def test_line_intersection():
assert asa(120, 8, 52) == Triangle(
Point(0, 0),
Point(8, 0),
Point(-4 * cos(19 * pi / 90) / sin(2 * pi / 45), 4 * sqrt(3) * cos(19 * pi / 90) / sin(2 * pi / 45)),
)
assert Line((0, 0), (1, 1)).intersection(Ray((1, 0), (1, 2))) == [Point(1, 1)]
assert Line((0, 0), (1, 1)).intersection(Segment((1, 0), (1, 2))) == [Point(1, 1)]
assert Ray((0, 0), (1, 1)).intersection(Ray((1, 0), (1, 2))) == [Point(1, 1)]
assert Ray((0, 0), (1, 1)).intersection(Segment((1, 0), (1, 2))) == [Point(1, 1)]
assert Ray((0, 0), (10, 10)).contains(Segment((1, 1), (2, 2))) is True
assert Segment((1, 1), (2, 2)) in Line((0, 0), (10, 10))
x = 8 * tan(13 * pi / 45) / (tan(13 * pi / 45) + sqrt(3))
y = (-8 * sqrt(3) * tan(13 * pi / 45) ** 2 + 24 * tan(13 * pi / 45)) / (-3 + tan(13 * pi / 45) ** 2)
assert Line(Point(0, 0), Point(1, -sqrt(3))).contains(Point(x, y)) is True
def test_line_intersection():
assert asa(120, 8, 52) == \
Triangle(
Point(0, 0),
Point(8, 0),
Point(-4 * cos(19 * pi / 90) / sin(2 * pi / 45),
4 * sqrt(3) * cos(19 * pi / 90) / sin(2 * pi / 45)))
assert Line((0, 0), (1, 1)).intersection(Ray((1, 0), (1, 2))) == [Point(1, 1)]
assert Line((0, 0), (1, 1)).intersection(Segment((1, 0), (1, 2))) == [Point(1, 1)]
assert Ray((0, 0), (1, 1)).intersection(Ray((1, 0), (1, 2))) == [Point(1, 1)]
assert Ray((0, 0), (1, 1)).intersection(Segment((1, 0), (1, 2))) == [Point(1, 1)]
assert Ray((0, 0), (10, 10)).contains(Segment((1, 1), (2, 2))) is True
assert Segment((1, 1), (2, 2)) in Line((0, 0), (10, 10))
x = 8 * tan(13 * pi / 45) / (tan(13 * pi / 45) + sqrt(3))
y = (-8 * sqrt(3) * tan(13 * pi / 45) ** 2 + 24 * tan(13 * pi / 45)) / (-3 + tan(13 * pi / 45) ** 2)
assert Line(Point(0, 0), Point(1, -sqrt(3))).contains(Point(x, y)) is True
def test_line_intersection():
assert asa(120, 8, 52) == \
Triangle(
Point(0, 0),
Point(8, 0),
Point((8*tan(13*pi/45)**2 + 8*sqrt(3)*tan(13*pi/45))/
(-3 + tan(13*pi/45)**2),
(-24*tan(13*pi/45) - 8*sqrt(3)*tan(13*pi/45)**2)/
(-3 + tan(13*pi/45)**2)))
assert Line((0, 0), (1, 1)).intersection(Ray((1, 0), (1, 2))) == \
[Point(1, 1)]
assert Line((0, 0), (1, 1)).intersection(Segment((1, 0), (1, 2))) == \
[Point(1, 1)]
assert Ray((0, 0), (1, 1)).intersection(Ray((1, 0), (1, 2))) == \
[Point(1, 1)]
assert Ray((0, 0), (1, 1)).intersection(Segment((1, 0), (1, 2))) == \
[Point(1, 1)]
assert Ray((0, 0), (10, 10)).contains(Segment((1, 1), (2, 2))) is True
assert Segment((1, 1), (2, 2)) in Line((0, 0), (10, 10))
x = 8*tan(13*pi/45)/(tan(13*pi/45) + sqrt(3))
y = (-8*sqrt(3)*tan(13*pi/45)**2 + 24*tan(13*pi/45))/ \
(-3 + tan(13*pi/45)**2)
