IC Python API:RLPy RMatrix3

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Main article: Modules.
Last modified: 04/13/2020

Description

This class represent a standard 3x3 matrix. This class provides access to RLPy's internal 3x3 matrix operators and related functions. iClone uses row-major order where consecutive elements of a row reside next to each other, and the data is read from left to right, top to bottom, in a vertical zig-zag: 

[0, 1, 2]
[3, 4, 5]
[6, 7, 8]

Constructor & Destructor

__init__(self, fM00, fM01, fM02, fM10, fM11, fM12, fM20, fM21, fM22)

The constructor. Initialize a new 3x3 matrix with another RMatrix3 object.

Parameters

fM00 [IN] Initialization value - float
fM01 [IN] Initialization value - float
fM02 [IN] Initialization value - float
fM10 [IN] Initialization value - float
fM11 [IN] Initialization value - float
fM12 [IN] Initialization value - float
fM20 [IN] Initialization value - float
fM21 [IN] Initialization value - float
fM22 [IN] Initialization value - float

Returns

Returns the row vector of the matrix - RMatrix3 
1 matrix3 = RLPy.RMatrix3( 1, 0, 0,
2                          0, 2, 0,
3                          0, 0, 3 )

__init__(self, fM00, fM11, fM22)

The constructor. Initialize a new 3x3 matrix with RMatrix3[0,0], RMatrix3[1,1], RMatrix3[2,2].

Parameters

fM00 [IN] Initialization value - float
fM11 [IN] Initialization value - float
fM22 [IN] Initialization value - float

Returns

Returns the row vector of the matrix - RMatrix3 
1 matrix3_init = RLPy.RMatrix3(1,2,3)
2 matrix3 = RLPy.RMatrix3( 1, 0, 0,
3                          0, 2, 0,
4                          0, 0, 3 )
5 
6 print( matrix3_init == matrix3 ) # true

__init__(self, args)

The constructor. Initialize a new 3x3 matrix with another RMatrix3 object.

Parameters

args [IN] A 3X3 matrix object - RMatrix3

Returns

Returns the row vector of the matrix - RMatrix3
1 matrix3 = RLPy.RMatrix3( 1, 0, 0,
2                          0, 2, 0,
3                          0, 0, 3 )
4 matrix3_copy = RLPy.RMatrix3(matrix3)                      
5 print( matrix3_copy == matrix3 ) # true

__init__(self, rAxis, fAngle)

The constructor. Initialize a new 3x3 matrix with RVector3 axis object and angle.

Parameters

rAxis [IN] a RVector3 object - RVector3
fAngle [IN] a float object - float

Returns

Returns the row vector of the matrix - RMatrix3 
1 matrix3 = RLPy.RMatrix3( RLPy.RVector3( 1, 0, 0 ), 3 )

Operators

+

The "addition" operator.

See Also: += 

 1 matrix3_a = RLPy.RMatrix3( 1, 2, 3,
 2                            0, 0, 0,
 3                            0, 0, 0 )
 4 matrix3_b = RLPy.RMatrix3( 2, 2, 2,
 5                            0, 0, 0,
 6                            0, 0, 0 )
 7 matrix3_result = matrix3_a + matrix3_b
 8 
 9 print( matrix3_result.GetRow(0)[0] == 1+2 ) # true
10 print( matrix3_result.GetRow(0)[1] == 2+2 ) # true
11 print( matrix3_result.GetRow(0)[2] == 3+2 ) # true

-

The "subtraction" operator.

See Also: -= 

 1 matrix3_a = RLPy.RMatrix3( 1, 2, 3,
 2                            0, 0, 0,
 3                            0, 0, 0 )
 4 matrix3_b = RLPy.RMatrix3( 2, 2, 2,
 5                            0, 0, 0,
 6                            0, 0, 0 )
 7 matrix3_result = matrix3_a - matrix3_b
 8 
 9 print( matrix3_result.GetRow(0)[0] == 1-2 ) # true
10 print( matrix3_result.GetRow(0)[1] == 2-2 ) # true
11 print( matrix3_result.GetRow(0)[2] == 3-2 ) # true

*

The "multiplication" operator.

