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use crate::{Coord, GeoFloat, Line};
use geo_types::coord;
use crate::BoundingRect;
use crate::Intersects;
#[derive(PartialEq, Eq, Clone, Copy, Debug)]
pub enum LineIntersection<F: GeoFloat> {
/// Lines intersect in a single point
SinglePoint {
intersection: Coord<F>,
/// For Lines which intersect in a single point, that point may be either an endpoint
/// or in the interior of each Line.
/// If the point lies in the interior of both Lines, we call it a _proper_ intersection.
///
/// # Note
///
/// Due to the limited precision of most float data-types, the
/// calculated intersection point may be snapped to one of the
/// end-points even though all the end-points of the two
/// lines are distinct points. In such cases, this field is
/// still set to `true`. Please refer test_case:
/// `test_central_endpoint_heuristic_failure_1` for such an
/// example.
is_proper: bool,
},
/// Overlapping Lines intersect in a line segment
Collinear { intersection: Line<F> },
}
impl<F: GeoFloat> LineIntersection<F> {
pub fn is_proper(&self) -> bool {
match self {
Self::Collinear { .. } => false,
Self::SinglePoint { is_proper, .. } => *is_proper,
}
}
}
/// Returns the intersection between two [`Lines`](Line).
///
/// Lines can intersect in a Point or, for Collinear lines, in a Line. See [`LineIntersection`]
/// for more details about the result.
///
/// # Examples
///
/// ```
/// use geo_types::coord;
/// use geo::{Line, Coord};
/// use geo::line_intersection::{line_intersection, LineIntersection};
///
/// let line_1 = Line::new(coord! {x: 0.0, y: 0.0}, coord! { x: 5.0, y: 5.0 } );
/// let line_2 = Line::new(coord! {x: 0.0, y: 5.0}, coord! { x: 5.0, y: 0.0 } );
/// let expected = LineIntersection::SinglePoint { intersection: coord! { x: 2.5, y: 2.5 }, is_proper: true };
/// assert_eq!(line_intersection(line_1, line_2), Some(expected));
///
/// let line_1 = Line::new(coord! {x: 0.0, y: 0.0}, coord! { x: 5.0, y: 5.0 } );
/// let line_2 = Line::new(coord! {x: 0.0, y: 1.0}, coord! { x: 5.0, y: 6.0 } );
/// assert_eq!(line_intersection(line_1, line_2), None);
///
/// let line_1 = Line::new(coord! {x: 0.0, y: 0.0}, coord! { x: 5.0, y: 5.0 } );
/// let line_2 = Line::new(coord! {x: 5.0, y: 5.0}, coord! { x: 5.0, y: 0.0 } );
/// let expected = LineIntersection::SinglePoint { intersection: coord! { x: 5.0, y: 5.0 }, is_proper: false };
/// assert_eq!(line_intersection(line_1, line_2), Some(expected));
///
/// let line_1 = Line::new(coord! {x: 0.0, y: 0.0}, coord! { x: 5.0, y: 5.0 } );
/// let line_2 = Line::new(coord! {x: 3.0, y: 3.0}, coord! { x: 6.0, y: 6.0 } );
/// let expected = LineIntersection::Collinear { intersection: Line::new(coord! { x: 3.0, y: 3.0 }, coord! { x: 5.0, y: 5.0 })};
/// assert_eq!(line_intersection(line_1, line_2), Some(expected));
/// ```
/// Strongly inspired by, and meant to produce the same results as, [JTS's RobustLineIntersector](https://github.com/locationtech/jts/blob/master/modules/core/src/main/java/org/locationtech/jts/algorithm/RobustLineIntersector.java#L26).