assert Line(Point(0, 0), Point(1, -sqrt(3))).contains(Point(x, y)) is True
def test_intersection_2d():
p1 = Point(0, 0)
p2 = Point(1, 1)
p3 = Point(x1, x1)
p4 = Point(y1, y1)
l1 = Line(p1, p2)
l3 = Line(Point(0, 0), Point(3, 4))
r1 = Ray(Point(1, 1), Point(2, 2))
r2 = Ray(Point(0, 0), Point(3, 4))
r4 = Ray(p1, p2)
r6 = Ray(Point(0, 1), Point(1, 2))
r7 = Ray(Point(0.5, 0.5), Point(1, 1))
s1 = Segment(p1, p2)
s2 = Segment(Point(0.25, 0.25), Point(0.5, 0.5))
s3 = Segment(Point(0, 0), Point(3, 4))
assert intersection(l1, p1) == [p1]
assert intersection(l1, Point(x1, 1 + x1)) == []
assert intersection(l1, Line(p3, p4)) in [[l1], [Line(p3, p4)]]
assert intersection(l1, l1.parallel_line(Point(x1, 1 + x1))) == []
assert intersection(l3, l3) == [l3]
assert intersection(l3, r2) == [r2]
assert intersection(l3, s3) == [s3]
assert intersection(s3, l3) == [s3]
assert (intersection(Segment(Point(-10, 10), Point(10, 10)),
Segment(Point(-5, -5), Point(-5, 5))) == [])
assert intersection(r2, l3) == [r2]
assert intersection(r1,
Ray(Point(2, 2),
Point(0,
0))) == [Segment(Point(1, 1), Point(2, 2))]
assert intersection(r1, Ray(Point(1, 1), Point(-1, -1))) == [Point(1, 1)]
assert intersection(r1, Segment(Point(0, 0), Point(
2, 2))) == [Segment(Point(1, 1), Point(2, 2))]
assert r4.intersection(s2) == [s2]
assert r4.intersection(Segment(Point(2, 3), Point(3, 4))) == []
assert r4.intersection(Segment(Point(-1, -1), Point(
0.5, 0.5))) == [Segment(p1, Point(0.5, 0.5))]
assert r4.intersection(Ray(p2, p1)) == [s1]
assert Ray(p2, p1).intersection(r6) == []
assert r4.intersection(r7) == r7.intersection(r4) == [r7]
assert Ray3D((0, 0), (3, 0)).intersection(Ray3D(
(1, 0), (3, 0))) == [Ray3D((1, 0), (3, 0))]
assert Ray3D((1, 0), (3, 0)).intersection(Ray3D(
(0, 0), (3, 0))) == [Ray3D((1, 0), (3, 0))]
assert Ray(Point(0, 0), Point(0, 4)).intersection(
Ray(Point(0, 1), Point(0, -1))) == [Segment(Point(0, 0), Point(0, 1))]
assert Segment3D((0, 0), (3, 0)).intersection(Segment3D(
(1, 0), (2, 0))) == [Segment3D((1, 0), (2, 0))]
assert Segment3D((1, 0), (2, 0)).intersection(Segment3D(
(0, 0), (3, 0))) == [Segment3D((1, 0), (2, 0))]
assert Segment3D((0, 0), (3, 0)).intersection(Segment3D(
(3, 0), (4, 0))) == [Point3D((3, 0))]
assert Segment3D((0, 0), (3, 0)).intersection(Segment3D(
(2, 0), (5, 0))) == [Segment3D((2, 0), (3, 0))]
assert Segment3D((0, 0), (3, 0)).intersection(Segment3D(
(-2, 0), (1, 0))) == [Segment3D((0, 0), (1, 0))]
assert Segment3D((0, 0), (3, 0)).intersection(Segment3D(
(-2, 0), (0, 0))) == [Point3D(0, 0)]
assert s1.intersection(Segment(Point(1, 1), Point(2, 2))) == [Point(1, 1)]
