91. opengl.matrix — opengl/matrix.py

Python OpenGL framework for pyFormex

This OpenGL framework is intended to replace (in due time) the current OpenGL framework in pyFormex.

3. 2013 Benedict Verhegghe and the pyFormex project.

91.1. Classes defined in module opengl.matrix

class opengl.matrix.Vector4

One or more homogeneous coordinates

class opengl.matrix.Matrix4

A 4x4 transformation matrix for homogeneous coordinates.

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

• data: if specified, should be a (4,4) float array or compatible. Else a 4x4 identity matrix is created.

Example:

>>> 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 (with another scaling factor):

>>> a = I.scale([4.,4.,4.]).rotate(45.,[0.,0.,1.])
>>> b = I.rotate(45.,[0.,0.,1.]).scale([2.,2.,2.])
>>> print(a)
[[ 0.  4.  0.  0.]
 [-4.  0.  0.  0.]
 [ 0.  0.  8.  0.]
 [ 0.  0.  0.  1.]]
>>> (a==b).all()
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.])

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.

91.2. Functions defined in module opengl.matrix