geometry

2D geometry primitives and implementation of some geometric algorithms.

class backpack.geometry.Point(x, y)

Bases: object

A point on the 2D plane.

Parameters

  • x (float) – The x coordinate of the point

  • y (float) – The y coordinate of the point

x: float

The x coordinate of the point

y: float

The y coordinate of the point

static ccw(pt1, pt2, pt3)

Determines if the three points form a counterclockwise angle. If two points are equal, or the three points are collinear, this method returns True.

Parameters

  • pt1 (Point) – The first point

  • pt2 (Point) – The second point

  • pt3 (Point) – The third point

Returns

True if the points form a counterclockwise angle

Return type

bool

distance(other)

Calculates the distance between this and an other point.

Parameters

other (Point) – The other point

Returns

The distance between this and an other point.

Return type

float

classmethod from_value(value)

Deserializes a Point from different formats.

Supported formats:

  • sequence containing exactly two numbers

  • dictionary containing numbers under ‘x’ and ‘y’ keys

  • Point instance (returns the same instance)

Parameters

value – the value to be converted

Return: The new Point instance

Raises: ValueError if the conversion was not successful.

class backpack.geometry.Line(pt1, pt2)

Bases: object

A line segment.

Parameters

  • pt1 (float) – The first point of the line segment

  • pt2 (float) – The second point of the line segment

pt1: Point

The first point of the line segment

pt2: Point

The second point of the line segment

intersects(other)

Determines if this line segment intersects an other one.

Parameters

other (Line) – The other line segment

Returns

True if the two segments intersect each other.

Return type

bool

classmethod from_value(value)

Deserializes a Line from different formats.

Supported formats:

  • sequence containing exactly two values that can be deserialized with Point.from_value

  • dictionary containing such Point values under ‘pt1’ and ‘pt2’ keys

  • Line instance (returns the same instance)

Parameters

value – the value to be converted

Returns: the Line instance

Raises: ValueError if the value could not be converted to a Line.

class backpack.geometry.Rectangle(pt1, pt2)

Bases: object

An axis aligned rectangle.

Parameters

  • pt1 (Point) – The first corner of the rectangle

  • pt2 (Point) – The second corner of the rectangle

pt1: Point

The first corner of the rectangle

pt2: Point

The second corner of the rectangle

has_inside(pt)

Determines if a point is inside this rectangle.

Parameters

pt (Point) – the point

Returns

True if the point lies inside this rectangle.

Return type

bool

property pt_min: Point

The point with the minimum coordinates of this rectangle.

property pt_max: Point

The point with the maximum coordinates of this rectangle.

property center: Point

The center of the rectangle.

property base: Point

Returns the center of the base of the rectangle.

property size: Tuple[float, float]

The width and height of the rectangle.

property width: float

The width of the rectangle.

property height: float

The height of the rectangle.

property area: float

The area of the rectangle.

property aspect_ratio: float

The aspect ratio of the rectangle.

property top: float

The top edge of the rectangle.

property left: float

The left edge of the rectangle.

property bottom: float

The bottom edge of the rectangle.

property right: float

The right edge of the rectangle.

property tlbr: Tuple[float, float, float, float]

Returns this rectangles coordinates as a top-left-bottom-right tuple.

property tlhw: Tuple[float, float, float, float]

Returns this rectangles coordinates as a top-left-width-height tuple.

classmethod from_value(value)

Converts a tuple in the form of ((0.1, 0.2), (0.3, 0.4)) to a Rectangle.

Parameters

value – the tuple

Returns: the Rectangle instance

Raises: ValueError if the tuple could not be converted to a Rectangle.

classmethod from_tlbr(tlbr)

Converts a top-left-bottom-right sequence of floats to a Rectangle.

Parameters

tlbr (Tuple[float, float, float, float]) – A top-left-bottom-right sequence of floats.

Return type

Rectangle

Returns: the Rectangle instance

Raises: ValueError if the sequence could not be converted to a Rectangle.

classmethod from_tlhw(tlhw)

Converts a top-left-width-height sequence of floats to a Rectangle.

Parameters
Return type

Rectangle

Returns: the Rectangle instance

Raises: ValueError if the sequence could not be converted to a Rectangle.

class backpack.geometry.PolyLine(points, closed=True)

Bases: object

A PolyLine is a connected series of line segments.

Parameters
points: Sequence[Point]

The list of the points of the PolyLine

closed: bool = True

True if the PolyLine is closed.

property lines: List[Line]

The line segments of this PolyLine

property boundingbox: Rectangle

The bounding box of this PolyLine

property self_intersects: bool

Determines if this PolyLine self-intersects.

property is_convex: bool

Determines if the polygon formed from this PolyLine is convex.

The result of this method is undefined for complex (self-intersecting) polygons.

Returns

True if the polygon is convex, False otherwise.

has_inside(point)

Determines if a point is inside this closed PolyLine.

This implementation uses the ray casting algorithm.

Parameters

point (Point) – The point

Returns

True if the point is inside this closed PolyLine.

Return type

bool

classmethod from_value(value, closed=True)

Converts a tuple in the form of ((0.1, 0.2), (0.3, 0.4), …) to a PolyLine.

Parameters

  • value – the tuple

  • closed – flags if the newly created PolyLine should be closed or not.

Returns: the PolyLine instance

Raises: ValueError if the tuple could not be converted to a PolyLine.