Module 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.

Class trafo

The trafo class represents a general linear transformation, which is defined for a vector \vec{x} as

\vec{x}' = \mathsf{A}\, \vec{x} + \vec{b}\ ,

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}.

class 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}).

Subclasses of trafo

The trafo module provides a number of subclasses of the trafo class, each of which corresponds to one trafo method.

class trafo.mirror(angle)

mirroring at line through (0,0) with direction angle in degrees.

class trafo.rotate(angle, x=None, y=None)

rotation by angle degrees around point (\mathtt{x}, \mathtt{y}), or (0,0), if not given.

class 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.

class trafo.slant(a, angle=0, x=None, y=None)

slant by angle around point (\mathtt{x}, \mathtt{y}), or (0,0), if not given.

class trafo.translate(x, y)

translation by vector (\mathtt{x}, \mathtt{y}).

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