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:math:`\mathsf{A}^{-1}` of the transformation matrix and the translation vector
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:math:`-\mathsf{A}^{-1}\vec{b}`.
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The methods of the ``trafo`` class are summarized in the following table.
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+-----------------------------------------+----------------------------------------------+
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| ``trafo`` method | function |
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+=========================================+==============================================+
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| ``__init__(matrix=((1,0),(0,1)), | create new ``trafo`` instance with |
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| vector=(0,0)):`` | transformation ``matrix`` and ``vector``. |
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+-----------------------------------------+----------------------------------------------+
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| ``apply(x, y)`` | apply ``trafo`` to point vector |
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| | :math:`(\mathtt{x}, \mathtt{y})`. |
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+-----------------------------------------+----------------------------------------------+
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| ``inverse()`` | returns inverse transformation of ``trafo``. |
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+-----------------------------------------+----------------------------------------------+
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| ``mirrored(angle)`` | returns ``trafo`` followed by mirroring at |
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| | line through :math:`(0,0)` with direction |
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| | ``angle`` in degrees. |
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+-----------------------------------------+----------------------------------------------+
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| ``rotated(angle, x=None, y=None)`` | returns ``trafo`` followed by rotation by |
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| | ``angle`` degrees around point |
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| | :math:`(\mathtt{x}, \mathtt{y})`, or |
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| | :math:`(0,0)`, if not given. |
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+-----------------------------------------+----------------------------------------------+
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| ``scaled(sx, sy=None, x=None, y=None)`` | returns ``trafo`` followed by scaling with |
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| | scaling factor ``sx`` in :math:`x`\ |
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| | -direction, ``sy`` in :math:`y`\ -direction |
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| | (:math:`\mathtt{sy}=\mathtt{sx}`, if not |
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| | given) with scaling center |
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| | :math:`(\mathtt{x}, \mathtt{y})`, or |
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| | :math:`(0,0)`, if not given. |
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+-----------------------------------------+----------------------------------------------+
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| ``translated(x, y)`` | returns ``trafo`` followed by translation by |
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| | vector :math:`(\mathtt{x}, \mathtt{y})`. |
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+-----------------------------------------+----------------------------------------------+
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| ``slanted(a, angle=0, x=None, y=None)`` | returns ``trafo`` followed by XXX |
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+-----------------------------------------+----------------------------------------------+
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.. class:: trafo(matrix=((1,0),(0,1)), vector=(0,0))
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create new ``trafo`` instance with transformation ``matrix`` and ``vector``
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.. method:: apply(x, y)
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apply ``trafo`` to point vector :math:`(\mathtt{x}, \mathtt{y})`.
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returns inverse transformation of ``trafo``.
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.. method:: mirrored(angle)
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returns ``trafo`` followed by mirroring at line through :math:`(0,0)` with
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direction ``angle`` in degrees.
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.. method:: rotated(angle, x=None, y=None)
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returns ``trafo`` followed by rotation by ``angle`` degrees around point
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:math:`(\mathtt{x}, \mathtt{y})`, or :math:`(0,0)`, if not given.
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.. method:: scaled(sx, sy=None, x=None, y=None)
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returns ``trafo`` followed by scaling with scaling factor ``sx`` in
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:math:`x`\ -direction, ``sy`` in :math:`y`\ -direction
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(:math:`\mathtt{sy}=\mathtt{sx}`, if not given) with scaling center
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:math:`(\mathtt{x}, \mathtt{y})`, or :math:`(0,0)`, if not given.
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.. method:: slanted(a, angle=0, x=None, y=None)
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returns ``trafo`` followed by slant by ``angle`` around point
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:math:`(\mathtt{x}, \mathtt{y})`, or :math:`(0,0)`, if not given.
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.. method:: translated(x, y)
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returns ``trafo`` followed by translation by vector :math:`(\mathtt{x}, \mathtt{y})`.
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Subclasses of :class:`trafo`
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============================
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The ``trafo`` module provides a number of subclasses of the ``trafo`` class,
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each of which corresponds to one ``trafo`` method. They are listed in the
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+----------------------------------------+----------------------------------------------+
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| ``trafo`` subclass | function |
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+========================================+==============================================+
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| ``mirror(angle)`` | mirroring at line through :math:`(0,0)` with |
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| | direction ``angle`` in degrees. |
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+----------------------------------------+----------------------------------------------+
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| ``rotate(angle, x=None, y=None)`` | rotation by ``angle`` degrees around point |
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| | :math:`(\mathtt{x}, \mathtt{y})`, or |
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| | :math:`(0,0)`, if not given. |
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+----------------------------------------+----------------------------------------------+
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| ``scale(sx, sy=None, x=None, y=None)`` | scaling with scaling factor ``sx`` in |
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| | :math:`x`\ -direction, ``sy`` in :math:`y`\ |
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| | -direction (:math:`\mathtt{sy}=\mathtt{sx}`, |
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| | if not given) with scaling center |
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| | :math:`(\mathtt{x}, \mathtt{y})`, or |
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| | :math:`(0,0)`, if not given. |
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+----------------------------------------+----------------------------------------------+
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| ``translate(x, y)`` | translation by vector :math:`(\mathtt{x}, |
101
+----------------------------------------+----------------------------------------------+
102
| ``slant(a, angle=0, x=None, y=None)`` | XXX |
103
+----------------------------------------+----------------------------------------------+
83
each of which corresponds to one ``trafo`` method.
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.. class:: mirror(angle)
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mirroring at line through :math:`(0,0)` with direction ``angle`` in degrees.
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.. class:: rotate(angle, x=None, y=None)
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rotation by ``angle`` degrees around point :math:`(\mathtt{x}, \mathtt{y})`, or :math:`(0,0)`, if not given.
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.. class:: scale(sx, sy=None, x=None, y=None)
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scaling with scaling factor ``sx`` in :math:`x`\ -direction, ``sy`` in
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:math:`y`\ -direction (:math:`\mathtt{sy}=\mathtt{sx}`, if not given) with
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scaling center :math:`(\mathtt{x}, \mathtt{y})`, or :math:`(0,0)`, if not
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.. class:: slant(a, angle=0, x=None, y=None)
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slant by ``angle`` around point :math:`(\mathtt{x}, \mathtt{y})`, or :math:`(0,0)`, if not given.
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.. class:: translate(x, y)
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translation by vector :math:`(\mathtt{x}, \mathtt{y})`.
added
removed
manual/trafo.rst
