Point

class Point(radius: float = 0, azimuth: float = 0, center_of_projection: Point | None = None, needs_center_of_projection: bool = True, is_relative: bool = False)

Represent a point in the hyperbolic plane using polar coordinates.

Parameters:

• radius – The hyperbolic distance between the Point an the origin of the hyperbolic plane.

• azimuth – The angle between the Point and the pole (ray starting at the origin and extending in positive x-direction).

• center_of_projection – The center of projection of the hyperbolic plane.

By default is_relative is False, meaning when converting the receiver to a point in the Euclidean plane, we first determine its coordinates relative to its center of projection and only then correct the point in Euclidean space. When is_relative is True, we do NOT determine the coordinates relative to the center of projection (since we assume that the point is relative already), and correct the point in Euclidean space as is. This can be useful as some classes like Circle deal with the projection themselves and only need the correction.

distance_to(other, curvature: float = -1) → float

Returns the hyperbolic distance between the receiver and the other Point.

get_projection_relative_point() → Point

Returns a Point whose coordinates represent the ones of the receiver, but as if its center of projection was the origin.

static normalize_angle(angle: float) → float

Given an angle in radians, returns the equivalent angle in [0, 2 PI].

rotated_by(angle: float) → Point

Rotates the receiver around the origin by the passed angle in radians.

set_center_of_projection(point: Point | None) → Point

Changes the center of projection of the receiver.

Parameters:

point (Point) – The new center of projection.

Returns:

The receiver with the new center of projection.

Return type:

Point

to_point_in_plane(plane: PolarPlane) → ndarray[tuple[int, ...], dtype[float64]]

Converts the receiver to a canvas Point2D, assuming that it lies in the passed PolarPlane.

translated_by(distance: float, curvature: float = -1) → Point

This translation represents a movement of a point from the origin along the x-axis by a specified distance. All other points in the plane, in particular the receiver Point, are moved in such a way, that the distance to the moving point remain unchanged.

Note

Does not actually move the other objects in the plane. But only the receiver.