# The Transformation Class

class pypdf.Transformation(ctm: = (1, 0, 0, 1, 0, 0))[source]

Bases: `object`

Represent a 2D transformation.

The transformation between two coordinate systems is represented by a 3-by-3 transformation matrix matrix with the following form:

```a b 0
c d 0
e f 1
```

Because a transformation matrix has only six elements that can be changed, it is usually specified in PDF as the six-element array [ a b c d e f ].

Coordinate transformations are expressed as matrix multiplications:

```                            a b 0
[ x′ y′ 1 ] = [ x y 1 ] ×   c d 0
e f 1
```

Example

```>>> from pypdf import Transformation
>>> op = Transformation().scale(sx=2, sy=3).translate(tx=10, ty=20)
```
property matrix: Tuple[Tuple[float, float, float], Tuple[float, float, float], Tuple[float, float, float]]

Return the transformation matrix as a tuple of tuples in the form:

((a, b, 0), (c, d, 0), (e, f, 1))

static compress(matrix: ) [source]

Compresses the transformation matrix into a tuple of (a, b, c, d, e, f).

Parameters

matrix – The transformation matrix as a tuple of tuples.

Returns

A tuple representing the transformation matrix as (a, b, c, d, e, f)

transform(m: Transformation) [source]

Apply one transformation to another.

Parameters

m – a Transformation to apply.

Returns

A new `Transformation` instance

Example

```>>> from pypdf import Transformation
>>> op = Transformation((1, 0, 0, -1, 0, height)) # vertical mirror
>>> op = Transformation().transform(Transformation((-1, 0, 0, 1, iwidth, 0))) # horizontal mirror
```
translate(tx: float = 0, ty: float = 0) [source]

Translate the contents of a page.

Parameters
• tx – The translation along the x-axis.

• ty – The translation along the y-axis.

Returns

A new `Transformation` instance

scale(sx: = None, sy: = None) [source]

Scale the contents of a page towards the origin of the coordinate system.

Typically, that is the lower-left corner of the page. That can be changed by translating the contents / the page boxes.

Parameters
• sx – The scale factor along the x-axis.

• sy – The scale factor along the y-axis.

Returns

A new Transformation instance with the scaled matrix.

rotate(rotation: float) [source]

Rotate the contents of a page.

Parameters

rotation – The angle of rotation in degrees.

Returns

A new `Transformation` instance with the rotated matrix.

apply_on(pt: Union[Tuple[float, float], List[float]], as_object: bool = False) Union[Tuple[float, float], List[float]][source]

Apply the transformation matrix on the given point.

Parameters

pt – A tuple or list representing the point in the form (x, y)

Returns

A tuple or list representing the transformed point in the form (x’, y’)