trafo
: Linear transformations¶With the trafo
module PyX supports linear transformations, which can then
be applied to canvases, Bézier paths and other objects. It consists of the main
class trafo
representing a general linear transformation and subclasses
thereof, which provide special operations like translation, rotation, scaling,
and mirroring.
trafo
¶The trafo
class represents a general linear transformation, which is defined
for a vector \(\vec{x}\) as
where \(\mathsf{A}\) is the transformation matrix and \(\vec{b}\) the translation vector. The transformation matrix must not be singular, i.e. we require \(\det \mathsf{A} \ne 0\).
Multiple trafo
instances can be multiplied, corresponding to a consecutive
application of the respective transformation. Note that trafo1*trafo2
means
that trafo1
is applied after trafo2
, i.e. the new transformation is
given by \(\mathsf{A} = \mathsf{A}_1 \mathsf{A}_2\) and \(\vec{b} =
\mathsf{A}_1 \vec{b}_2 + \vec{b}_1\). Use the trafo
methods described below,
if you prefer thinking the other way round. The inverse of a transformation can
be obtained via the trafo
method inverse()
, defined by the inverse
\(\mathsf{A}^{-1}\) of the transformation matrix and the translation vector
\(-\mathsf{A}^{-1}\vec{b}\).
trafo.
trafo
(matrix=((1, 0), (0, 1)), vector=(0, 0))¶create new trafo
instance with transformation matrix
and vector
trafo.
apply
(x, y)¶apply trafo
to point vector \((\mathtt{x}, \mathtt{y})\).
trafo.
inverse
()¶returns inverse transformation of trafo
.
trafo.
mirrored
(angle)¶returns trafo
followed by mirroring at line through \((0,0)\) with
direction angle
in degrees.
trafo.
rotated
(angle, x=None, y=None)¶returns trafo
followed by rotation by angle
degrees around point
\((\mathtt{x}, \mathtt{y})\), or \((0,0)\), if not given.
trafo.
scaled
(sx, sy=None, x=None, y=None)¶returns trafo
followed by scaling with scaling factor sx
in
\(x\)-direction, sy
in \(y\)-direction
(\(\mathtt{sy}=\mathtt{sx}\), if not given) with scaling center
\((\mathtt{x}, \mathtt{y})\), or \((0,0)\), if not given.
trafo.
slanted
(a, angle=0, x=None, y=None)¶returns trafo
followed by slant by angle
around point
\((\mathtt{x}, \mathtt{y})\), or \((0,0)\), if not given.
trafo.
translated
(x, y)¶returns trafo
followed by translation by vector \((\mathtt{x}, \mathtt{y})\).
trafo
¶The trafo
module provides a number of subclasses of the trafo
class,
each of which corresponds to one trafo
method.
trafo.
mirror
(angle)¶mirroring at line through \((0,0)\) with direction angle
in degrees.
trafo.
rotate
(angle, x=None, y=None)¶rotation by angle
degrees around point \((\mathtt{x}, \mathtt{y})\), or \((0,0)\), if not given.
trafo.
scale
(sx, sy=None, x=None, y=None)¶scaling with scaling factor sx
in \(x\)-direction, sy
in
\(y\)-direction (\(\mathtt{sy}=\mathtt{sx}\), if not given) with
scaling center \((\mathtt{x}, \mathtt{y})\), or \((0,0)\), if not
given.
trafo.
slant
(a, angle=0, x=None, y=None)¶slant by angle
around point \((\mathtt{x}, \mathtt{y})\), or \((0,0)\), if not given.
trafo.
translate
(x, y)¶translation by vector \((\mathtt{x}, \mathtt{y})\).