pub fn line_intersection<F>(p: Line<F>, q: Line<F>) -> Option<LineIntersection<F>>
where
F: GeoFloat,
{
if !p.bounding_rect().intersects(&q.bounding_rect()) {
return None;
}
use crate::kernels::{Kernel, Orientation::*, RobustKernel};
let p_q1 = RobustKernel::orient2d(p.start, p.end, q.start);
let p_q2 = RobustKernel::orient2d(p.start, p.end, q.end);
if matches!(
(p_q1, p_q2),
(Clockwise, Clockwise) | (CounterClockwise, CounterClockwise)
) {
return None;
}
let q_p1 = RobustKernel::orient2d(q.start, q.end, p.start);
let q_p2 = RobustKernel::orient2d(q.start, q.end, p.end);
if matches!(
(q_p1, q_p2),
(Clockwise, Clockwise) | (CounterClockwise, CounterClockwise)
) {
return None;
}
if matches!(
(p_q1, p_q2, q_p1, q_p2),
(Collinear, Collinear, Collinear, Collinear)
) {
return collinear_intersection(p, q);
}
// At this point we know that there is a single intersection point (since the lines are not
// collinear).
//
// Check if the intersection is an endpoint. If it is, copy the endpoint as the
// intersection point. Copying the point rather than computing it ensures the point has the
// exact value, which is important for robustness. It is sufficient to simply check for an
// endpoint which is on the other line, since at this point we know that the inputLines
// must intersect.
if p_q1 == Collinear || p_q2 == Collinear || q_p1 == Collinear || q_p2 == Collinear {
// Check for two equal endpoints.
// This is done explicitly rather than by the orientation tests below in order to improve
// robustness.
//
// [An example where the orientation tests fail to be consistent is the following (where
// the true intersection is at the shared endpoint
// POINT (19.850257749638203 46.29709338043669)
//
// LINESTRING ( 19.850257749638203 46.29709338043669, 20.31970698357233 46.76654261437082 )
// and
// LINESTRING ( -48.51001596420236 -22.063180333403878, 19.850257749638203 46.29709338043669 )
//
// which used to produce the INCORRECT result: (20.31970698357233, 46.76654261437082, NaN)
let intersection: Coord<F>;
// false positives for this overzealous clippy https://github.com/rust-lang/rust-clippy/issues/6747
#[allow(clippy::suspicious_operation_groupings)]
if p.start == q.start || p.start == q.end {
intersection = p.start;
} else if p.end == q.start || p.end == q.end {
intersection = p.end;
// Now check to see if any endpoint lies on the interior of the other segment.
} else if p_q1 == Collinear {
intersection = q.start;
} else if p_q2 == Collinear {
intersection = q.end;
} else if q_p1 == Collinear {
intersection = p.start;
} else {
assert_eq!(q_p2, Collinear);
intersection = p.end;
}
Some(LineIntersection::SinglePoint {
intersection,
is_proper: false,
})
} else {
let intersection = proper_intersection(p, q);
Some(LineIntersection::SinglePoint {
intersection,
is_proper: true,
})
}
}
fn collinear_intersection<F: GeoFloat>(p: Line<F>, q: Line<F>) -> Option<LineIntersection<F>> {
fn collinear<F: GeoFloat>(intersection: Line<F>) -> LineIntersection<F> {
LineIntersection::Collinear { intersection }
}
fn improper<F: GeoFloat>(intersection: Coord<F>) -> LineIntersection<F> {
LineIntersection::SinglePoint {
intersection,
is_proper: false,
}
}
let p_bounds = p.bounding_rect();
let q_bounds = q.bounding_rect();
Some(
match (
p_bounds.intersects(&q.start),
p_bounds.intersects(&q.end),
q_bounds.intersects(&p.start),
q_bounds.intersects(&p.end),
) {
(true, true, _, _) => collinear(q),
(_, _, true, true) => collinear(p),
(true, false, true, false) if q.start == p.start => improper(q.start),
(true, _, true, _) => collinear(Line::new(q.start, p.start)),
(true, false, false, true) if q.start == p.end => improper(q.start),
(true, _, _, true) => collinear(Line::new(q.start, p.end)),
(false, true, true, false) if q.end == p.start => improper(q.end),
(_, true, true, _) => collinear(Line::new(q.end, p.start)),
(false, true, false, true) if q.end == p.end => improper(q.end),
(_, true, _, true) => collinear(Line::new(q.end, p.end)),
_ => return None,
},
)
}
/// Finds the endpoint of the segments P and Q which is closest to the other segment. This is
/// a reasonable surrogate for the true intersection points in ill-conditioned cases (e.g.
