raygeo.geo.shape.point

Individual point operations.

Provides equality testing within a configurable tolerance, midpoint computation between two points, 2D/3D get_circumcenter of three points, and applying a 4x4 affine transformation matrix to a single point.

Functions

are_points_equal_3d()

are_points_equal_3d(
    p1: types.Point3D,
    p2: types.Point3D,
    tolerance: float,
) -> bool

Check if two 3D points are equal within tolerance.

Parameter	Type	Description
p1	types.Point3D	First point (x, y, z).
p2	types.Point3D	Second point (x, y, z).
tolerance	float	Maximum allowed difference.
Returns	bool	True if points are equal within tolerance.
Complexity		O(1) time, O(1) space

get_circumcenter()

get_circumcenter(
    a: types.Point,
    b: types.Point,
    c: types.Point,
) -> tuple[types.Point, float]

Compute the get_circumcenter and radius of three 2D points.

Returns the center of the unique circle passing through all three points along with its radius. Returns ((0.0, 0.0), -1.0) when the points are collinear.

Parameter	Type	Description
a	types.Point	First point (x, y).
b	types.Point	Second point (x, y).
c	types.Point	Third point (x, y).
Returns	tuple[types.Point, float]	(center, radius) where center is (x, y).
Complexity		O(1) time, O(1) space

get_circumcenter_3d()

get_circumcenter_3d(
    a: types.Point3D,
    b: types.Point3D,
    c: types.Point3D,
) -> Optional[types.Point3D]

Compute the get_circumcenter of three 3D points.

Returns the center of the unique circle passing through all three points. Returns None when the points are collinear.

Parameter	Type	Description
a	types.Point3D	First point (x, y, z).
b	types.Point3D	Second point (x, y, z).
c	types.Point3D	Third point (x, y, z).
Returns	Optional[types.Point3D]	Circumcenter (x, y, z) or None if collinear.
Complexity		O(1) time, O(1) space

Circumcenter of three 3D points with circumcircle

get_midpoint_3d()

get_midpoint_3d(p1: types.Point3D, p2: types.Point3D) -> types.Point3D

Get the midpoint between two 3D points.

Parameter	Type	Description
p1	types.Point3D	First point (x, y, z).
p2	types.Point3D	Second point (x, y, z).
Returns	types.Point3D	Midpoint (x, y, z).
Complexity		O(1) time, O(1) space

Midpoint of a 3D segment

rotate_point()

rotate_point(point: types.Point, angle: float) -> types.Point

Rotate a 2D point around the origin.

Parameter	Type	Description
point	types.Point	Point (x, y) to rotate.
angle	float	Rotation angle in radians (counter-clockwise).
Returns	types.Point	Rotated point (x, y).
Complexity		O(1) time, O(1) space

transform_point_3d()

transform_point_3d(
    matrix: Sequence[Sequence[float]],
    x: float,
    y: float,
    z: float,
) -> types.Point3D

Apply an affine transformation matrix to a 3D point.

Parameter	Type	Description
matrix	Sequence[Sequence[float]]	4x4 affine transformation matrix.
x	float	X coordinate.
y	float	Y coordinate.
z	float	Z coordinate.
Returns	types.Point3D	Transformed point (x, y, z).
Complexity		O(1) time, O(1) space