of formula
[in]	scale2	The scale factor to apply to Matrix2

double SumOffDiagonalSquares ( ) const

Computes the sum of the squares of the off-diagonal entries of this instance matrix.

Returns: sum of square of off-diagonal entries of the matrix.

double SumSquares ( ) const

Return the sum of squares of coefficients in a matrix.

Returns: Sum of squares of all entries in matrix

void Transpose ( )

Transposes a matrix in place.

void TransposeOf ( RotMatrixCR matrix )

Initializes this instance as the transpose of a matrix.

Parameters

[in] matrix The input matrix

DRange1d UpperTriangleAbsRange ( )

return the range of absolute values strictly above the diagonal.

double UpperTriangleMaxAbs ( )

return the largest absolute value in the upper triangle.

void Zero ( )

returns a zero matrix.

Member Data Documentation

double form3d[3][3]

matrix coefficients. These are public, but direct use of the arrays is discouraged.

The documentation for this struct was generated from the following file:

rotmatrix.h

Public Member Functions

Static Public Member Functions

Public Attributes

Detailed Description

Member Function Documentation

Member Data Documentation