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Update line intersection

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*Change line<>line intersection to be ray<>line.
*Update tests accordingly
*Clean up and simplify intersection logic
This commit is contained in:
Brandon Waskiewicz 2014-05-29 21:42:04 -04:00
parent 4a45bf3b53
commit 814b845de7
2 changed files with 71 additions and 101 deletions
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87
src/line.rs
View file

@ -17,9 +17,10 @@
use std::num::{Zero, zero, One, one};
use num::{BaseFloat, BaseNum};
use num::{BaseNum, BaseFloat};
use point::{Point, Point2, Point3};
use vector::{Vector, Vector2};
use ray::{Ray2};
use intersect::Intersect;
/// A generic directed line segment from `origin` to `dest`.
@ -38,71 +39,51 @@ impl<S: BaseNum, V: Vector<S>, P: Point<S, V>> Line<P> {
pub type Line2<S> = Line<Point2<S>>;
pub type Line3<S> = Line<Point3<S>>;
/// Determines if an intersection between two line segments is found. If the segments are
/// collinear and overlapping, the intersection point that will be returned will be the first
/// intersection point found by traversing the first line segment, starting at its origin.
impl<S: BaseFloat> Intersect<Option<Point2<S>>> for (Line2<S>, Line2<S>) {
/// Determines if an intersection between a ray and a line segments is found.
impl<S: BaseFloat> Intersect<Option<Point2<S>>> for (Ray2<S>, Line2<S>) {
fn intersection(&self) -> Option<Point2<S>> {
match *self {
(ref l1, ref l2) => {
let p = l1.origin;
let mut q = l2.origin;
let r = Vector2::new(l1.dest.x - l1.origin.x, l1.dest.y - l1.origin.y);
let mut s = Vector2::new(l2.dest.x - l2.origin.x, l2.dest.y - l2.origin.y);
(ref ray, ref line) => {
let p = ray.origin;
let q = line.origin;
let r = ray.direction;
let s = Vector2::new(line.dest.x - line.origin.x, line.dest.y - line.origin.y);
let zero: S = Zero::zero();
let cross = r.perp_dot(&s);
let mut q_minus_p = Vector2::new(q.x - p.x, q.y - p.y);
let mut p_minus_q = Vector2::new(p.x - q.x, p.y - q.y);
let cross_r = q_minus_p.perp_dot(&r);
let cross_s = q_minus_p.perp_dot(&s);
let cross_1 = r.perp_dot(&s);
let qmp = Vector2::new(q.x - p.x, q.y - p.y);
let cross_2 = qmp.perp_dot(&r);
if cross.is_zero() {
if cross_r.is_zero() {
// line segments are collinear
if cross_1 == zero {
if cross_2 != zero {
// parallel
return None;
}
// special case of both lines being the same single point
if r.x == zero && r.y == zero && s.x == zero && s.y == zero && p == q {
return Some(p);
// collinear
let q2mp = Vector2::new(line.dest.x - p.x, line.dest.y - p.y);
let dot_1 = qmp.dot(&r);
let dot_2 = q2mp.dot(&r);
if (dot_1 <= zero && dot_2 >= zero) || (dot_1 >= zero && dot_2 <= zero) {
return Some(p);
}
else if dot_1 >= zero && dot_2 >= zero {
if dot_1 <= dot_2 {
return Some(q);
}
// ensure l2 (q,q+s) is pointing the same direction as l1 (p,p+r)
// if it is not, then swap the two endpoints of the second segment.
// If this is not done, the algorithm below will not find an
// intersection if the two directed line segments point towards the
// opposite segment's origin.