See Also: *= 

1 matrix3_a = RLPy.RMatrix3( 1, 2, 3,
2                            0, 0, 0,
3                            0, 0, 0 )
4 matrix3_b = RLPy.RMatrix3( 2, 0, 0,
5                            2, 0, 0,
6                            2, 0, 0 )
7 matrix3_result = matrix3_a * matrix3_b
8 print( matrix3_result.GetRow(0)[0] == 1*2 + 2*2 + 3*2 ) # true

/

The "division" operator.

See Also: /= 

1 matrix3_a = RLPy.RMatrix3( 1, 2, 3,
2                            0, 0, 0,
3                            0, 0, 0 )
4 matrix3_result = matrix3_a / 2
5 
6 print( matrix3_result.GetRow(0)[0] == 1/2 ) # true
7 print( matrix3_result.GetRow(0)[1] == 2/2 ) # true
8 print( matrix3_result.GetRow(0)[2] == 3/2 ) # true

-

The "unary minus" operator. 

1 matrix3_a = RLPy.RMatrix3( 1, 2, 3,
2                            0, 0, 0,
3                            0, 0, 0 )
4 matrix3_result = -matrix3_a
5 
6 print( matrix3_result.GetRow(0)[0] == -1 ) # true
7 print( matrix3_result.GetRow(0)[1] == -2 ) # true
8 print( matrix3_result.GetRow(0)[2] == -3 ) # true

==

The "equal to" operator. Performs a one-by-one comparison of the matrix array.

See Also: != 

1 matrix3_a = RLPy.RMatrix3( 1, 2, 3,
2                            0, 0, 0,
3                            0, 0, 0 )
4 matrix3_b = RLPy.RMatrix3( 1, 2, 3,
5                            0, 0, 0,
6                            0, 0, 0 )
7 print( matrix3_a == matrix3_b ) # true

!=

The "not equal to" operator. Performs a one-by-one comparison of the matrix array.

See Also: == 

1 matrix3_a = RLPy.RMatrix3( 1, 2, 3,
2                            0, 0, 0,
3                            0, 0, 0 )
4 matrix3_b = RLPy.RMatrix3( 4, 5, 6,
5                            0, 0, 0,
6                            0, 0, 0 )
7 print( matrix3_a != matrix3_b ) # true

>

The "greater than" operator. Performs a one-by-one comparison of the matrix array.

See Also: >= 

1 matrix3_a = RLPy.RMatrix3( 2, 0, 0,
2                            0, 0, 0,
3                            0, 0, 0 )
4 matrix3_b = RLPy.RMatrix3( 5, 0, 0,
5                            0, 0, 0,
6                            0, 0, 0 )
7 print( matrix3_b >matrix3_a ) # true

>=

The "greater than or equal to" operator. Performs a one-by-one comparison of the matrix array.

See Also: > 

1 matrix3_a = RLPy.RMatrix3( 1, 1, 3,
2                            0, 0, 0,
3                            0, 0, 0 )
4 matrix3_b = RLPy.RMatrix3( 1, 1, 9,
5                            0, 0, 0,
6                            0, 0, 0 )
7 print( matrix3_b >= matrix3_a ) # true

<

The "less than" operator. Performs a one-by-one comparison of the matrix array.

See Also: <= 

1 matrix3_a = RLPy.RMatrix3( 2, 0, 0,
2                            0, 0, 0,
3                            0, 0, 0 )
4 matrix3_b = RLPy.RMatrix3( 5, 0, 0,
5                            0, 0, 0,
6                            0, 0, 0 )
7 print( matrix3_a< matrix3_b ) # true

<=

The "less than" operator. Performs a one-by-one comparison of the matrix array.

See Also: < 

1 matrix3_a = RLPy.RMatrix3( 1, 1, 3,
2                            0, 0, 0,
3                            0, 0, 0 )
4 matrix3_b = RLPy.RMatrix3( 1, 1, 9,
5                            0, 0, 0,
6                            0, 0, 0 )
7 print( matrix3_a<= matrix3_b ) # true

+=

The "addition assignment" operator.

