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Matrix3D

Class full path: NemAll_Python_Geometry.Matrix3D

Representation class for 3D matrix

Matrix2D describes transformation (translation, rotation and scaling) of a two dimensional element

Matrix data organization in memory

|0, 1, 2, 3 |
|4, 5, 6, 7 |
|8, 9, 10,11|
|12,13,14,15|
  • [0..15] indexes of array values
  • 0,1,2, 4,5,6, 8,9,10 - rotation, scaling and shrinking
  • 12,13,14 - translation

All operations are correct only in geometry calculation context and can not be used for calculating with regular 4x4 matrix.

Functions

Determinant()

Calculate determinant

Returns:

Type Description
float

Determinant.

GaussInvert()

Inverse matrix by Gauss

Returns:

Type Description
bool

True when operation is successful, otherwise false.

GetScaleX()

Get scale X

Returns:

Type Description
float

scale X

GetScaleY()

Get scale Y

Returns:

Type Description
float

scale Y

GetScaleZ()

Get scale Z

Returns:

Type Description
float

scale Z

GetScaling()

Calculates the scaling factors from the matrix

Returns:

Type Description
float

Scale in X axis
float

Scale in Y axis
float

Scale in Z axis

GetTranslationVector()

Get translation part of a matrix

Returns:

Type Description
Vector3D

The vector of translation

GetVectorX()

Get vector X

Returns:

Type Description
Vector3D

Vector X

GetVectorY()

Get vector Y

Returns:

Type Description
Vector3D

Vector Y

GetVectorZ()

Get vector Z

Returns:

Type Description
Vector3D

Vector Z

IsIdentity()

Check to identity matrix

Returns:

Type Description
bool

Return true when is matrix identity, otherwise false.

LaplaceTransform()

Transformation matrix by Laplace

Multiply(matrix)

Matrix multiplication

Formula: A = B or A = AB A is this matrix.

Parameters:

Name Type Description Default
matrix Matrix3D

B matrix

 required

Returns:

Type Description
Matrix3D

Product of matrices

ReduceZDimension()

Create a 2D matrix from this 3D matrix

Returns:

Type Description
Matrix2D

a 2D matrix from this 3D matrix

Reflection(plane)

Reflection across a plane

Parameters:

Name Type Description Default
plane Plane3D

Reflection plane

 required

Examples:

Reflection relative to yz plane

>>> matrix = Matrix3D()
>>> matrix.Reflection(Plane3D(Point3D(0, 0, 0), Vector3D(1.0, 0.0, 0.0)))
    [-1, 0,  0,  0
     0,  1,  0,  0
     0,  0,  1,  0
     0,  0,  0,  1]

Reverse()

Reverse matrix

This method provide geometrical inverse matrix and can not be used with regular inverse 4x4 matrix calculations.

Returns:

Type Description
bool

True when operation is successful, otherwise false.

Examples:

when reversed_matrix is the inverted matrix, this expression will return True

>>> geometry == geometry * matrix * reversed_matrix
    True

Rotation(line, angle)

Rotate the matrix

Rotate current matrix, not created new one.

Parameters:

Name Type Description Default
line Line3D

Axis of rotation.

 required
angle Angle

Angle of rotation.

 required

Returns:

Type Description
bool

True when successful, otherwise false.

Scaling(scaleX, scaleY, scaleZ)

Scale the matrix

Scale current matrix, not created new one.

Parameters:

Name Type Description Default
scaleX float

Scale in X axis.

 required
scaleY float

Scale in Y axis.

 required
scaleZ float

Scale in Z axis.

 required

Examples:

>>> matrix = Matrix3D()
>>> matrix.Scaling(2, 3, 4)
    [2,  0,  0,  0
     0,  3,  0,  0
     0,  0,  4,  0
     0,  0,  0,  1]

SetIdentity()

Initialize identity matrix

SetProjection(proj)

Create a matrix for the required projection

Method throw THROW_GEO_EXCEPTION_INCORRECT_PARAMETERS_ geometry exception in case of invalid proj.

Parameters:

Name Type Description Default
proj eProjectionMatrixType

The required projection

 required

SetReflection(plane)

Initialize matrix only with reflection

Parameters:

Name Type Description Default
plane Plane3D

Reflection plane

 required

Examples:

Reflection relative to xz plane

>>> matrix = Matrix3D()
>>> matrix.Reflection(Plane3D(Point3D(0, 0, 0), Vector3D(0.0, 1.0, 0.0)))
    [1,  0,  0,  0
     0, -1,  0,  0
     0,  0,  1,  0
     0,  0,  0,  1]

SetRotation overload

SetRotation(axis, angle)

Initialize matrix only with rotation

Parameters:

Name Type Description Default
axis Line3D

Axis of rotation.

 required
angle Angle

Angle of rotation.

 required

Returns:

Type Description
bool

True when successful, otherwise false.

Examples:

90 deg rotation around z axis

>>> matrix = Matrix3D()
>>> matrix.SetRotation(Line3D(Point3D(0, 0, 0), Vector3D(0, 0, 100)), Angle(math.pi/2))
    [0,  1,  0,  0
    -1,  0,  0,  0
     0,  0,  1,  0
     0,  0,  0, 1]
SetRotation(startDirection, endDirection)

Initialize matrix only with rotation defined by start and end direction vectors

Parameters:

Name Type Description Default
startDirection Vector3D

direction vector for start of rotation.

 required
endDirection Vector3D

direction vector for end of rotation.

 required

Returns:

Type Description
bool

True when successful, otherwise false.