if (r.x != zero && s.x != zero && r.x.signum() != s.x.signum()) ||
(r.y != zero && s.y != zero && r.y.signum() != s.y.signum()) {
q = Point2::new(q.x + s.x, q.y + s.y);
s = Vector2::new(-s.x, -s.y);
q_minus_p = Vector2::new(q.x - p.x, q.y - p.y);
p_minus_q = Vector2::new(p.x - q.x, p.y - q.y);
}
let d1 = q_minus_p.dot(&r);
let d2 = p_minus_q.dot(&s);
let rdotr = r.dot(&r);
let sdots = s.dot(&s);
// make sure to take into account that one or both of the segments could
// be a single point (r.r or s.s = 0) and ignore that case
if (rdotr > zero && zero <= d1 && d1 <= rdotr) ||
(sdots > zero && zero <= d2 && d2 <= sdots) {
// overlapping
if (q_minus_p.x != zero && q_minus_p.x.signum() == r.x.signum()) ||
(q_minus_p.y != zero && q_minus_p.y.signum() == r.y.signum()) {
return Some(q);
}
return Some(p);
else {
return Some(line.dest);
}
}
// no overlap exists
return None;
}
let t = cross_s / cross;
let u = cross_r / cross;
let t = qmp.perp_dot(&s) / cross_1;
let u = cross_2 / cross_1;
if zero <= t && t <= One::one() &&
zero <= One::one() && u <= One::one() {
if zero <= t && u >= zero && u <= One::one() {
return Some(Point2::new(p.x + t*r.x, p.y + t*r.y));
}

85
tests/line.rs
View file

@ -19,65 +19,54 @@ extern crate cgmath;
use cgmath::line::*;
use cgmath::point::*;
use cgmath::ray::*;
use cgmath::vector::*;
use cgmath::intersect::Intersect;
#[test]
fn test_line_intersection() {
// collinear, origins pointing towards each other, first intersection
// from l1.origin is in an endpoint in l2
let l1 = Line::new(Point2::new(0.0f64, 0.0f64), Point2::new(10.0f64, 0.0f64));
let l2 = Line::new(Point2::new(1.5f64, 0.0f64), Point2::new(0.5f64, 0.0f64));
assert_eq!((l1, l2).intersection(), Some(Point2::new(0.5f64, 0.0f64)));
// collinear, intersection is line dest
let r1 = Ray::new(Point2::new(0.0f32, 0.0), Vector2::new(0.25, 0.0));
let l1 = Line::new(Point2::new(1.5f32, 0.0), Point2::new(0.5, 0.0));
assert_eq!((r1, l1).intersection(), Some(Point2::new(0.5, 0.0)));
// collinear, first intersection from p1.origin is at p1.origin itself
let l3 = Line::new(Point2::new(0.0f64, 0.0f64), Point2::new(10.0f64, 0.0f64));
let l4 = Line::new(Point2::new(-11.0f64, 0.0f64), Point2::new(1.0f64, 0.0f64));
assert_eq!((l3, l4).intersection(), Some(Point2::new(0.0f64, 0.0f64)));
// collinear, intersection is at ray origin
let r2 = Ray::new(Point2::new(0.0f32, 0.0), Vector2::new(5.0, 0.0));
let l2 = Line::new(Point2::new(-11.0f32, 0.0), Point2::new(1.0, 0.0));
assert_eq!((r2, l2).intersection(), Some(Point2::new(0.0, 0.0)));
// no intersection
let l5 = Line::new(Point2::new(5.0f64, 5.0f64), Point2::new(10.0f64, 6.0f64));
let l6 = Line::new(Point2::new(5.0f64, 4.8f64), Point2::new(10.0f64, 4.1f64));
assert_eq!((l5, l6).intersection(), None); // no intersection
// collinear, origins pointing same direction
let l7 = Line::new(Point2::new(0.0f64, 1.0f64), Point2::new(0.0f64, 0.0f64));
let l8 = Line::new(Point2::new(0.0f64, 0.5f64), Point2::new(0.0f64, -0.5f64));
assert_eq!((l7, l8).intersection(), Some(Point2::new(0.0f64, 0.5f64)));
// collinear, intersection is line origin
let r3 = Ray::new(Point2::new(0.0f32, 1.0), Vector2::new(0.0, -0.25));
let l3 = Line::new(Point2::new(0.0f32, 0.5), Point2::new(0.0, -0.5));
assert_eq!((r3, l3).intersection(), Some(Point2::new(0.0, 0.5)));
