# transform¶

Affine 2D transformation matrix class.

The Transform class implements various transformation matrix operations, both on the matrix itself, as well as on 2D coordinates.

Transform instances are effectively immutable: all methods that operate on the transformation itself always return a new instance. This has as the interesting side effect that Transform instances are hashable, ie. they can be used as dictionary keys.

This module exports the following symbols:

Transform – this is the main class Identity – Transform instance set to the identity transformation Offset – Convenience function that returns a translating transformation Scale – Convenience function that returns a scaling transformation

Examples

```>>> t = Transform(2, 0, 0, 3, 0, 0)
>>> t.transformPoint((100, 100))
(200, 300)
>>> t = Scale(2, 3)
>>> t.transformPoint((100, 100))
(200, 300)
>>> t.transformPoint((0, 0))
(0, 0)
>>> t = Offset(2, 3)
>>> t.transformPoint((100, 100))
(102, 103)
>>> t.transformPoint((0, 0))
(2, 3)
>>> t2 = t.scale(0.5)
>>> t2.transformPoint((100, 100))
(52.0, 53.0)
>>> import math
>>> t3 = t2.rotate(math.pi / 2)
>>> t3.transformPoint((0, 0))
(2.0, 3.0)
>>> t3.transformPoint((100, 100))
(-48.0, 53.0)
>>> t = Identity.scale(0.5).translate(100, 200).skew(0.1, 0.2)
>>> t.transformPoints([(0, 0), (1, 1), (100, 100)])
[(50.0, 100.0), (50.550167336042726, 100.60135501775433), (105.01673360427253, 160.13550177543362)]
>>>
```
`fontTools.misc.transform.``Offset`(x=0, y=0)[source]

Return the identity transformation offset by x, y.

Example

```>>> Offset(2, 3)
<Transform [1 0 0 1 2 3]>
>>>
```
`fontTools.misc.transform.``Scale`(x, y=None)[source]

Return the identity transformation scaled by x, y. The ‘y’ argument may be None, which implies to use the x value for y as well.

Example

```>>> Scale(2, 3)
<Transform [2 0 0 3 0 0]>
>>>
```
class `fontTools.misc.transform.``Transform`(xx: float = 1, xy: float = 0, yx: float = 0, yy: float = 1, dx: float = 0, dy: float = 0)[source]

2x2 transformation matrix plus offset, a.k.a. Affine transform. Transform instances are immutable: all transforming methods, eg. rotate(), return a new Transform instance.

Examples

```>>> t = Transform()
>>> t
<Transform [1 0 0 1 0 0]>
>>> t.scale(2)
<Transform [2 0 0 2 0 0]>
>>> t.scale(2.5, 5.5)
<Transform [2.5 0 0 5.5 0 0]>
>>>
>>> t.scale(2, 3).transformPoint((100, 100))
(200, 300)
```

Transform’s constructor takes six arguments, all of which are optional, and can be used as keyword arguments:

```>>> Transform(12)
<Transform [12 0 0 1 0 0]>
>>> Transform(dx=12)
<Transform [1 0 0 1 12 0]>
>>> Transform(yx=12)
<Transform [1 0 12 1 0 0]>
```
Transform instances also behave like sequences of length 6:
```>>> len(Identity)
6
>>> list(Identity)
[1, 0, 0, 1, 0, 0]
>>> tuple(Identity)
(1, 0, 0, 1, 0, 0)
```
Transform instances are comparable:
```>>> t1 = Identity.scale(2, 3).translate(4, 6)
>>> t2 = Identity.translate(8, 18).scale(2, 3)
>>> t1 == t2
1
```
But beware of floating point rounding errors:
```>>> t1 = Identity.scale(0.2, 0.3).translate(0.4, 0.6)
>>> t2 = Identity.translate(0.08, 0.18).scale(0.2, 0.3)
>>> t1
<Transform [0.2 0 0 0.3 0.08 0.18]>
>>> t2
<Transform [0.2 0 0 0.3 0.08 0.18]>
>>> t1 == t2
0
```

