105. opengl.matrix — opengl/matrix.py

Python OpenGL framework for pyFormex

class opengl.matrix.Matrix4(data=None)

A 4x4 transformation matrix for homogeneous coordinates.

The matrix is to be used with post-multiplication on row vectors (i.e. OpenGL convention).

Parameters:

data (array_like (4,4), optional) – If specified, should be a (4,4) float array or compatible. Else a 4x4 identity matrix is created.

Examples

>>> I = Matrix4()
>>> print(I)
[[1.  0.  0.  0.]
 [0.  1.  0.  0.]
 [0.  0.  1.  0.]
 [0.  0.  0.  1.]]

We can first scale and then rotate, or first rotate and then scale:

>>> a = Matrix4().scale([4.,4.,4.]).rotate(45.,[0.,0.,1.])
>>> a
Matrix4([[ 2.8284,  2.8284,  0.    ,  0.    ],
         [-2.8284,  2.8284,  0.    ,  0.    ],
         [ 0.    ,  0.    ,  4.    ,  0.    ],
         [ 0.    ,  0.    ,  0.    ,  1.    ]])
>>> b = Matrix4().rotate(45.,[0.,0.,1.]).scale([4.,4.,4.])
>>> np.allclose(a,b)
True

gl()

Get the transformation matrix as a ‘ready-to-use’-gl version.

Returns the (4,4) Matrix as a rowwise flattened array of type float32.

Example:

>>> Matrix4().gl()
Matrix4([1., 0., 0., 0., 0., 1., 0., 0., 0., 0., 1., 0., 0.,
    0., 0., 1.], dtype=float32)

property rot

Return the (3,3) rotation matrix

property trl

Return the (3,) translation vector

identity()

Reset the matrix to a 4x4 identity matrix.

translate(vector)

Translate a 4x4 matrix by a (3,) vector.

• vector: (3,) float array: the translation vector

Changes the Matrix in place and also returns the result

Example:

>>> Matrix4().translate([1.,2.,3.])
Matrix4([[1., 0., 0., 0.],
         [0., 1., 0., 0.],
         [0., 0., 1., 0.],
         [1., 2., 3., 1.]])

rotate(angle, axis=None)

Rotate a Matrix4.

The rotation can be specified by

• an angle and axis,

• a 3x3 rotation matrix,

• a 4x4 trtransformation matrix (Matrix4).

Parameters:

• angle: float: the rotation angle. A 3x3 or 4x4 matrix may be

  give instead, to directly specify the roation matrix.

• axis: int or (3,) float: the axis to rotate around

Changes the Matrix in place and also returns the result.

Example:

>>> Matrix4().rotate(90.,[0.,1.,0.])
Matrix4([[ 0., 0., -1., 0.],
         [ 0., 1.,  0., 0.],
         [ 1., 0.,  0., 0.],
         [ 0., 0.,  0., 1.]])

scale(vector)

Scale a 4x4 matrix by a (3,) vector.

• vector: (3,) float array: the scaling vector

Changes the Matrix in place and also returns the result

Example:

>>> Matrix4().scale([1.,2.,3.])
Matrix4([[1., 0., 0., 0.],
         [0., 2., 0., 0.],
         [0., 0., 3., 0.],
         [0., 0., 0., 1.]])

swapRows(row1, row2)

Swap two rows.

• row1, row2: index of the rows to swap

swapCols(col1, col2)

Swap two columns.

• col1, col2: index of the columns to swap

inverse()

Return the inverse matrix

transform(x)

Transform a vertex using this matrix.

• x: a (3,) or (4,) vector.

If the vector has length 4, it holds homogeneous coordinates, and the result is the dot product of the vector with the Matrix: x * M. If the vector has length 3, the 4th homogeneous coordinate is assumed to be 1, and the product is computed in an optimized way.

invtransform(x)

Transform a vertex with the inverse of this matrix.

• x: a (3,) or (4,) vector.

transinv()

Return the transpose of the inverse.