Represents a four-sided mathematical shape (also called “quadrilateral” or “tetragon”) in the plane, defined as a sequence of four Point objects ul, ur, ll, lr (conveniently called upper left, upper right, lower left, lower right).

Quads can be obtained as results of text search methods (Page.search_for()), and they are used to define text marker annotations (see e.g. Page.add_squiggly_annot() and friends), and in several draw methods (like Page.draw_quad() / Shape.draw_quad(), Page.draw_oval()/ Shape.draw_quad()).


  • If the corners of a rectangle are transformed with a rotation, scale or translation Matrix, then the resulting quad is rectangular (= congruent to a rectangle), i.e. all of its corners again enclose angles of 90 degrees. Property Quad.is_rectangular checks whether a quad can be thought of being the result of such an operation.
  • This is not true for all matrices: e.g. shear matrices produce parallelograms, and non-invertible matrices deliver “degenerate” tetragons like triangles or lines.
  • Attribute Quad.rect obtains the envelopping rectangle. Vice versa, rectangles now have attributes Rect.quad, resp. IRect.quad to obtain their respective tetragon versions.
Methods / Attributes Short Description
Quad.transform() transform with a matrix
Quad.morph() transform with a point and matrix
Quad.ul upper left point
Quad.ur upper right point
Quad.ll lower left point
Quad.lr lower right point
Quad.is_convex true if quad is a convex set
Quad.is_empty true if quad is an empty set
Quad.is_rectangular true if quad is congruent to a rectangle
Quad.rect smallest containing Rect
Quad.width the longest width value
Quad.height the longest height value

Class API

class Quad
__init__(self, ul, ur, ll, lr)
__init__(self, quad)
__init__(self, sequence)

Overloaded constructors: “ul”, “ur”, “ll”, “lr” stand for point_like objects (the four corners), “sequence” is a Python sequence with four point_like objects.

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

Without parameters, a quad consisting of 4 copies of Point(0, 0) is created.


Modify the quadrilateral by transforming each of its corners with a matrix.

Parameters:matrix (matrix_like) – the matrix.
morph(fixpoint, matrix)

(New in version 1.17.0) “Morph” the quad with a matrix-like using a point-like as fixed point.

  • fixpoint (point_like) – the point.
  • matrix (matrix_like) – the matrix.

a new quad (no operation if this is the infinite quad).


The smallest rectangle containing the quad, represented by the blue area in the following picture.


Upper left point.


Upper right point.


Lower left point.


Lower right point.


(New in version 1.16.1)

Checks if for any two points of the quad, all points on their connecting line also belong to the quad.


True if enclosed area is zero, which means that at least three of the four corners are on the same line. If this is false, the quad may still be degenerate or not look like a tetragon at all (triangles, parallelograms, trapezoids, …).


True if all corner angles are 90 degrees. This implies that the quad is convex and not empty.


The maximum length of the top and the bottom side.


The maximum length of the left and the right side.



This class adheres to the sequence protocol, so components can be dealt with via their indices, too. Also refer to Using Python Sequences as Arguments in PyMuPDF.

We are still in process to extend algebraic operations to quads. Multiplication and division with / by numbers and matrices are already defined. Addition, subtraction and any unary operations may follow when we see an actual need.

Containment Checks

Independent from the previous remark, the following containment checks are possible:

  • point in quad – check whether a point is inside a quadrilateral.
  • rect in quad – check whether a rectangle is inside a quadrilateral. This is done by checking the containment of its four corners.
  • quad in quad – check whether some quad is contained in some other quadrilateral. This is done by checking the containment of its four corners.

Please note the following interesting detail:

For a rectangle, only its top-left point belongs to it. Since v1.19.0, rectangles are defined to be “open”, such that its bottom and its right edge do not belong to it – including the respective corners. But for quads there exists no notion like “openness”, so we have the following surprising situation:

>>> rect.br in rect
>>> # but:
>>> rect.br in rect.quad