raygeo.geo.shape.bezier

Cubic bezier curve queries and conversions.

Provides point evaluation at a parameter t, splitting into two halves, bounding rectangle computation, flattening to line segments (both fixed-step and adaptive subdivision), rectangle clipping, flatness testing, perpendicular distance measurement, and conversion from cubic to quadratic form.

Functions

bezier_flatness_sq()

bezier_flatness_sq(a: Point3D, b: Point3D, c: Point3D, d: Point3D) -> float

Compute the flatness squared of a cubic bezier.

Returns: Flatness squared value.

Parameter	Type	Description
a	Point3D	Start point (x, y, z).
b	Point3D	First control point (x, y, z).
c	Point3D	Second control point (x, y, z).
d	Point3D	End point (x, y, z).
Returns	float

clip_bezier_with_rect()

clip_bezier_with_rect(p0: Point, p1: Point, p2: Point, p3: Point, rect: Rect) -> list[tuple[Point, Point, Point, Point]]

Clip a cubic bezier with a rectangle.

Returns: List of bezier segments inside the rectangle.

Parameter	Type	Description
p0	Point	Start control point (x, y).
p1	Point	First control point (x, y).
p2	Point	Second control point (x, y).
p3	Point	End control point (x, y).
rect	Rect	Clipping rectangle (x_min, y_min, x_max, y_max).
Returns	list[tuple[Point, Point, Point, Point]]

convert_cubic_bezier_to_quadratic()

convert_cubic_bezier_to_quadratic(p0: Point, p1: Point, p2: Point, p3: Point) -> tuple[Point, Point, Point]

Convert a cubic bezier to a quadratic bezier.

Returns: Quadratic bezier (p0, p1, p2).

Parameter	Type	Description
p0	Point	Start control point (x, y).
p1	Point	First control point (x, y).
p2	Point	Second control point (x, y).
p3	Point	End control point (x, y).
Returns	tuple[Point, Point, Point]

flatten_bezier()

flatten_bezier(p0: Point3D, p1: Point3D, p2: Point3D, p3: Point3D, tolerance: float, max_subdivisions: int, pts: list) -> None

Flatten a bezier curve into points.

Parameter	Type	Description
p0	Point3D	Start control point (x, y, z).
p1	Point3D	First control point (x, y, z).
p2	Point3D	Second control point (x, y, z).
p3	Point3D	End control point (x, y, z).
tolerance	float	Flattening tolerance.
max_subdivisions	int	Maximum recursion depth.
pts	list	Output list to append points to.
Returns	None

get_bezier_bounds()

get_bezier_bounds(p0: Point, p1: Point, p2: Point, p3: Point) -> Rect

Get the bounding rectangle of a cubic bezier.

Returns: Bounding rectangle as (x_min, y_min, x_max, y_max).

Parameter	Type	Description
p0	Point	Start control point (x, y).
p1	Point	First control point (x, y).
p2	Point	Second control point (x, y).
p3	Point	End control point (x, y).
Returns	Rect

get_bezier_point_at()

get_bezier_point_at(p0: Point, p1: Point, p2: Point, p3: Point, t: float) -> Point

Get a point on a cubic bezier at parameter t.

Returns: Point on the bezier curve (x, y).

Parameter	Type	Description
p0	Point	Start control point (x, y).
p1	Point	First control point (x, y).
p2	Point	Second control point (x, y).
p3	Point	End control point (x, y).
t	float	Parameter value (0..1).
Returns	Point

get_bezier_rect_intersections()

get_bezier_rect_intersections(p0: Point, p1: Point, p2: Point, p3: Point, rect: Rect) -> list[float]

Get intersection t-values of a bezier with a rectangle.

Returns: List of t-values where the bezier intersects.

Parameter	Type	Description
p0	Point	Start control point (x, y).
p1	Point	First control point (x, y).
p2	Point	Second control point (x, y).
p3	Point	End control point (x, y).
rect	Rect	Rectangle (x_min, y_min, x_max, y_max).
Returns	list[float]

is_bezier_inside_polygons()

is_bezier_inside_polygons(p0: Point, p1: Point, p2: Point, p3: Point, polygons: Any) -> bool

Check if a bezier curve is inside a set of polygons.

Returns: True if the bezier is inside all polygons.

Parameter	Type	Description
p0	Point	Start control point (x, y).
p1	Point	First control point (x, y).
p2	Point	Second control point (x, y).
p3	Point	End control point (x, y).
polygons	Any	List of polygons to check against.
Returns	bool

linearize_bezier()

linearize_bezier(p0: Point3D, p1: Point3D, p2: Point3D, p3: Point3D, num_steps: int) -> list[tuple[Point3D, Point3D]]

Linearize a bezier into line segments.

Returns: List of (p1, p2) segment pairs.

Parameter	Type	Description
p0	Point3D	Start control point (x, y, z).
p1	Point3D	First control point (x, y, z).
p2	Point3D	Second control point (x, y, z).
p3	Point3D	End control point (x, y, z).
num_steps	int	Number of linearization steps.
Returns	list[tuple[Point3D, Point3D]]

linearize_bezier_adaptive()

linearize_bezier_adaptive(p0: Point, p1: Point, p2: Point, p3: Point, tolerance_sq: float, max_subdivisions: int = 20) -> Polygon

Adaptively linearize a bezier curve.

Returns: List of linearized points (x, y).

Parameter	Type	Description
p0	Point	Start control point (x, y).
p1	Point	First control point (x, y).
p2	Point	Second control point (x, y).
p3	Point	End control point (x, y).
tolerance_sq	float	Squared tolerance for subdivision.
max_subdivisions	int = 20	Maximum recursion depth.
Returns	Polygon

linearize_bezier_segment()

linearize_bezier_segment(p0: Point3D, p1: Point3D, p2: Point3D, p3: Point3D, tolerance: float = 0.1) -> list[Point3D]

Linearize a single bezier segment.

Returns: List of linearized points (x, y, z).

Parameter	Type	Description
p0	Point3D	Start control point (x, y, z).
p1	Point3D	First control point (x, y, z).
p2	Point3D	Second control point (x, y, z).
p3	Point3D	End control point (x, y, z).
tolerance	float = 0.1	Linearization tolerance.
Returns	list[Point3D]

perp_dist_sq()

perp_dist_sq(pt: Point3D, origin: Point3D, vx: float, vy: float, vz: float = 0, norm_sq: float = 0) -> float

Compute the perpendicular distance squared.

Returns: Perpendicular distance squared.

Parameter	Type	Description
pt	Point3D	Point to measure from.
origin	Point3D	Origin of the line.
vx	float	X component of line direction.
vy	float	Y component of line direction.
vz	float = 0	Z component of line direction.
norm_sq	float = 0	Precomputed squared norm (optional).
Returns	float

split_bezier()

split_bezier(p0: Point, p1: Point, p2: Point, p3: Point, t: float) -> tuple[tuple[Point, Point, Point, Point], tuple[Point, Point, Point, Point]]

Split a cubic bezier at parameter t.

Returns: Two bezier curves (left, right).

Parameter	Type	Description
p0	Point	Start control point (x, y).
p1	Point	First control point (x, y).
p2	Point	Second control point (x, y).
p3	Point	End control point (x, y).
t	float	Split parameter (0..1).
Returns	tuple[tuple[Point, Point, Point, Point], tuple[Point, Point, Point, Point]]