See Also: + 

 1 matrix3 =  RLPy.RMatrix3( 1, 2, 3,
 2                           0, 0, 0,
 3                           0, 0, 0 )
 4 matrix3 += RLPy.RMatrix3( 2, 2, 2,
 5                           0, 0, 0,
 6                           0, 0, 0 )
 7 
 8 print( matrix3.GetRow(0)[0] == 1+2 ) # true
 9 print( matrix3.GetRow(0)[1] == 2+2 ) # true
10 print( matrix3.GetRow(0)[2] == 3+2 ) # true

-=

The "subtraction assignment" operator.

See Also: - 

 1 matrix3 =  RLPy.RMatrix3( 1, 2, 3,
 2                           0, 0, 0,
 3                           0, 0, 0 )
 4 matrix3 -= RLPy.RMatrix3( 2, 2, 2,
 5                           0, 0, 0,
 6                           0, 0, 0 )
 7 
 8 print( matrix3.GetRow(0)[0] == 1-2 ) # true
 9 print( matrix3.GetRow(0)[1] == 2-2 ) # true
10 print( matrix3.GetRow(0)[2] == 3-2 ) # true

*=

The "multiplication assignment" operator.

See Also: * 

1 matrix3 =  RLPy.RMatrix3( 1, 2, 3,
2                           0, 0, 0,
3                           0, 0, 0 )
4 matrix3 *= 2
5 
6 print( matrix3.GetRow(0)[0] == 1*2 ) # true
7 print( matrix3.GetRow(0)[1] == 2*2 ) # true
8 print( matrix3.GetRow(0)[2] == 3*2 ) # true

/=

The "division assignment" operator.

See Also: / 

1 matrix3 =  RLPy.RMatrix3( 1, 2, 3,
2                           0, 0, 0,
3                           0, 0, 0 )
4 matrix3 /= 2
5 
6 print( matrix3.GetRow(0)[0] == 1/2 ) # true
7 print( matrix3.GetRow(0)[1] == 2/2 ) # true
8 print( matrix3.GetRow(0)[2] == 3/2 ) # true

Member Functions

MakeIdentity ( self )

This function can be used to initialize the 3x3 matrix. It is equivalent to setting the matrix to: 

[1 0 0]
[0 1 0]
[0 0 1]

Returns

This object - RMatrix3 

1 matrix3 = RLPy.RMatrix3()
2 matrix3.MakeIdentity()

M ( self, args )

Get the value of an element in a 3x3 matrix by row and column index.

Parameters

nRow [IN] Index of the row in the matrix - int
nCol [IN] Index of the column in the matrix - int

Returns

The matrix element specified by row and column - float
1 matrix3 = RLPy.RMatrix3()
2 matrix3.MakeIdentity()
3 
4 print(matrix3.M(0,0))  # <Swig Object of type 'float *' at 0x0000020316B015A0>

E ( self, args )

Get the value of an element in a 3x3 matrix by index number (from 0 to 8);

Parameters

nRow [IN] Index of the matrix.

Returns

The matrix element specified by index - float
1 matrix3 = RLPy.RMatrix3()
2 matrix3.MakeIdentity()
3 
4 print(matrix3.E(0)) #

GetRow ( self, nRow )

Retreive a row inside a 3x3 matrix.

Parameters

nRow [IN] Index of the row in the matrix - int

Returns

The row vector of the matrix - RVector3
1 matrix3 = RLPy.RMatrix3()
2 matrix3.MakeIdentity()
3 row0 = matrix3.GetRow(0)
4 
5 print(row0[0])
6 print(row0[1])
7 print(row0[2])

GetColumn( self, nCol )

Retreive a column inside a 3x3 matrix.

Parameters

nCol [IN] Index of the row in the matrix - int

Returns

The column vector of the matrix - RVector3
1 matrix3 = RLPy.RMatrix3()
2 matrix3.MakeIdentity()
3 col0 = matrix3.GetColumn(0)
4 
5 print(col0[0])
6 print(col0[1])
7 print(col0[2])

Transpose( self )

Obtain the transposed matrix by transposing the current m * n matrix into an n * m matrix by row-column swapping.

