raygeo.geo.algo.engagement

Engagement angle, area, and chord depth as a function of signed distance from the cleared boundary. Circle-boundary overlap (engagement) metrics.

Functions

angular_engagement()

angular_engagement(
    center: tuple[float, float],
    radius: float,
    fragments: list[list[tuple[float, float]]],
) -> float

Angular engagement (exact circle–polygon intersection).

Returns uncleared angular extent in [0, 2π].

Parameter	Type	Description
center	tuple[float, float]	Disk centre (x, y).
radius	float	Disk radius (mm).
fragments	list[list[tuple[float, float]]]	List of polygons (cleared fragments).
Returns	float	Angular engagement in radians.

Comparison of exact polygon-intersection angular engagement with the analytical signed-distance estimate along a scan line crossing the boundary.

compute_engagement()

compute_engagement(
    d_to_boundary: float,
    radius: float,
) -> tuple[float, float, float]

Compute engagement angle, area, and chord depth.

Parameter	Type	Description
d_to_boundary	float	Signed distance from the point to the nearest boundary (mm). Positive = outside the boundary.
radius	float	Disk radius (mm).
Returns	tuple[float, float, float]	(angle_rad, area, chord_depth).

Circle at three signed distances from the boundary. Shaded red arc is the contact arc (engagement).

Engagement heatmap around a circular cleared area. Green = low, red = high engagement.

disk_segment_area()

disk_segment_area(x: float, r: float) -> float

Area under 2*sqrt(r²-x²) from x to r.

Equivalent to the area of the circular segment to the right of the vertical line at x for a disk of radius r centred at the origin.

Parameter	Type	Description
x	float	Left boundary of the segment.
r	float	Disk radius.
Returns	float	Area of the circular segment.

Left: a disk of radius 5 mm with the circular segment to the right of the vertical line x = 1.5 shaded. Right: the segment area as a function of x, from -r to +r.

point_engagement()

point_engagement(
    center: tuple[float, float],
    radius: float,
    fragments: list[list[tuple[float, float]]],
) -> tuple[float, float, float]

Engagement angle, area, and chord depth at a disk centre.

Parameter	Type	Description
center	tuple[float, float]	Disk centre (x, y).
radius	float	Disk radius (mm).
fragments	list[list[tuple[float, float]]]	List of polygons (cleared fragments).
Returns	tuple[float, float, float]	(angle_rad, area, chord_depth).

Engagement angle field around a square cleared area for a disk of radius 3 mm.