point¶

A point as a collection of coordinates in real space.

class parityos.utils.point.RealT¶

A constrained TypeVar representing a real number. Restricted to int, float and decimal.Decimal.

alias of TypeVar(‘RealT’, int, float, ~decimal.Decimal)

class parityos.utils.point.Point¶

Bases: Generic[RealT], ABC

Base class for Points in real space.

Coordinates can be of type float or decimal.Decimal.

property coordinates: tuple[RealT, ...]¶: Coordinates of the point as tuple.

abstractmethod classmethod from_coordinates(coordinates: Sequence[RealT], /) → Self¶: Construct a Point from a sequence of its coordinates.

property squared_norm: RealT¶

The squared Euclidean norm of the point.

Returns:: The sum of squares of the coordinates.

property norm: float¶

The Euclidean norm of the point.

Returns:: The square root of the sum of squares of the coordinates.

__getitem__(index: int, /) → RealT¶

Get coordinate at index.

Returns:: Coordinate at index.
Raises:: IndexError – If index is out of bounds.

__neg__() → Self¶

The negative of the point.

Returns:: A Point with the same coordinates, but of opposite sign.

__add__(other: Self, /) → Self¶

The addition operator +.

Addition is element-wise in the coordinates. Only supported between equal type Point instances.

Parameters:

other – Another Point.

Returns:

The sum of the two points as new Point.

Raises:

TypeError – If other is not of the same type as self.
TypeError – If addition between different coordinate types is not supported (e.g. float and decimal.Decimal)

__sub__(other: Self, /) → Self¶

Subtraction operator -.

Subtraction is element-wise in the coordinates. Only supported between equal type Point instances.

Parameters:

other – Another Point.

Returns:

The difference between the two points as new Point.

Raises:

TypeError – If other is not of the same type as self.
TypeError – If subtraction between different coordinate types is not supported (e.g. float and decimal.Decimal)

__mul__(other: RealT, /) → Self¶

Scalar multiplication operator *.

Type checking is only supported for multiplication with a scalar of same type as the coordinates of self.

Parameters:: other – Scalar factor to multiply self with.
Returns:: A new Point with the coordinates of self multiplied with other.

class parityos.utils.point.Point1D(x: RealT)¶

Bases: Point[RealT]

A one-dimensional Point on a line with a single coordinate x.

x: RealT¶: The x coordinate of this point.

coordinates: tuple[RealT]¶

classmethod from_coordinates(coordinates: Sequence[RealT]) → Self¶: Construct a Point from a sequence of its coordinates.

class parityos.utils.point.Point2D(x: RealT, y: RealT)¶

Bases: Point[RealT]

A two-dimensional Point on a plane with coordinates x and y.

x: RealT¶: The x coordinate of this point.

y: RealT¶: The y coordinate of this point.

coordinates: tuple[RealT, RealT]¶

classmethod from_coordinates(coordinates: Sequence[RealT]) → Self¶: Construct a Point from a sequence of its coordinates.

class parityos.utils.point.Point3D(x: RealT, y: RealT, z: RealT)¶

Bases: Point[RealT]

A three-dimensional Point in space with coordinates x, y and z.

x: RealT¶: The x coordinate of this point.

y: RealT¶: The y coordinate of this point.

z: RealT¶: The z coordinate of this point.

coordinates: tuple[RealT, RealT, RealT]¶

classmethod from_coordinates(coordinates: Sequence[RealT]) → Self¶: Construct a Point from a sequence of its coordinates.

class parityos.utils.point.PointT¶

A TypeVar representing a Point.

alias of TypeVar(‘PointT’, bound=Point)

parityos.utils.point.get_point(x: RealT) → Point1D[RealT]¶
parityos.utils.point.get_point(x: RealT, y: RealT) → Point2D[RealT]
parityos.utils.point.get_point(x: RealT, y: RealT, z: RealT) → Point3D[RealT]: Convenience function for creating points of arbitrary dimensionality.