assert s1.intersection(Segment(Point(0.5, 0.5), Point(
1.5, 1.5))) == [Segment(Point(0.5, 0.5), p2)]
assert s1.intersection(Segment(Point(4, 4), Point(5, 5))) == []
assert s1.intersection(Segment(Point(-1, -1), p1)) == [p1]
assert s1.intersection(Segment(Point(-1, -1), Point(
0.5, 0.5))) == [Segment(p1, Point(0.5, 0.5))]
assert s1.intersection(Line(Point(1, 0), Point(2, 1))) == []
assert s1.intersection(s2) == [s2]
assert s2.intersection(s1) == [s2]
assert asa(120, 8, 52) == Triangle(
Point(0, 0),
Point(8, 0),
Point(
-4 * cos(19 * pi / 90) / sin(2 * pi / 45),
4 * sqrt(3) * cos(19 * pi / 90) / sin(2 * pi / 45),
),
)
assert Line((0, 0), (1, 1)).intersection(Ray((1, 0),
(1, 2))) == [Point(1, 1)]
assert Line((0, 0), (1, 1)).intersection(Segment((1, 0),
(1, 2))) == [Point(1, 1)]
assert Ray((0, 0), (1, 1)).intersection(Ray((1, 0),
(1, 2))) == [Point(1, 1)]
assert Ray((0, 0), (1, 1)).intersection(Segment((1, 0),
(1, 2))) == [Point(1, 1)]
assert Ray((0, 0), (10, 10)).contains(Segment((1, 1), (2, 2))) is True
assert Segment((1, 1), (2, 2)) in Line((0, 0), (10, 10))
assert s1.intersection(Ray((1, 1), (4, 4))) == [Point(1, 1)]
def test_intersection_2d():
p1 = Point(0, 0)
p2 = Point(1, 1)
p3 = Point(x1, x1)
p4 = Point(y1, y1)
l1 = Line(p1, p2)
l3 = Line(Point(0, 0), Point(3, 4))
r1 = Ray(Point(1, 1), Point(2, 2))
r2 = Ray(Point(0, 0), Point(3, 4))
r4 = Ray(p1, p2)
r6 = Ray(Point(0, 1), Point(1, 2))
r7 = Ray(Point(0.5, 0.5), Point(1, 1))
s1 = Segment(p1, p2)
s2 = Segment(Point(0.25, 0.25), Point(0.5, 0.5))
s3 = Segment(Point(0, 0), Point(3, 4))
assert intersection(l1, p1) == [p1]
assert intersection(l1, Point(x1, 1 + x1)) == []
assert intersection(l1, Line(p3, p4)) in [[l1], [Line(p3, p4)]]
assert intersection(l1, l1.parallel_line(Point(x1, 1 + x1))) == []
assert intersection(l3, l3) == [l3]
assert intersection(l3, r2) == [r2]
assert intersection(l3, s3) == [s3]
assert intersection(s3, l3) == [s3]
assert intersection(Segment(Point(-10, 10), Point(10, 10)), Segment(Point(-5, -5), Point(-5, 5))) == []
assert intersection(r2, l3) == [r2]
assert intersection(r1, Ray(Point(2, 2), Point(0, 0))) == [Segment(Point(1, 1), Point(2, 2))]
assert intersection(r1, Ray(Point(1, 1), Point(-1, -1))) == [Point(1, 1)]
assert intersection(r1, Segment(Point(0, 0), Point(2, 2))) == [Segment(Point(1, 1), Point(2, 2))]
assert r4.intersection(s2) == [s2]
assert r4.intersection(Segment(Point(2, 3), Point(3, 4))) == []
assert r4.intersection(Segment(Point(-1, -1), Point(0.5, 0.5))) == [Segment(p1, Point(0.5, 0.5))]
assert r4.intersection(Ray(p2, p1)) == [s1]
assert Ray(p2, p1).intersection(r6) == []
