# Rect

Rect represents a rectangle defined by four floating point numbers x0, y0, x1, y1. They are treated as being coordinates of two diagonally opposite points. The first two numbers are regarded as the “top left” corner P(x0,y0) and P(x1,y1) as the “bottom right” one. However, these two properties need not coincide with their intuitive meanings – read on.

The following remarks are also valid for IRect objects:

• A rectangle in the sense of (Py-) MuPDF (and PDF) always has borders parallel to the x- resp. y-axis. A general orthogonal tetragon is not a rectangle – in contrast to the mathematical definition.

• The constructing points can be (almost! – see below) anywhere in the plane – they need not even be different, and e.g. “top left” need not be the geometrical “north-western” point.

• For any given quadruple of numbers, the geometrically “same” rectangle can be defined in four different ways:
1. Rect(P(x0,y0), P(x1,y1))

2. Rect(P(x1,y1), P(x0,y0))

3. Rect(P(x0,y1), P(x1,y0))

4. Rect(P(x1,y0), P(x0,y1))

(Changed in v1.19.0) Hence some classification:

• A rectangle is called valid if `x0 <= x1` and `y0 <= y1` (i.e. the bottom right point is “south-eastern” to the top left one), otherwise invalid. Of the four alternatives above, only the first is valid. Please take into account, that in MuPDF’s coordinate system, the y-axis is oriented from top to bottom. Invalid rectangles have been called infinite in earlier versions.

• A rectangle is called empty if `x0 >= x1` or `y0 >= y1`. This implies, that invalid rectangles are also always empty. And `width` (resp. `height`) is set to zero if `x0 > x1` (resp. `y0 > y1`). In previous versions, a rectangle was empty only if one of width or height was zero.

• Rectangle coordinates cannot be outside the number range from `FZ_MIN_INF_RECT = -2147483648` to `FZ_MAX_INF_RECT = 2147483520`. Both values have been chosen, because they are the smallest / largest 32bit integers that survive C float conversion roundtrips. In previous versions there was no limit for coordinate values.

• There is exactly one “infinite” rectangle, defined by `x0 = y0 = FZ_MIN_INF_RECT` and `x1 = y1 = FZ_MAX_INF_RECT`. It contains every other rectangle. It is mainly used for technical purposes – e.g. when a function call should ignore a formally required rectangle argument. This rectangle is not empty.

• Rectangles are (semi-) open: The right and the bottom edges (including the resp. corners) are not considered part of the rectangle. This implies, that only the top-left corner `(x0, y0)` can ever belong to the rectangle - the other three corners never do. An empty rectangle contains no corners at all.

• Here is an overview of the changes.

Notion

Versions < 1.19.0

Versions 1.19.*

empty

x0 = x1 or y0 = y1

x0 >= x1 or y0 >= y1 – includes invalid rects

valid

n/a

x0 <= x1 and y0 <= y1

infinite

all rects where x0 > x1 or y1 > y0

exactly one infinite rect / irect!

coordinate values

all numbers

`FZ_MIN_INF_RECT <= number <= FZ_MAX_INF_RECT`

borders, corners

are parts of the rectangle

right and bottom corners and edges are outside

• There are new top level functions defining infinite and standard empty rectangles and quads, see `INFINITE_RECT()` and friends.

Methods / Attributes

Short Description

`Rect.contains()`

checks containment of point_likes and rect_likes

`Rect.get_area()`

calculate rectangle area

`Rect.include_point()`

enlarge rectangle to also contain a point

`Rect.include_rect()`

enlarge rectangle to also contain another one

`Rect.intersect()`

common part with another rectangle

`Rect.intersects()`

checks for non-empty intersections

`Rect.morph()`

transform with a point and a matrix

`Rect.torect()`

the matrix that transforms to another rectangle

`Rect.norm()`

the Euclidean norm

`Rect.normalize()`

makes a rectangle valid

`Rect.round()`

create smallest IRect containing rectangle

`Rect.transform()`

transform rectangle with a matrix

`Rect.bottom_left`

bottom left point, synonym bl

`Rect.bottom_right`

bottom right point, synonym br

`Rect.height`

rectangle height

`Rect.irect`

equals result of method round()

`Rect.is_empty`

whether rectangle is empty

`Rect.is_valid`

whether rectangle is valid

`Rect.is_infinite`

whether rectangle is infinite

`Rect.top_left`

top left point, synonym tl

`Rect.top_right`

top_right point, synonym tr

`Rect.quad`

`Rect.width`

rectangle width

`Rect.x0`

left corners’ x coordinate

`Rect.x1`

right corners’ x -coordinate

`Rect.y0`

top corners’ y coordinate

`Rect.y1`

bottom corners’ y coordinate

Class API

class Rect
__init__(self)
__init__(self, x0, y0, x1, y1)
__init__(self, top_left, bottom_right)
__init__(self, top_left, x1, y1)
__init__(self, x0, y0, bottom_right)
__init__(self, rect)
__init__(self, sequence)

Overloaded constructors: top_left, bottom_right stand for `point_like` objects, “sequence” is a Python sequence type of 4 numbers (see Using Python Sequences as Arguments in PyMuPDF), “rect” means another `rect_like`, while the other parameters mean coordinates.

If “rect” is specified, the constructor creates a new copy of it.

Without parameters, the empty rectangle Rect(0.0, 0.0, 0.0, 0.0) is created.

round()

Creates the smallest containing IRect. This is not the same as simply rounding the rectangle’s edges: The top left corner is rounded upwards and to the left while the bottom right corner is rounded downwards and to the right.

```>>> fitz.Rect(0.5, -0.01, 123.88, 455.123456).round()
IRect(0, -1, 124, 456)
```
1. If the rectangle is empty, the result is also empty.