// collinear, no overlap
let l9 = Line::new(Point2::new(0.0f64, 0.0f64), Point2::new(3.0f64, 0.0f64));
let l10 = Line::new(Point2::new(10.0f64, 0.0f64), Point2::new(5.0f64, 0.0f64));
assert_eq!((l9, l10).intersection(), None);
let r4 = Ray::new(Point2::new(0.0f32, 0.0), Vector2::new(3.0, 0.0));
let l4 = Line::new(Point2::new(-10.0f32, 0.0), Point2::new(-5.0, 0.0));
assert_eq!((r4, l4).intersection(), None);
// intersection found
let l11 = Line::new(Point2::new(0.0f64, 0.0f64), Point2::new(10.0f64, 10.0f64));
let l12 = Line::new(Point2::new(0.0f64, 10.0f64), Point2::new(10.0f64, 0.0f64));
assert_eq!((l11, l12).intersection(), Some(Point2::new(5.0f64, 5.0f64)));
// no intersection
let r5 = Ray::new(Point2::new(5.0f32, 5.0), Vector2::new(40.0, 8.0));
let l5 = Line::new(Point2::new(5.0f32, 4.8), Point2::new(10.0, 4.1));
assert_eq!((r5, l5).intersection(), None); // no intersection
// special case of both lines being the same point
let l13 = Line::new(Point2::new(0.0f64, 0.0f64), Point2::new(0.0f64, 0.0f64));
let l14 = Line::new(Point2::new(0.0f64, 0.0f64), Point2::new(0.0f64, 0.0f64));
assert_eq!((l13, l14).intersection(), Some(Point2::new(0.0f64, 0.0f64)));
// non-collinear intersection
let r6 = Ray::new(Point2::new(0.0f32, 0.0), Vector2::new(10.0, 10.0));
let l6 = Line::new(Point2::new(0.0f32, 10.0), Point2::new(10.0, 0.0));
assert_eq!((r6, l6).intersection(), Some(Point2::new(5.0, 5.0)));
// both lines are points that are distinct
let l15 = Line::new(Point2::new(0.0f64, 0.0f64), Point2::new(0.0f64, 0.0f64));
let l16 = Line::new(Point2::new(1.0f64, 0.0f64), Point2::new(1.0f64, 0.0f64));
assert_eq!((l15, l16).intersection(), None);
// line is a point that does not intersect
let r7 = Ray::new(Point2::new(0.0f32, 0.0), Vector2::new(1.0, 1.0));
let l7 = Line::new(Point2::new(1.0f32, 0.0), Point2::new(1.0, 0.0));
assert_eq!((r7, l7).intersection(), None);
// one line is a point that intersects the other segment
let l15 = Line::new(Point2::new(0.0f64, 0.0f64), Point2::new(10.0f64, 0.0f64));
let l16 = Line::new(Point2::new(3.0f64, 0.0f64), Point2::new(3.0f64, 0.0f64));
assert_eq!((l15, l16).intersection(), Some(Point2::new(3.0f64, 0.0f64)));
// line is a point that does intersect
let r8 = Ray::new(Point2::new(0.0f32, 0.0), Vector2::new(1.0, 0.0));
let l8 = Line::new(Point2::new(3.0f32, 0.0), Point2::new(3.0, 0.0));
assert_eq!((r8, l8).intersection(), Some(Point2::new(3.0, 0.0)));
// one line is a point that is collinear but does not intersect with
// the other line
let l17 = Line::new(Point2::new(0.0f64, 0.0f64), Point2::new(0.0f64, 0.0f64));
let l18 = Line::new(Point2::new(1.0f64, 0.0f64), Point2::new(3.0f64, 0.0f64));
assert_eq!((l17, l18).intersection(), None);
// one line is a point that is not collinear but does not intersect
// with the other line
let l19 = Line::new(Point2::new(0.0f64, 0.0f64), Point2::new(0.0f64, 0.0f64));
let l20 = Line::new(Point2::new(1.0f64, 0.0f64), Point2::new(2.0f64, 10.0f64));
assert_eq!((l19, l20).intersection(), None);
// line is a collinear point but no intersection
let r9 = Ray::new(Point2::new(0.0f32, 0.0), Vector2::new(1.0, 0.0));
let l9 = Line::new(Point2::new(-1.0f32, 0.0), Point2::new(-1.0, 0.0));
assert_eq!((r9, l9).intersection(), None);
}