assert r4.intersection(r7) == r7.intersection(r4) == [r7]
assert Ray3D((0, 0), (3, 0)).intersection(Ray3D((1, 0), (3, 0))) == [Ray3D((1, 0), (3, 0))]
assert Ray3D((1, 0), (3, 0)).intersection(Ray3D((0, 0), (3, 0))) == [Ray3D((1, 0), (3, 0))]
assert Ray(Point(0, 0), Point(0, 4)).intersection(Ray(Point(0, 1), Point(0, -1))) == \
[Segment(Point(0, 0), Point(0, 1))]
assert Segment3D((0, 0), (3, 0)).intersection(
Segment3D((1, 0), (2, 0))) == [Segment3D((1, 0), (2, 0))]
assert Segment3D((1, 0), (2, 0)).intersection(
Segment3D((0, 0), (3, 0))) == [Segment3D((1, 0), (2, 0))]
assert Segment3D((0, 0), (3, 0)).intersection(
Segment3D((3, 0), (4, 0))) == [Point3D((3, 0))]
assert Segment3D((0, 0), (3, 0)).intersection(
Segment3D((2, 0), (5, 0))) == [Segment3D((2, 0), (3, 0))]
assert Segment3D((0, 0), (3, 0)).intersection(
Segment3D((-2, 0), (1, 0))) == [Segment3D((0, 0), (1, 0))]
assert Segment3D((0, 0), (3, 0)).intersection(
Segment3D((-2, 0), (0, 0))) == [Point3D(0, 0)]
assert s1.intersection(Segment(Point(1, 1), Point(2, 2))) == [Point(1, 1)]
assert s1.intersection(Segment(Point(0.5, 0.5), Point(1.5, 1.5))) == [Segment(Point(0.5, 0.5), p2)]
assert s1.intersection(Segment(Point(4, 4), Point(5, 5))) == []
assert s1.intersection(Segment(Point(-1, -1), p1)) == [p1]
assert s1.intersection(Segment(Point(-1, -1), Point(0.5, 0.5))) == [Segment(p1, Point(0.5, 0.5))]
assert s1.intersection(Line(Point(1, 0), Point(2, 1))) == []
assert s1.intersection(s2) == [s2]
assert s2.intersection(s1) == [s2]
assert asa(120, 8, 52) == \
Triangle(
Point(0, 0),
Point(8, 0),
Point(-4 * cos(19 * pi / 90) / sin(2 * pi / 45),
4 * sqrt(3) * cos(19 * pi / 90) / sin(2 * pi / 45)))
assert Line((0, 0), (1, 1)).intersection(Ray((1, 0), (1, 2))) == [Point(1, 1)]
assert Line((0, 0), (1, 1)).intersection(Segment((1, 0), (1, 2))) == [Point(1, 1)]
assert Ray((0, 0), (1, 1)).intersection(Ray((1, 0), (1, 2))) == [Point(1, 1)]
assert Ray((0, 0), (1, 1)).intersection(Segment((1, 0), (1, 2))) == [Point(1, 1)]
assert Ray((0, 0), (10, 10)).contains(Segment((1, 1), (2, 2))) is True
assert Segment((1, 1), (2, 2)) in Line((0, 0), (10, 10))
assert s1.intersection(Ray((1, 1), (4, 4))) == [Point(1, 1)]
# 16628 - this should be fast
p0 = Point2D(Rational(249, 5), Rational(497999, 10000))
p1 = Point2D((-58977084786*sqrt(405639795226) + 2030690077184193 +
20112207807*sqrt(630547164901) + 99600*sqrt(255775022850776494562626))
/(2000*sqrt(255775022850776494562626) + 1991998000*sqrt(405639795226)
+ 1991998000*sqrt(630547164901) + 1622561172902000),
(-498000*sqrt(255775022850776494562626) - 995999*sqrt(630547164901) +