SetScaling(scaleX, scaleY, scaleZ)

Initialize matrix only with scaling factors

Parameters:

Name Type Description Default
scaleX float

Scale in X axis.

 required
scaleY float

Scale in Y axis.

 required
scaleZ float

Scale in Z axis.

 required

Examples:

>>> matrix = Matrix3D()
>>> matrix.SetScaling(2, 3, 4)
    [2,  0,  0,  0
     0,  3,  0,  0
     0,  0,  4,  0
     0,  0,  0,  1]

SetTranslation(vec)

Initialize matrix only with translation

Parameters:

Name Type Description Default
vec Vector3D

Vector of translation.

 required

Examples:

>>> matrix = Matrix3D()
>>> matrix.SetTranslation(Vector3D(100, 100, 100))
    [1 , 0,  0,  0
     0,  1,  0,  0
     0,  0,  1,  0
    100,100,100, 1]

SetValue(index, value)

Set the matrix element at a specified position

Use this method when you don't want to catch exception by operator[].

Parameters:

Name Type Description Default
index int

Position index <0..15>

 required
value float

Value for set

 required

Returns:

Type Description
bool

True when operation successful (index is not out of range), otherwise false.

SetValues(v00, v01, v02, v03, v10, v11, v12, v13, v20, v21, v22, v23, v30, v31, v32, v33)

Sets each matrix-element

Parameters:

Name Type Description Default
v00 float

first row, first element

 required
v01 float

first row, second element

 required
v02 float

first row, third element

 required
v03 float

first row, fourth element

 required
v10 float

second row, first element

 required
v11 float

second row, second element

 required
v12 float

second row, third element

 required
v13 float

second row, fourth element

 required
v20 float

third row, first element

 required
v21 float

third row, second element

 required
v22 float

third row, third element

 required
v23 float

third row, fourth element

 required
v30 float

fourth row, first element

 required
v31 float

fourth row, second element

 required
v32 float

fourth row, third element

 required
v33 float

fourth row, fourth element

 required

Translate(vec)

Translate the matrix

Parameters:

Name Type Description Default
vec Vector3D

Vector of translation.

 required

Examples:

>>> matrix = Matrix3D()
>>> matrix.SetTranslation(Vector3D(100, 100, 100))
    [1 , 0,  0,  0
     0,  1,  0,  0
     0,  0,  1,  0
    100,100,100, 1]
>>> matrix.Translate(Vector3D(100, 100, 100))
    [1 , 0,  0,  0
     0,  1,  0,  0
     0,  0,  1,  0
    200,200,200, 1]

Transpose()

Transpose matrix

All transform-services multiply transformation-matrix from the right side: If you need the result as it would be multiplication from the left side you need the transposed Matrix

Examples:

>>> [x,y,z,1.0] x |  0, 1, 2, 3 |
                  |  4, 5, 6, 7 |
                  |  8, 9,10,11 |
                  | 12,13,14,15 |

moving-part: 12,13,14

>>> |  0, 1, 2, 3 |      | x |
    |  4, 5, 6, 7 |  x   | y |
    |  8, 9,10,11 |      | z |
    | 12,13,14,15 |      |1.0|

moving-part: 3, 7, 11

__add__(matrix)

Matrix addition

Formula: Result(new matrix) = A+B

A is this matrix.

Parameters:

Name Type Description Default
matrix Matrix3D

B matrix

 required

Returns:

Type Description
Matrix3D

Addition of matrices

__eq__(mat)

Comparison of matrices without tolerance.

Be careful, this method work without tolerance!

Parameters:

Name Type Description Default
mat Matrix3D

Compared matrix.

 required

Returns:

Type Description
bool

True when matrices are equal, otherwise false.

__getitem__(index)

Get the matrix element at a specified position

This method is checked and throwing Geometry::Exception when index is out of range.

Parameters:

Name Type Description Default
index int

Position index <0..15>

 required

Returns:

Type Description
float

Returns an element at a specified position.

__iadd__(matrix)

Matrix addition

Formula: A += B or A = A+B A is this matrix.

Parameters:

Name Type Description Default
matrix Matrix3D

B matrix

 required

Returns:

Type Description
Matrix3D

Addition of matrices

__imul__(matrix)

Matrix multiplication

Formula: A = B or A = AB. A is this matrix.

Parameters:

Name Type Description Default
matrix Matrix3D

B matrix

 required

Returns:

Type Description
Matrix3D

Product of matrices

__isub__(matrix)

Matrix addition

Formula: A -= B or A = A-B A is this matrix.

Parameters:

Name Type Description Default
matrix Matrix3D

B matrix

 required

Returns:

Type Description
Matrix3D

Addition of matrices

__mul__(matrix)

Matrix multiplication

Formula: Result(new matrix) = A*B A is this matrix.

Parameters:

Name Type Description Default
matrix Matrix3D

B matrix

 required

Returns:

Type Description
Matrix3D

Product of matrices

__repr__()

Convert to string

__sub__(matrix)

Matrix addition

Formula: Result(new matrix) = A-B A is this matrix.

Parameters:

Name Type Description Default
matrix Matrix3D

B matrix

 required

Returns:

Type Description
Matrix3D

Addition of matrices