Returns

A new matrix containing this matrix's transpose - RMatrix3
 1 matrix3_orgin = RLPy.RMatrix3( 1, 2, 3,
 2                                4, 5, 6,
 3                                7, 8, 9 )
 4 matrix3_transpose = matrix3_orgin.Transpose()
 5 row0 = matrix3_orgin.GetRow(0)
 6 col0 = matrix3_transpose.GetColumn(0)
 7 
 8 print(row0[0] == col0[0])
 9 print(row0[1] == col0[1])
10 print(row0[2] == col0[2])

TransposeTimes( self, mM )

Multiply a transposed version of a 3x3 matrix with itself.

Parameters

mM [IN] the matrix - RMatrix3

Returns

A new matrix. (this^T * mM) - RMatrix3
 1 matrix3_orgin = RLPy.RMatrix3( 1, 2, 3,
 2                                4, 5, 6,
 3                                7, 8, 9 )
 4 matrix3_transpose_value = RLPy.RMatrix3( 2, 0, 0,
 5                                          0, 2, 0,
 6                                          0, 0, 2 )
 7 matrix3_transpose_times = matrix3_orgin.TransposeTimes(matrix3_transpose_value)
 8 row0 = matrix3_orgin.GetRow(0)
 9 col0 = matrix3_transpose_times.GetColumn(0)
10 
11 print(row0[0]*2 == col0[0])
12 print(row0[1]*2 == col0[1])
13 print(row0[2]*2 == col0[2])

TimesTranspose( self, mM )

Multiply this 3x3 matrix with a transposed version of itself.

Parameters

mM [IN] the matrix - RMatrix3

Returns

A new matrix. (this * M^T) - RMatrix3
 1 matrix3_orgin = RLPy.RMatrix3( 1, 2, 3,
 2                                4, 5, 6,
 3                                7, 8, 9 )
 4 matrix3_transpose_value = RLPy.RMatrix3( 3, 0, 0,
 5                                          0, 3, 0,
 6                                          0, 0, 3 )
 7 matrix3_times_transpose = matrix3_orgin.TimesTranspose(matrix3_transpose_value)
 8 row0 = matrix3_orgin.GetColumn(0)
 9 col0 = matrix3_times_transpose.GetColumn(0)
10 
11 print(row0[0]*3 == col0[0])
12 print(row0[1]*3 == col0[1])
13 print(row0[2]*3 == col0[2])

Inverse( self )

Obtain the inverse (reciprocal) of this 3x3 matrix (A^-1).

Returns

A new matrix containing this matrix's inverse - RMatrix3
1 matrix3_value = RLPy.RMatrix3( 1, 2, 3,
2                                2, 3, 4,
3                                4, 2, 1 )
4 matrix3_inverse = matrix3_value.Inverse()
5 row0 = matrix3_inverse.GetRow(0)
6 
7 print(row0[0])
8 print(row0[1])
9 print(row0[2])

Adjoint( self )

Adjugate this 3x3 matrix.

Returns

A new matrix containing this matrix's adjoint - RMatrix3
1 matrix3_value = RLPy.RMatrix3( 1, 2, 3,
2                                2, 3, 4,
3                                4, 2, 1 )
4 matrix3_Adjoint = matrix3_value.Adjoint()
5 row0 = matrix3_Adjoint.GetRow(0)
6 
7 print(row0[0])
8 print(row0[1])
9 print(row0[2])

AdjointTranspose( self )

Adjugate and transpose this 3x3 matrix.

Returns

A new adjugated and transposed matrix - RMatrix3
1 matrix3_value = RLPy.RMatrix3( 1, 2, 3,
2                                2, 3, 4,
3                                4, 2, 1 )
4 matrix3_Adjoint_transpose = matrix3_value.AdjointTranspose()
5 col0_Adjoint_transpose = matrix3_Adjoint_transpose.GetColumn(0)
6 
7 print(col0_Adjoint_transpose[0])
8 print(col0_Adjoint_transpose[1])
9 print(col0_Adjoint_transpose[2])

InverseTranspose( self )

Invert and transpose this 3x3 matrix.

