raygeo.geo.shape.arc

Arc geometry queries and conversions.

Provides bounding rectangle computation, intersection tests (arc-rect, arc-circle, arc-polygons), arc linearization into line segments for rendering or further processing, angle utilities (normalize, direction, containment), and arc midpoint / closest-point lookups.

Functions

does_arc_intersect_circle()

does_arc_intersect_circle(
    arc_start: types.Point,
    arc_end: types.Point,
    arc_center: types.Point,
    clockwise: bool,
    circle_center: types.Point,
    circle_radius: float,
) -> bool

Check if an arc intersects a circle.

Parameter	Type	Description
arc_start	types.Point	Arc start point (x, y).
arc_end	types.Point	Arc end point (x, y).
arc_center	types.Point	Arc center point (x, y).
clockwise	bool	Whether the arc is clockwise.
circle_center	types.Point	Circle center (x, y).
circle_radius	float	Circle radius.
Returns	bool	True if the arc intersects the circle.
Complexity		O(n) time, O(1) space

does_arc_intersect_rect()

does_arc_intersect_rect(
    arc_start: types.Point,
    arc_end: types.Point,
    arc_center: types.Point,
    clockwise: bool,
    rect: types.Rect,
) -> bool

Check if an arc intersects a rectangle.

Parameter	Type	Description
arc_start	types.Point	Arc start point (x, y).
arc_end	types.Point	Arc end point (x, y).
arc_center	types.Point	Arc center point (x, y).
clockwise	bool	Whether the arc is clockwise.
rect	types.Rect	Rectangle (x_min, y_min, x_max, y_max).
Returns	bool	True if the arc intersects the rectangle.
Complexity		O(n) time, O(1) space

get_arc_angles()

get_arc_angles(
    start: types.Point,
    end: types.Point,
    center: types.Point,
    clockwise: bool,
) -> types.Point3D

Get the start, end, and sweep angles of an arc.

Parameter	Type	Description
start	types.Point	Arc start point (x, y).
end	types.Point	Arc end point (x, y).
center	types.Point	Arc center point (x, y).
clockwise	bool	Whether the arc is clockwise.
Returns	types.Point3D	Tuple of (start_angle, end_angle, sweep_angle) in radians.
Complexity		O(1) time, O(1) space

get_arc_bounds()

get_arc_bounds(
    start: types.Point,
    end: types.Point,
    center: types.Point,
    clockwise: bool,
) -> types.Rect

Get the bounding rectangle of an arc.

Parameter	Type	Description
start	types.Point	Arc start point (x, y).
end	types.Point	Arc end point (x, y).
center	types.Point	Arc center point (x, y).
clockwise	bool	Whether the arc is clockwise.
Returns	types.Rect	Bounding rectangle as (x_min, y_min, x_max, y_max).
Complexity		O(1) time, O(1) space

get_arc_closest_point()

get_arc_closest_point(
    arc_cmd: Any,
    start_pos: types.Point3D,
    x: float,
    y: float,
) -> Optional[tuple[float, types.Point, float]]

Get the closest point on an arc to a given point.

Parameter	Type	Description
arc_cmd	Any	Arc command row or MockArc-like object.
start_pos	types.Point3D	Start position (x, y, z).
x	float	X coordinate of target point.
y	float	Y coordinate of target point.
Returns	Optional[tuple[float, types.Point, float]]	Tuple of (parameter, closest_point, distance) or None.
Complexity		O(n) time, O(1) space

get_arc_direction()

get_arc_direction(
    center: types.Point,
    start: types.Point,
    mouse: types.Point,
) -> bool

Get the direction (CW/CCW) of an arc at a mouse point.

Parameter	Type	Description
center	types.Point	Arc center (x, y).
start	types.Point	Arc start point (x, y).
mouse	types.Point	Mouse point (x, y).
Returns	bool	True if clockwise, False if counter-clockwise.
Complexity		O(1) time, O(1) space

get_arc_length()

get_arc_length(
    start_pos: types.Point,
    end_pos: types.Point,
    center_offset: types.Point,
    clockwise: bool,
) -> float

Compute the arc length of a circular arc.

Parameter	Type	Description
start_pos	types.Point	Start point (x, y).
end_pos	types.Point	End point (x, y).
center_offset	types.Point	Center offset (i, j) from start.
clockwise	bool	True for clockwise, False for counter-clockwise.
Returns	float	Arc length.
Complexity		O(1) time, O(1) space

get_arc_midpoint()

get_arc_midpoint(
    start: types.Point,
    end: types.Point,
    center: types.Point,
    clockwise: bool,
) -> types.Point

Get the midpoint of an arc.