Transform instances are hashable, meaning you can use them as keys in dictionaries:

```>>> d = {Scale(12, 13): None}
>>> d
{<Transform [12 0 0 13 0 0]>: None}
```
But again, beware of floating point rounding errors:
```>>> t1 = Identity.scale(0.2, 0.3).translate(0.4, 0.6)
>>> t2 = Identity.translate(0.08, 0.18).scale(0.2, 0.3)
>>> t1
<Transform [0.2 0 0 0.3 0.08 0.18]>
>>> t2
<Transform [0.2 0 0 0.3 0.08 0.18]>
>>> d = {t1: None}
>>> d
{<Transform [0.2 0 0 0.3 0.08 0.18]>: None}
>>> d[t2]
Traceback (most recent call last):
File "<stdin>", line 1, in ?
KeyError: <Transform [0.2 0 0 0.3 0.08 0.18]>
```
`count`(value, /)

Return number of occurrences of value.

`dx`: float

Alias for field number 4

`dy`: float

Alias for field number 5

`index`(value, start=0, stop=9223372036854775807, /)

Return first index of value.

Raises ValueError if the value is not present.

`inverse`()[source]

Return the inverse transformation.

Example

```>>> t = Identity.translate(2, 3).scale(4, 5)
>>> t.transformPoint((10, 20))
(42, 103)
>>> it = t.inverse()
>>> it.transformPoint((42, 103))
(10.0, 20.0)
>>>
```
`reverseTransform`(other)[source]

Return a new transformation, which is the other transformation transformed by self. self.reverseTransform(other) is equivalent to other.transform(self).

Example

```>>> t = Transform(2, 0, 0, 3, 1, 6)
>>> t.reverseTransform((4, 3, 2, 1, 5, 6))
<Transform [8 6 6 3 21 15]>
>>> Transform(4, 3, 2, 1, 5, 6).transform((2, 0, 0, 3, 1, 6))
<Transform [8 6 6 3 21 15]>
>>>
```
`rotate`(angle)[source]

Return a new transformation, rotated by ‘angle’ (radians).

Example

```>>> import math
>>> t = Transform()
>>> t.rotate(math.pi / 2)
<Transform [0 1 -1 0 0 0]>
>>>
```
`scale`(x=1, y=None)[source]

Return a new transformation, scaled by x, y. The ‘y’ argument may be None, which implies to use the x value for y as well.

Example

```>>> t = Transform()
>>> t.scale(5)
<Transform [5 0 0 5 0 0]>
>>> t.scale(5, 6)
<Transform [5 0 0 6 0 0]>
>>>
```
`skew`(x=0, y=0)[source]

Return a new transformation, skewed by x and y.

Example

```>>> import math
>>> t = Transform()
>>> t.skew(math.pi / 4)
<Transform [1 0 1 1 0 0]>
>>>
```
`toPS`()[source]

Return a PostScript representation: >>> t = Identity.scale(2, 3).translate(4, 5) >>> t.toPS() ‘[2 0 0 3 8 15]’ >>>

`transform`(other)[source]

Return a new transformation, transformed by another transformation.

Example

```>>> t = Transform(2, 0, 0, 3, 1, 6)
>>> t.transform((4, 3, 2, 1, 5, 6))
<Transform [8 9 4 3 11 24]>
>>>
```
`transformPoint`(p)[source]

Transform a point.

Example

```>>> t = Transform()
>>> t = t.scale(2.5, 5.5)
>>> t.transformPoint((100, 100))
(250.0, 550.0)
```
`transformPoints`(points)[source]

Transform a list of points.

Example

```>>> t = Scale(2, 3)
>>> t.transformPoints([(0, 0), (0, 100), (100, 100), (100, 0)])
[(0, 0), (0, 300), (200, 300), (200, 0)]
>>>
```
`translate`(x=0, y=0)[source]

Return a new transformation, translated (offset) by x, y.

Example

```>>> t = Transform()
>>> t.translate(20, 30)
<Transform [1 0 0 1 20 30]>
>>>
```
`xx`: float

Alias for field number 0

`xy`: float

Alias for field number 1

`yx`: float

Alias for field number 2

`yy`: float

Alias for field number 3