90004251917891999 +
496005510002*sqrt(405639795226))/(10000*sqrt(255775022850776494562626)
+ 9959990000*sqrt(405639795226) + 9959990000*sqrt(630547164901) +
8112805864510000))
p2 = Point2D(Rational(497, 10), Rational(-497, 10))
p3 = Point2D(Rational(-497, 10), Rational(-497, 10))
l = Line(p0, p1)
s = Segment(p2, p3)
n = (-52673223862*sqrt(405639795226) - 15764156209307469 -
9803028531*sqrt(630547164901) +
33200*sqrt(255775022850776494562626))
d = sqrt(405639795226) + 315274080450 + 498000*sqrt(
630547164901) + sqrt(255775022850776494562626)
assert intersection(l, s) == [
Point2D(n/d*Rational(3, 2000), Rational(-497, 10))]
def test_intersection_2d():
p1 = Point(0, 0)
p2 = Point(1, 1)
p3 = Point(x1, x1)
p4 = Point(y1, y1)
l1 = Line(p1, p2)
l3 = Line(Point(0, 0), Point(3, 4))
r1 = Ray(Point(1, 1), Point(2, 2))
r2 = Ray(Point(0, 0), Point(3, 4))
r4 = Ray(p1, p2)
r6 = Ray(Point(0, 1), Point(1, 2))
r7 = Ray(Point(0.5, 0.5), Point(1, 1))
s1 = Segment(p1, p2)
s2 = Segment(Point(0.25, 0.25), Point(0.5, 0.5))
s3 = Segment(Point(0, 0), Point(3, 4))
assert intersection(l1, p1) == [p1]
assert intersection(l1, Point(x1, 1 + x1)) == []
assert intersection(l1, Line(p3, p4)) in [[l1], [Line(p3, p4)]]
assert intersection(l1, l1.parallel_line(Point(x1, 1 + x1))) == []
assert intersection(l3, l3) == [l3]
assert intersection(l3, r2) == [r2]
assert intersection(l3, s3) == [s3]
assert intersection(s3, l3) == [s3]
assert intersection(Segment(Point(-10, 10), Point(10, 10)), Segment(Point(-5, -5), Point(-5, 5))) == []
assert intersection(r2, l3) == [r2]
assert intersection(r1, Ray(Point(2, 2), Point(0, 0))) == [Segment(Point(1, 1), Point(2, 2))]
assert intersection(r1, Ray(Point(1, 1), Point(-1, -1))) == [Point(1, 1)]
assert intersection(r1, Segment(Point(0, 0), Point(2, 2))) == [Segment(Point(1, 1), Point(2, 2))]
assert r4.intersection(s2) == [s2]
assert r4.intersection(Segment(Point(2, 3), Point(3, 4))) == []
assert r4.intersection(Segment(Point(-1, -1), Point(0.5, 0.5))) == [Segment(p1, Point(0.5, 0.5))]
assert r4.intersection(Ray(p2, p1)) == [s1]
assert Ray(p2, p1).intersection(r6) == []
assert r4.intersection(r7) == r7.intersection(r4) == [r7]
assert Ray3D((0, 0), (3, 0)).intersection(Ray3D((1, 0), (3, 0))) == [Ray3D((1, 0), (3, 0))]
assert Ray3D((1, 0), (3, 0)).intersection(Ray3D((0, 0), (3, 0))) == [Ray3D((1, 0), (3, 0))]
assert Ray(Point(0, 0), Point(0, 4)).intersection(Ray(Point(0, 1), Point(0, -1))) == \
[Segment(Point(0, 0), Point(0, 1))]
assert Segment3D((0, 0), (3, 0)).intersection(
Segment3D((1, 0), (2, 0))) == [Segment3D((1, 0), (2, 0))]
assert Segment3D((1, 0), (2, 0)).intersection(