/// where two segments are nearly coincident, or where the endpoint of one segment lies almost
/// on the other segment).
///
/// This replaces the older CentralEndpoint heuristic, which chose the wrong endpoint in some
/// cases where the segments had very distinct slopes and one endpoint lay almost on the other
/// segment.
///
/// `returns` the nearest endpoint to the other segment
fn nearest_endpoint<F: GeoFloat>(p: Line<F>, q: Line<F>) -> Coord<F> {
use geo_types::private_utils::point_line_euclidean_distance;
let mut nearest_pt = p.start;
let mut min_dist = point_line_euclidean_distance(p.start, q);
let dist = point_line_euclidean_distance(p.end, q);
if dist < min_dist {
min_dist = dist;
nearest_pt = p.end;
}
let dist = point_line_euclidean_distance(q.start, p);
if dist < min_dist {
min_dist = dist;
nearest_pt = q.start;
}
let dist = point_line_euclidean_distance(q.end, p);
if dist < min_dist {
nearest_pt = q.end;
}
nearest_pt
}
fn raw_line_intersection<F: GeoFloat>(p: Line<F>, q: Line<F>) -> Option<Coord<F>> {
let p_min_x = p.start.x.min(p.end.x);
let p_min_y = p.start.y.min(p.end.y);
let p_max_x = p.start.x.max(p.end.x);
let p_max_y = p.start.y.max(p.end.y);
let q_min_x = q.start.x.min(q.end.x);
let q_min_y = q.start.y.min(q.end.y);
let q_max_x = q.start.x.max(q.end.x);
let q_max_y = q.start.y.max(q.end.y);
let int_min_x = p_min_x.max(q_min_x);
let int_max_x = p_max_x.min(q_max_x);
let int_min_y = p_min_y.max(q_min_y);
let int_max_y = p_max_y.min(q_max_y);
let two = F::one() + F::one();
let mid_x = (int_min_x + int_max_x) / two;
let mid_y = (int_min_y + int_max_y) / two;
// condition ordinate values by subtracting midpoint
let p1x = p.start.x - mid_x;
let p1y = p.start.y - mid_y;
let p2x = p.end.x - mid_x;
let p2y = p.end.y - mid_y;
let q1x = q.start.x - mid_x;
let q1y = q.start.y - mid_y;
let q2x = q.end.x - mid_x;
let q2y = q.end.y - mid_y;
// unrolled computation using homogeneous coordinates eqn
let px = p1y - p2y;
let py = p2x - p1x;
let pw = p1x * p2y - p2x * p1y;
let qx = q1y - q2y;
let qy = q2x - q1x;
let qw = q1x * q2y - q2x * q1y;
let xw = py * qw - qy * pw;
let yw = qx * pw - px * qw;
let w = px * qy - qx * py;
let x_int = xw / w;
let y_int = yw / w;
// check for parallel lines
if (x_int.is_nan() || x_int.is_infinite()) || (y_int.is_nan() || y_int.is_infinite()) {
None
} else {
// de-condition intersection point
Some(coord! {
x: x_int + mid_x,
y: y_int + mid_y,
})
}
}
/// This method computes the actual value of the intersection point.
/// To obtain the maximum precision from the intersection calculation,
/// the coordinates are normalized by subtracting the minimum
/// ordinate values (in absolute value). This has the effect of
/// removing common significant digits from the calculation to
/// maintain more bits of precision.
fn proper_intersection<F: GeoFloat>(p: Line<F>, q: Line<F>) -> Coord<F> {
// Computes a segment intersection using homogeneous coordinates.
// Round-off error can cause the raw computation to fail,
// (usually due to the segments being approximately parallel).