2. Possible paradox: The result may be empty, even if the rectangle is not empty! In such cases, the result obviously does not contain the rectangle. This is because MuPDF’s algorithm allows for a small tolerance (1e-3). Example:

```>>> r = fitz.Rect(100, 100, 200, 100.001)
>>> r.is_empty  # rect is NOT empty
False
>>> r.round()  # but its irect IS empty!
fitz.IRect(100, 100, 200, 100)
>>> r.round().is_empty
True
```
Return type

IRect

transform(m)

Transforms the rectangle with a matrix and replaces the original. If the rectangle is empty or infinite, this is a no-operation.

Parameters

m (Matrix) – The matrix for the transformation.

Return type

Rect

Returns

the smallest rectangle that contains the transformed original.

intersect(r)

The intersection (common rectangular area, largest rectangle contained in both) of the current rectangle and r is calculated and replaces the current rectangle. If either rectangle is empty, the result is also empty. If r is infinite, this is a no-operation. If the rectangles are (mathematically) disjoint sets, then the result is invalid. If the result is valid but empty, then the rectangles touch each other in a corner or (part of) a side.

Parameters

r (Rect) – Second rectangle

include_rect(r)

The smallest rectangle containing the current one and r is calculated and replaces the current one. If either rectangle is infinite, the result is also infinite. If one is empty, the other one will be taken as the result.

Parameters

r (Rect) – Second rectangle

include_point(p)

The smallest rectangle containing the current one and point p is calculated and replaces the current one. The infinite rectangle remains unchanged. To create a rectangle containing a series of points, start with (the empty) fitz.Rect(p1, p1) and successively include the remaining points.

Parameters

p (Point) – Point to include.

get_area([unit])

Calculate the area of the rectangle and, with no parameter, equals abs(rect). Like an empty rectangle, the area of an infinite rectangle is also zero. So, at least one of fitz.Rect(p1, p2) and fitz.Rect(p2, p1) has a zero area.

Parameters

unit (str) – Specify required unit: respective squares of px (pixels, default), in (inches), cm (centimeters), or mm (millimeters).

Return type

float

contains(x)

Checks whether x is contained in the rectangle. It may be an IRect, Rect, Point or number. If x is an empty rectangle, this is always true. If the rectangle is empty this is always False for all non-empty rectangles and for all points. `x in rect` and `rect.contains(x)` are equivalent.

Parameters

x (`rect_like` or `point_like`.) – the object to check.

Return type

bool

intersects(r)

Checks whether the rectangle and a `rect_like` “r” contain a common non-empty Rect. This will always be False if either is infinite or empty.

Parameters

r (rect_like) – the rectangle to check.

Return type

bool

torect(rect)
• New in version 1.19.3

Compute the matrix which transforms this rectangle to a given one.

Parameters

rect (rect_like) – the target rectangle. Must not be empty or infinite.

Return type

Matrix

Returns

a matrix `mat` such that `self * mat = rect`. Can for example be used to transform between the page and the pixmap coordinates.

Note

Suppose you want to check whether any of the words “pixmap” is invisible, because the text color equals the ambient color – e.g. white on white. We make a pixmap and check the “color environment” of each word:

```>>> # make a pixmap of the page
>>> pix = page.get_pixmap(dpi=150)
>>> # make a matrix that transforms to pixmap coordinates
>>> mat = page.rect.torect(pix.irect)
>>> # search for text locations
>>> rlist = page.search_for("pixmap")
>>> # check color environment of each occurrence
>>> # we will check for "almost unicolor"
>>> for r in rlist:
if pix.color_topusage(clip=r * mat) > 0.95:
print("'pixmap' invisible here:", r)
>>>
```

Method `Pixmap.color_topusage()` computes the percentage of pixels showing the same color.

morph(fixpoint, matrix)
• New in version 1.17.0

Return a new quad after applying a matrix to the rectangle using the fixed point `fixpoint`.

Parameters
• fixpoint (point_like) – the fixed point.

• matrix (matrix_like) – the matrix.

Returns

a new Quad. This a wrapper for the same-named quad method. If infinite, the infinite quad is returned.

norm()
• New in version 1.16.0

Return the Euclidean norm of the rectangle treated as a vector of four numbers.

normalize()

Replace the rectangle with its valid version. This is done by shuffling the rectangle corners. After completion of this method, the bottom right corner will indeed be south-eastern to the top left one (but may still be empty).

irect

Equals result of method round().

top_left
tl

Equals Point(x0, y0).

Type

Point

top_right
tr

Equals `Point(x1, y0)`.

Type

Point

bottom_left
bl

Equals `Point(x0, y1)`.

Type

Point

bottom_right
br

Equals `Point(x1, y1)`.

Type

Point

The quadrilateral `Quad(rect.tl, rect.tr, rect.bl, rect.br)`.

Type

width

Width of the rectangle. Equals `max(x1 - x0, 0)`.

Return type

float

height

Height of the rectangle. Equals `max(y1 - y0, 0)`.

Return type

float

x0

X-coordinate of the left corners.

Type

float

y0

Y-coordinate of the top corners.

Type

float

x1

X-coordinate of the right corners.

Type

float

y1

Y-coordinate of the bottom corners.

Type

float

is_infinite

`True` if this is the infinite rectangle.

Type

bool

is_empty

`True` if rectangle is empty.

Type

bool

is_valid

`True` if rectangle is valid.

Type

bool

Note

This software is provided AS-IS with no warranty, either express or implied. This software is distributed under license and may not be copied, modified or distributed except as expressly authorized under the terms of that license. Refer to licensing information at artifex.com or contact Artifex Software Inc., 39 Mesa Street, Suite 108A, San Francisco CA 94129, United States for further information. 