Parameter	Type	Description
start	types.Point	Arc start point (x, y).
end	types.Point	Arc end point (x, y).
center	types.Point	Arc center point (x, y).
clockwise	bool	Whether the arc is clockwise.
Returns	types.Point	Midpoint (x, y).
Complexity		O(1) time, O(1) space

get_arc_sweep()

get_arc_sweep(start_angle: float, end_angle: float, clockwise: bool) -> float

Compute the signed sweep angle for an arc.

Handles direction (CW/CCW) and full-circle detection.

Parameter	Type	Description
start_angle	float	Start angle in radians.
end_angle	float	End angle in radians.
clockwise	bool	Whether the arc is clockwise.
Returns	float	Signed sweep angle in radians.
Complexity		O(1) time, O(1) space

get_arc_through_point()

get_arc_through_point(
    t_start: types.Point,
    t_end: types.Point,
    t_mid: types.Point,
    center: types.Point,
    radius: float,
) -> types.Polygon

Build a circular arc through three points around a centre.

Returns a polyline approximation of the arc from t_start to t_end that passes through t_mid, with the given centre and radius.

Parameter	Type	Description
t_start	types.Point	Arc start point (x, y).
t_end	types.Point	Arc end point (x, y).
t_mid	types.Point	Point the arc must pass through (x, y).
center	types.Point	Arc centre (x, y).
radius	float	Arc radius.
Returns	types.Polygon	Polyline approximation as list of (x, y) points.

Construct a circular arc through a given point

get_polyline_turn_sign()

get_polyline_turn_sign(polyline: Sequence[types.Point]) -> float

Determine the turn direction of a polyline at its midpoint.

Computes the cross product of the edge vectors just before and just after the midpoint vertex. Returns +1.0 for a counter-clockwise (left) turn and -1.0 for a clockwise (right) turn.

Parameter	Type	Description
polyline	Sequence[types.Point]	Open polyline as (x, y) points.
Returns	float	+1.0 (CCW) or -1.0 (CW).
Complexity		O(1) time, O(1) space

Determine turn direction of a polyline at its midpoint vertex

is_angle_between()

is_angle_between(
    angle: float,
    start: float,
    end: float,
    clockwise: bool,
) -> bool

Check if an angle is between two other angles.

Parameter	Type	Description
angle	float	Angle to test.
start	float	Start angle.
end	float	End angle.
clockwise	bool	Whether the arc is clockwise.
Returns	bool	True if angle is between start and end.
Complexity		O(1) time, O(1) space

is_arc_clockwise()

is_arc_clockwise(
    points: Sequence[types.Point2DOr3D],
    center: types.Point2DOr3D,
) -> bool

Check if an arc is clockwise.

Parameter	Type	Description
points	Sequence[types.Point2DOr3D]	Sequence of (x, y) points on the arc.
center	types.Point2DOr3D	Arc center (x, y).
Returns	bool	True if the arc is clockwise.
Complexity		O(n) time, O(1) space

is_arc_inside_polygons()

is_arc_inside_polygons(
    arc_start: types.Point,
    arc_end: types.Point,
    arc_center: types.Point,
    clockwise: bool,
    polygons: Any,
) -> bool

Check if an arc is inside a set of polygons.

Parameter	Type	Description
arc_start	types.Point	Arc start point (x, y).
arc_end	types.Point	Arc end point (x, y).
arc_center	types.Point	Arc center point (x, y).
clockwise	bool	Whether the arc is clockwise.
polygons	Any	List of polygons to check against.
Returns	bool	True if the arc is inside all polygons.
Complexity		O(n * m) time, O(1) space

linearize_arc()

linearize_arc(
    arc_cmd: Any,
    start_point: types.Point3D,
    resolution: float = 0.1,
) -> list[tuple[types.Point3D, types.Point3D]]

Linearize an arc into line segments.

Parameter	Type	Description
arc_cmd	Any	Arc command row or MockArc-like object.
start_point	types.Point3D	Start point (x, y, z).
resolution	float = 0.1	Maximum segment length.
Returns	list[tuple[types.Point3D, types.Point3D]]	List of (p1, p2) segment pairs.
Complexity		O(n) time, O(n) space

Arc linearization: coarse and fine resolution

normalize_angle()

normalize_angle(angle: float) -> float

Normalize an angle to the range [0, 2*pi).

Parameter	Type	Description
angle	float	Angle in radians.
Returns	float	Normalized angle in [0, 2*pi).
Complexity		O(1) time, O(1) space

normalize_angle_signed()

normalize_angle_signed(angle: float) -> float

Normalize an angle to the range [-pi, pi).

Parameter	Type	Description
angle	float	Angle in radians.
Returns	float	Normalized angle in [-pi, pi).
Complexity		O(1) time, O(1) space