// If this happens, a reasonable approximation is computed instead.
let mut int_pt = raw_line_intersection(p, q).unwrap_or_else(|| nearest_endpoint(p, q));
// NOTE: At this point, JTS does a `Envelope::contains(coord)` check, but confusingly,
// Envelope::contains(coord) in JTS is actually an *intersection* check, not a true SFS
// `contains`, because it includes the boundary of the rect.
if !(p.bounding_rect().intersects(&int_pt) && q.bounding_rect().intersects(&int_pt)) {
// compute a safer result
// copy the coordinate, since it may be rounded later
int_pt = nearest_endpoint(p, q);
}
int_pt
}
#[cfg(test)]
mod test {
use super::*;
use geo_types::coord;
/// Based on JTS test `testCentralEndpointHeuristicFailure`
/// > Following cases were failures when using the CentralEndpointIntersector heuristic.
/// > This is because one segment lies at a significant angle to the other,
/// > with only one endpoint is close to the other segment.
/// > The CE heuristic chose the wrong endpoint to return.
/// > The fix is to use a new heuristic which out of the 4 endpoints
/// > chooses the one which is closest to the other segment.
/// > This works in all known failure cases.
#[test]
fn test_central_endpoint_heuristic_failure_1() {
let line_1 = Line::new(
coord! {
x: 163.81867067,
y: -211.31840378,
},
coord! {
x: 165.9174252,
y: -214.1665075,
},
);
let line_2 = Line::new(
coord! {
x: 2.84139601,
y: -57.95412726,
},
coord! {
x: 469.59990601,
y: -502.63851732,
},
);
let actual = line_intersection(line_1, line_2);
let expected = LineIntersection::SinglePoint {
intersection: coord! {
x: 163.81867067,
y: -211.31840378,
},
is_proper: true,
};
assert_eq!(actual, Some(expected));
}
/// Based on JTS test `testCentralEndpointHeuristicFailure2`
/// > Test from Tomas Fa - JTS list 6/13/2012
/// >
/// > Fails using original JTS DeVillers determine orientation test.
/// > Succeeds using DD and Shewchuk orientation
#[test]
fn test_central_endpoint_heuristic_failure_2() {
let line_1 = Line::new(
coord! {
x: -58.00593335955,
y: -1.43739086465,
},
coord! {
x: -513.86101637525,
y: -457.29247388035,
},
);
let line_2 = Line::new(
coord! {
x: -215.22279674875,
y: -158.65425425385,
},
coord! {
x: -218.1208801283,
y: -160.68343590235,
},
);
let actual = line_intersection(line_1, line_2);
let expected = LineIntersection::SinglePoint {
intersection: coord! {
x: -215.22279674875,
y: -158.65425425385,
},
is_proper: true,
};
assert_eq!(actual, Some(expected));
}
/// Based on JTS test `testTomasFa_1`
/// > Test from Tomas Fa - JTS list 6/13/2012
/// >
/// > Fails using original JTS DeVillers determine orientation test.
/// > Succeeds using DD and Shewchuk orientation
#[test]
fn test_tomas_fa_1() {
let line_1 = Line::new(coord! { x: -42.0, y: 163.2 }, coord! { x: 21.2, y: 265.2 });
let line_2 = Line::new(coord! { x: -26.2, y: 188.7 }, coord! { x: 37.0, y: 290.7 });
let actual = line_intersection(line_1, line_2);
let expected = None;
assert_eq!(actual, expected);
}
/// Based on JTS test `testTomasFa_2`
///
/// > Test from Tomas Fa - JTS list 6/13/2012
/// >
/// > Fails using original JTS DeVillers determine orientation test.
#[test]
fn test_tomas_fa_2() {
let line_1 = Line::new(coord! { x: -5.9, y: 163.1 }, coord! { x: 76.1, y: 250.7 });
let line_2 = Line::new(coord! { x: 14.6, y: 185.0 }, coord! { x: 96.6, y: 272.6 });
let actual = line_intersection(line_1, line_2);
let expected = None;
assert_eq!(actual, expected);
}
/// Based on JTS test `testLeduc_1`
///
/// > Test involving two non-almost-parallel lines.
