Matrix

Matrix is a row-major 3x3 matrix used by image transformations in MuPDF (which complies with the respective concepts laid down in the Adobe PDF Reference 1.7). With matrices you can manipulate the rendered image of a page in a variety of ways: (parts of) the page can be rotated, zoomed, flipped, sheared and shifted by setting some or all of just six float values.

Since all points or pixels live in a two-dimensional space, one column vector of that matrix is a constant unit vector, and only the remaining six elements are used for manipulations. These six elements are usually represented by [a, b, c, d, e, f]. Here is how they are positioned in the matrix:

Please note:

• the below methods are just convenience functions - everything they do, can also be achieved by directly manipulating the six numerical values
• all manipulations can be combined - you can construct a matrix that rotates and shears and scales and shifts, etc. in one go. If you however choose to do this, do have a look at the remarks further down or at the Adobe PDF Reference 1.7.

Class API

class Matrix

__init__(self)

__init__(self, zoom-x, zoom-y)

__init__(self, shear-x, shear-y, 1)

__init__(self, a, b, c, d, e, f)

__init__(self, matrix)

__init__(self, degree)

__init__(self, list)

Overloaded constructors.

Without parameters, Matrix(0.0, 0.0, 0.0, 0.0, 0.0, 0.0) will be created.

zoom-* and shear-* specify zoom or shear values (float), respectively.

matrix specifies another Matrix from which a new copy will be made.

Float value degree specifies the creation of a rotation matrix.

Python sequence list (list, tuple, etc.) must contain exactly 6 values when specified. Non-numeric entries will raise an exception.

fitz.Matrix(1, 1), fitz.Matrix(0.0)) and fitz.Matrix(fitz.Identity) create modifyable versions of the Identity matrix, which looks like [1, 0, 0, 1, 0, 0].

preRotate(deg)

Modify the matrix to perform a counter-clockwise rotation for positive deg degrees, else clockwise. The matrix elements of an identity matrix will change in the following way:

[1, 0, 0, 1, 0, 0] -> [cos(deg), sin(deg), -sin(deg), cos(deg), 0, 0].

Parameters:	deg (float) – The rotation angle in degrees (use conventional notation based on Pi = 180 degrees).

preScale(sx, sy)

Modify the matrix to scale by the zoom factors sx and sy. Has effects on attributes a thru d only: [a, b, c, d, e, f] -> [a*sx, b*sx, c*sy, d*sy, e, f].

Parameters:	sx (float) – Zoom factor in X direction. For the effect see description of attribute a. sy (float) – Zoom factor in Y direction. For the effect see description of attribute d.

preShear(sx, sy)

Modify the matrix to perform a shearing, i.e. transformation of rectangles into parallelograms (rhomboids). Has effects on attributes a thru d only: [a, b, c, d, e, f] -> [c*sy, d*sy, a*sx, b*sx, e, f].

Parameters:	sx (float) – Shearing effect in X direction. See attribute c. sy (float) – Shearing effect in Y direction. See attribute b.

preTranslate(tx, ty)

Modify the matrix to perform a shifting / translation operation along the x and / or y axis. Has effects on attributes e and f only: [a, b, c, d, e, f] -> [a, b, c, d, tx*a + ty*c, tx*b + ty*d].

Parameters:	tx (float) – Translation effect in X direction. See attribute e. ty (float) – Translation effect in Y direction. See attribute f.

concat(m1, m2)

Calculate the matrix product m1 * m2 and store the result in the current matrix. Any of m1 or m2 may be the current matrix. Be aware that matrix multiplication is not commutative. So the sequence of m1, m2 is important.

Parameters:	m1 (Matrix) – First (left) matrix. m2 (Matrix) – Second (right) matrix.

invert(m)

Calculate the matrix inverse of m and store the result in the current matrix. Returns 1 if m is not invertible (“degenerate”). In this case the current matrix will not change. Returns 0 if m is invertible, and the current matrix is replaced with the inverted m.

Parameters:	m (Matrix) – Matrix to be inverted.
Return type:	int

a

Scaling in X-direction (width). For example, a value of 0.5 performs a shrink of the width by a factor of 2. If a < 0, a left-right flip will (additionally) occur.

Type:	float

b

Causes a shearing effect: each Point(x, y) will become Point(x, y - b*x). Therefore, looking from left to right, e.g. horizontal lines will be “tilt” - downwards if b > 0, upwards otherwise (b is the tangens of the tilting angle).

Type:	float

c

Causes a shearing effect: each Point(x, y) will become Point(x - c*y, y). Therefore, looking upwards, vertical lines will be “tilt” - to the left if c > 0, to the right otherwise (c ist the tangens of the tilting angle).

Type:	float

d

Scaling in Y-direction (height). For example, a value of 1.5 performs a stretch of the height by 50%. If d < 0, an up-down flip will (additionally) occur.

Type:	float

e

Causes a horizontal shift effect: Each Point(x, y) will become Point(x + e, y). Positive (negative) values of e will shift right (left).

Type:	float

f

Causes a vertical shift effect: Each Point(x, y) will become Point(x, y - f). Positive (negative) values of f will shift down (up).

Type:	float

>>> m45p = fitz.Matrix(45)            # rotate 45 degrees clockwise
>>> m45m = fitz.Matrix(-45)           # rotate 45 degrees counterclockwise
>>> m90p = fitz.Matrix(90)            # rotate 90 degrees clockwise
>>>
>>> abs(m45p * ~m45p - fitz.Identity) # should be (close to) zero:
8.429369702178807e-08
>>>
>>> abs(m90p - m45p * m45p)           # should be (close to) zero:
8.429369702178807e-08
>>>
>>> abs(m45p * m45m - fitz.Identity)  # should be (close to) zero:
2.1073424255447017e-07
>>>
>>> abs(m45p - ~m45m)                 # should be (close to) zero:
2.384185791015625e-07
>>>
>>> m90p * m90p * m90p * m90p         # should be 360 degrees = fitz.Identity
fitz.Matrix(1.0, -0.0, 0.0, 1.0, 0.0, 0.0)