Returns

A new inverted and transposed matrix - RMatrix3
1 matrix3_value = RLPy.RMatrix3( 1, 2, 3,
2                                2, 3, 4,
3                                4, 2, 1 )
4 matrix3_inverse_transpose = matrix3_value.InverseTranspose()
5 row0_inverse_transpose = matrix3_inverse_transpose.GetRow(0)
6 
7 print(row0_inverse_transpose[0])
8 print(row0_inverse_transpose[1])
9 print(row0_inverse_transpose[2])

Determinant( self )

Obtain the scalar value for this 3x3 matrix (|A|).

Returns

The determinant of the matrix - float
1 matrix3_value = RLPy.RMatrix3( 1, 2, 3,
2                                2, 3, 4,
3                                4, 2, 1 )
4 
5 print(matrix3_value.Determinant())

MaxColumn( self )

Find the maximum absolute value within this 3x3 matrix, and return the column in which the value is located. If all of the elements within the 3x3 matrix are 0 then return -1.

Returns

Index of column of M containing maximum abs entry, or -1 if M = 0 - int
1 matrix3_value = RLPy.RMatrix3( 10, 20, -30,
2                                 0,  0,   0,
3                                 0,  0,   0 )
4 
5 print(matrix3_value.MaxColumn()) # column:2 ->abs(-30)

MaxRow( self )

Find the maximum absolute value within this 3x3 matrix, and return the row in which the value is located. If all of the elements within the 3x3 matrix are 0 then return -1.

Returns

Index of row of M containing maximum abs entry, or -1 if M = 0 - int
1 matrix3_value = RLPy.RMatrix3( 10, 0, 0,
2                                20, 0, 0,
3                               -30, 0, 0 )
4 print(matrix3_value.MaxRow()) # Row:2 ->abs(-30)

OneNorm( self )

Return the sum of the column elements that contain the largest absolute values.

Returns

Norm of this 3x3 matrix - float
1 matrix3_row_value = RLPy.RMatrix3( 10, 0, 0,
2                                    20, 0, 0,
3                                   -30, 0, 0 )
4 print(matrix3_row_value.OneNorm()) # 10+20+abs(-30) = 60

InfNorm( self )

Return the sum of the row elements that contain the largest absolute values.

Returns

InfNorm of this 3x3 matrix - float
1 matrix3_column_value = RLPy.RMatrix3( 10, 20, -30,
2                                        0,  0,   0,
3                                        0,  0,   0 )
4 print(matrix3_column_value.InfNorm()) # 10+20+abs(-30) = 60

FromAxisAngle( self, rkAxis, fAngle )

Rotation matrix from axis angle。

Parameters

rkAxis [IN] axis vector - RVector3
fAngle [IN] angle in radians - float

Returns

A new matrix from specified axis angle - RMatrix3
 1 matrix3_orgin = RLPy.RMatrix3()
 2 matrix3_orgin.MakeIdentity()
 3 
 4 x_axis_vector = RLPy.RVector3( 1, 0, 0 )  # axis = "X"
 5 y_axis_vector = RLPy.RVector3( 0, 1, 0 )  # axis = "Y"
 6 z_axis_vector = RLPy.RVector3( 0, 0, 1 )  # axis = "Z"    
 7 
 8 matrix3_orgin.FromAxisAngle( x_axis_vector, 90 * RLPy.RMath.CONST_DEG_TO_RAD )
 9 matrix3_orgin.FromAxisAngle( y_axis_vector, 90 * RLPy.RMath.CONST_DEG_TO_RAD )
10 matrix3_orgin.FromAxisAngle( z_axis_vector, 90 * RLPy.RMath.CONST_DEG_TO_RAD )

RotationX( self, fAngle )

Rotate this 3x3 matrix around the x-axis.

Parameters

fAngle [IN] angle in radians - float

Returns

The rotated 3x3 matrix around the x-axis - RMatrix3
1 matrix3_orgin = RLPy.RMatrix3()
2 matrix3_orgin.MakeIdentity()
3 matrix3_orgin.RotationX( 90 * RLPy.RMath.CONST_DEG_TO_RAD )

RotationY( self, fAngle )

Rotate this 3x3 matrix around the y-axis。

Parameters

fAngle [IN] angle in radians - float

Returns

The rotated 3x3 matrix around the y-axis - RMatrix3
1 matrix3_orgin = RLPy.RMatrix3()
2 matrix3_orgin.MakeIdentity()
3 matrix3_orgin.RotationY( 90 * RLPy.RMath.CONST_DEG_TO_RAD )

RotationZ( self, fAngle )

Rotation this 3x3 matrix around the z-axis.