Segment3D((0, 0), (3, 0))) == [Segment3D((1, 0), (2, 0))]
assert Segment3D((0, 0), (3, 0)).intersection(
Segment3D((3, 0), (4, 0))) == [Point3D((3, 0))]
assert Segment3D((0, 0), (3, 0)).intersection(
Segment3D((2, 0), (5, 0))) == [Segment3D((2, 0), (3, 0))]
assert Segment3D((0, 0), (3, 0)).intersection(
Segment3D((-2, 0), (1, 0))) == [Segment3D((0, 0), (1, 0))]
assert Segment3D((0, 0), (3, 0)).intersection(
Segment3D((-2, 0), (0, 0))) == [Point3D(0, 0)]
assert s1.intersection(Segment(Point(1, 1), Point(2, 2))) == [Point(1, 1)]
assert s1.intersection(Segment(Point(0.5, 0.5), Point(1.5, 1.5))) == [Segment(Point(0.5, 0.5), p2)]
assert s1.intersection(Segment(Point(4, 4), Point(5, 5))) == []
assert s1.intersection(Segment(Point(-1, -1), p1)) == [p1]
assert s1.intersection(Segment(Point(-1, -1), Point(0.5, 0.5))) == [Segment(p1, Point(0.5, 0.5))]
assert s1.intersection(Line(Point(1, 0), Point(2, 1))) == []
assert s1.intersection(s2) == [s2]
assert s2.intersection(s1) == [s2]
assert asa(120, 8, 52) == \
Triangle(
Point(0, 0),
Point(8, 0),
Point(-4 * cos(19 * pi / 90) / sin(2 * pi / 45),
4 * sqrt(3) * cos(19 * pi / 90) / sin(2 * pi / 45)))
assert Line((0, 0), (1, 1)).intersection(Ray((1, 0), (1, 2))) == [Point(1, 1)]
assert Line((0, 0), (1, 1)).intersection(Segment((1, 0), (1, 2))) == [Point(1, 1)]
assert Ray((0, 0), (1, 1)).intersection(Ray((1, 0), (1, 2))) == [Point(1, 1)]
assert Ray((0, 0), (1, 1)).intersection(Segment((1, 0), (1, 2))) == [Point(1, 1)]
assert Ray((0, 0), (10, 10)).contains(Segment((1, 1), (2, 2))) is True
assert Segment((1, 1), (2, 2)) in Line((0, 0), (10, 10))
# 16628 - this should be fast
p0 = Point2D(S(249)/5, S(497999)/10000)
p1 = Point2D((-58977084786*sqrt(405639795226) + 2030690077184193 +
20112207807*sqrt(630547164901) + 99600*sqrt(255775022850776494562626))
/(2000*sqrt(255775022850776494562626) + 1991998000*sqrt(405639795226)
+ 1991998000*sqrt(630547164901) + 1622561172902000),
(-498000*sqrt(255775022850776494562626) - 995999*sqrt(630547164901) +
90004251917891999 +
496005510002*sqrt(405639795226))/(10000*sqrt(255775022850776494562626)
+ 9959990000*sqrt(405639795226) + 9959990000*sqrt(630547164901) +
8112805864510000))
p2 = Point2D(S(497)/10, -S(497)/10)
p3 = Point2D(-S(497)/10, -S(497)/10)
l = Line(p0, p1)
s = Segment(p2, p3)
n = (-52673223862*sqrt(405639795226) - 15764156209307469 -
9803028531*sqrt(630547164901) +
33200*sqrt(255775022850776494562626))
d = sqrt(405639795226) + 315274080450 + 498000*sqrt(
630547164901) + sqrt(255775022850776494562626)
assert intersection(l, s) == [
Point2D(n/d*S(3)/2000, -S(497)/10)]
