Working with Transformation Matrices and Placement Objects

[shoogen]

Hi,
is there a way to analyse if a given transformation matrix can be represented using a placement object?
So if this is the case i can apply the transformation on the Placement object.
In the (rare) case when there are operations like shearing and scaling involved I'd like to chave a PythonFeature that applies the Transformation to the Shape.

Version: 0.13.0681 (32bit) on Win7 (64bit)

[wmayer]

A placement is described by a translation and a rotation. The first three elements of the 4th column of the 4x4 matrix is the translation part and the 3x3 sub-matrix is the rotation part. The 4th row is always 0, 0, 0, 1.

A rotation matrix is always a so called orthonormal matrix which means that if you consider the three columns or rows as vectors that they have a length of 1 and that the vectors are orthogonal to each other.

[shoogen]

A rotation matrix is always a so called orthonormal matrix.

Thank You

I found out that i also have to check for a determinant of +1.
The question is, whether it makes any difference in testing the 4x4 or the 3x3 matrix?

[shoogen]

I tried to implement a python feature to applay a transformation matrix. But unfortunately it breaks boolean operations.

Code: Select all

>>> [(f.Shape.check(), f.Shape.ShapeType) for f in App.ActiveDocument.union.Shapes]
[(None, 'Solid'), (None, 'Solid'), (None, 'Solid')]
>>> App.ActiveDocument.union.Shape.check()
StandardError

Code: Select all

class MatrixTransform:
    def __init__(self, obj,matrix=None,child=None):
        obj.Proxy = self
        self.matrix = matrix
        self.child = child

    def execute(self, fp):
        if self.matrix and self.child:
            sh=self.child.Shape#.copy()
            m=self.child.Placement.toMatrix().multiply(self.matrix)
            fp.Shape = sh.transformGeometry(m)
            #fp.Shape = sh.transformShape(m)

transformShape doesn't work at all in 0.13.0681 (This object is immutable, ...)
Please do not expect the Feature in the attached file to do recomputation as I got 'PropertyPythonObject::toString: can't pickle Matrix objects' errors.
To recreate the file execute

Code: Select all

import csgparser
csgparser.parsenode(csgparser.csgstr)[0].flattengroups().addtofreecad(App.ActiveDocument)

https://raw.github.com/gist/1967104/csgparser.py

[wmayer]

Do not use transformGeometry() because this changes the underlying geometry to b-spline and the boolean ops have problems with that. Instead assign the matrix directly to the placement.

Code: Select all

            sh=self.child.Shape.copy()
            m=self.child.Placement.toMatrix().multiply(self.matrix)
            fp.Shape.Placement = m

[shoogen]

Instead assign the matrix directly to the placement.

Thanks You,
but is doesn't work in Version: 0.13.0681
And will an assignment of an Matrix to a Placement keep scaling, and mirroring?

Code: Select all

>>> App.ActiveDocument.multmatrix.Shape.Placement=FreeCAD.Matrix()
Traceback (most recent call last):
  File "<input>", line 1, in <module>
ReferenceError: This object is immutable, you can not set any attribute or call a method

[shoogen]

Hi Werner,
Thank you very much.
I found a way (for orthonormal matrices)

Code: Select all

obj.Placement=FreeCAD.Placement(m1).multiply(obj.Placement)

for non orthonormal matrices I have to stick with transformGeometry for the moment.
And that's it

[shoogen]

A placement is described by a translation and a rotation. The first three elements of the 4th column of the 4x4 matrix is the translation part and the 3x3 sub-matrix is the rotation part. The 4th row is always 0, 0, 0, 1.

A rotation matrix is always a so called orthonormal matrix which means that if you consider the three columns or rows as vectors that they have a length of 1 and that the vectors are orthogonal to each other.

I've added the code to check if a "Placement object can represent a given transformation matrix" <==> 3x3 Submatrix is in Rotation group SO(3) <==> 3x3 Submatrix is special orthogonal

Code: Select all

>>> fcmatrix=FreeCAD.Matrix(); csgparser.isspecialorthogonal(csgparser.fcsubmatrix(fcmatrix))
True
>>> fcmatrix.rotateX(2); csgparser.isspecialorthogonal(csgparser.fcsubmatrix(fcmatrix))
True
>>> fcmatrix.move((1,2,3)); csgparser.isspecialorthogonal(csgparser.fcsubmatrix(fcmatrix))
True
>>> fcmatrix.scale(2,2,2); csgparser.isspecialorthogonal(csgparser.fcsubmatrix(fcmatrix))
False

https://raw.github.com/gist/1967104/csgparser.py