Parameters

fAngle [IN] angle in radians - float

Returns

A new 3x3 matrix of for rotations around z-axis - RMatrix3
1 matrix3_orgin = RLPy.RMatrix3()
2 matrix3_orgin.MakeIdentity()
3 matrix3_orgin.RotationZ( 90 * RLPy.RMath.CONST_DEG_TO_RAD )

AccuScale( self, rkScale )

Accumulate 3x3 matrix with scale vector.

Parameters

rkScale [IN] Scale vector - RVector3

Returns

A newly scaled matrix - RMatrix3
1 matrix3_orgin = RLPy.RMatrix3()
2 matrix3_orgin.MakeIdentity()
3 scale_vector = RLPy.RVector3( 2, 2, 2 )
4 matrix3_orgin.AccuScale(scale_vector)

ToEulerAngle( self, rkScaleself, Order, rx, ry, rz )

Convert 3x3 matrix to Euler angles.

Parameters

Order [IN] Euler order - RLPy.Rotation_Order
rx [OUT] Angle of x-axis in radians - float
ry [OUT] Angle of y-axis in radians - float
rz [OUT] Angle of z-axis in radians - float
 1 matrix3_value = RLPy.RMatrix3( -0, -0,  1,
 2                                 0, -1, -0,
 3                                 1,  0, -0 )
 4 euler_angle_x = 0
 5 euler_angle_y = 0
 6 euler_angle_z = 0
 7 result = matrix3_value.ToEulerAngle( RLPy.EEulerOrder_XYZ, euler_angle_x, euler_angle_y, euler_angle_z )
 8 
 9 print(result[0] * RLPy.RMath.CONST_RAD_TO_DEG) # 180
10 print(result[1] * RLPy.RMath.CONST_RAD_TO_DEG) # 90
11 print(result[2] * RLPy.RMath.CONST_RAD_TO_DEG) # 0

FromEulerAngle( self, Order, rx, ry, rz )

Convert Euler angle to a 3x3 matrix according to a rotation axis order.

Parameters

Order [IN] Euler order - RLPy.Rotation_Order
rx [IN] Angle of x-axis in radians - float
ry [IN] Angle of y-axis in radians - float
rz [IN] Angle of z-axis in radians - float

Returns

A new matrix from specified axis angle - RMatrix3
 1 matrix3_orgin = RLPy.RMatrix3()
 2 euler_angle_x = 90 * RLPy.RMath.CONST_DEG_TO_RAD
 3 euler_angle_y = 0
 4 euler_angle_z = 0
 5 matrix3_result = matrix3_orgin.FromEulerAngle( RLPy.EEulerOrder_XYZ, euler_angle_x, euler_angle_y, euler_angle_z)
 6 row0 = matrix3_result[0].GetRow(0)
 7 
 8 print(row0[0])
 9 print(row0[1])
10 print(row0[2])

FromSphereUnitVec( self, rkVec )

Convert Euler angle to matrix.

Parameters

rkVec [IN] vector - RVector3

Returns

A new 3x3 matrix from sphere unit vector - RMatrix3
1 vector = RLPy.RVector3( 0, 1, 0 )
2 matrix3_result =  RLPy.RMatrix3().FromSphereUnitVec( vector )
3 row0 = matrix3_result.GetRow(0)
4 
5 print(row0[0])
6 print(row0[1])
7 print(row0[2])

IsRightHandCoordinate( self )

Obtain this 3x3 matrix's coordinate system. True stands for right-handed coordinate system while False for left-handed.

Returns

True Right hand coordinate - bool
False Left hand coordinate - bool
1 matrix3_value = RLPy.RMatrix3( 1, 0, 0,
2                                0, 1, 0,
3                                0, 0, 1 )
4 result = matrix3_value.IsRightHandCoordinate()
5 
6 print(result)
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