/// > Does not seem to cause problems with basic line intersection algorithm.
#[test]
fn test_leduc_1() {
let line_1 = Line::new(
coord! {
x: 305690.0434123494,
y: 254176.46578338774,
},
coord! {
x: 305601.9999843455,
y: 254243.19999846347,
},
);
let line_2 = Line::new(
coord! {
x: 305689.6153764265,
y: 254177.33102743194,
},
coord! {
x: 305692.4999844298,
y: 254171.4999983967,
},
);
let actual = line_intersection(line_1, line_2);
let expected = LineIntersection::SinglePoint {
intersection: coord! {
x: 305690.0434123494,
y: 254176.46578338774,
},
is_proper: true,
};
assert_eq!(actual, Some(expected));
}
/// Based on JTS test `testGEOS_1()`
///
/// > Test from strk which is bad in GEOS (2009-04-14).
#[test]
fn test_geos_1() {
let line_1 = Line::new(
coord! {
x: 588750.7429703881,
y: 4518950.493668233,
},
coord! {
x: 588748.2060409798,
y: 4518933.9452804085,
},
);
let line_2 = Line::new(
coord! {
x: 588745.824857241,
y: 4518940.742239175,
},
coord! {
x: 588748.2060437313,
y: 4518933.9452791475,
},
);
let actual = line_intersection(line_1, line_2);
let expected = LineIntersection::SinglePoint {
intersection: coord! {
x: 588748.2060416829,
y: 4518933.945284994,
},
is_proper: true,
};
assert_eq!(actual, Some(expected));
}
/// Based on JTS test `testGEOS_2()`
///
/// > Test from strk which is bad in GEOS (2009-04-14).
#[test]
fn test_geos_2() {
let line_1 = Line::new(
coord! {
x: 588743.626135934,
y: 4518924.610969561,
},
coord! {
x: 588732.2822865889,
y: 4518925.4314047815,
},
);
let line_2 = Line::new(
coord! {
x: 588739.1191384895,
y: 4518927.235700594,
},
coord! {
x: 588731.7854614238,
y: 4518924.578370095,
},
);
let actual = line_intersection(line_1, line_2);
let expected = LineIntersection::SinglePoint {
intersection: coord! {
x: 588733.8306132929,
y: 4518925.319423238,
},
is_proper: true,
};
assert_eq!(actual, Some(expected));
}
/// Based on JTS test `testDaveSkeaCase()`
///
/// > This used to be a failure case (exception), but apparently works now.
/// > Possibly normalization has fixed this?
#[test]
fn test_dave_skea_case() {
let line_1 = Line::new(
coord! {
x: 2089426.5233462777,
y: 1180182.387733969,
},
coord! {
x: 2085646.6891757075,
y: 1195618.7333999649,
},
);
let line_2 = Line::new(
coord! {
x: 1889281.8148903656,
y: 1997547.0560044837,
},
coord! {
x: 2259977.3672236,
y: 483675.17050843034,
},
);
let actual = line_intersection(line_1, line_2);
let expected = LineIntersection::SinglePoint {
intersection: coord! {
x: 2087536.6062609926,
y: 1187900.560566967,
},
is_proper: true,
};
assert_eq!(actual, Some(expected));
}
/// Based on JTS test `testCmp5CaseWKT()`
///
/// > Outside envelope using HCoordinate method.
#[test]
fn test_cmp_5_cask_wkt() {
let line_1 = Line::new(
coord! {
x: 4348433.262114629,
y: 5552595.478385733,
},
coord! {
x: 4348440.849387404,
y: 5552599.272022122,
},
);
let line_2 = Line::new(
coord! {
x: 4348433.26211463,
y: 5552595.47838573,
},
coord! {
x: 4348440.8493874,
y: 5552599.27202212,
},
);
let actual = line_intersection(line_1, line_2);
let expected = LineIntersection::SinglePoint {
intersection: coord! {
x: 4348440.8493874,
y: 5552599.27202212,
},
is_proper: true,
};
assert_eq!(actual, Some(expected));
}
}