Function cavalier_contours::core::math::line_line_intr

pub fn line_line_intr<T>(
    v1: Vector2<T>,
    v2: Vector2<T>,
    u1: Vector2<T>,
    u2: Vector2<T>,
    epsilon: T
) -> LineLineIntr<T>where
    T: Real,

Finds the intersects between two lines segments.

This function returns the parametric solution(s) using the general line segment equation P(t) = p0 + t * (p1 - p0). Where t then goes from 0 to 1. For t < 0 or t > 1 the result is on the same line but not within the line segment.

epsilon is used for fuzzy float comparisons.

Explanation on result cases LineLineIntr

NoIntersect

Either of the following cases:

• Lines are (or almost, using epsilon to determine) parallel
• Both line segments are points and distinct from each other
• One line segment is a point and distinct from the other line segment

TrueIntersect

Either of the following cases:

• Line segments are not parallel and intersect at one point
• Both line segments are points and lie over each other (using epsilon for position compare)
• One line segment is a point and lies in other line segment (again using epsilon)

FalseIntersect

Either of the following cases:

• Line segments are not parallel and at least one must be extended to intersect (that is for 0 <= t <= 1 for both segments there is no intersect)

Overlapping

Either of the following cases:

• The lines are collinear and overlap, the segments may fully, partially or not overlap at all (determined by parametric t values returned)

Examples

// A line segment tangent-intersecting a circle with one of the line segments end points.
let v1 = Vector2::new(0.0, 0.0);
let v2 = Vector2::new(1.0, 0.0);
let u1 = Vector2::new(0.5, -1.0);
let u2 = Vector2::new(0.5, 1.0);
if let LineLineIntr::TrueIntersect {
    seg1_t: t1,
    seg2_t: t2,
} = line_line_intr(v1, v2, u1, u2, 1e-5)
{
    assert_eq!(t1, 0.5);
    assert_eq!(t2, 0.5);
} else {
    unreachable!("expected true intersection between line segments");
}

Line segments are defined by v1->v2 and u1->u2. Handles the cases where the lines may be parallel, collinear, or single points.