from sympy import Dummy, S, symbols, pi, sqrt, asin, sin, cos, Rational
from sympy.geometry import Line, Point, Ray, Segment, Point3D, Line3D, Ray3D, Segment3D, Plane, Circle
from sympy.geometry.util import are_coplanar
from sympy.testing.pytest import raises


def test_plane():
    x, y, z, u, v = symbols('x y z u v', real=True)
    p1 = Point3D(0, 0, 0)
    p2 = Point3D(1, 1, 1)
    p3 = Point3D(1, 2, 3)
    pl3 = Plane(p1, p2, p3)
    pl4 = Plane(p1, normal_vector=(1, 1, 1))
    pl4b = Plane(p1, p2)
    pl5 = Plane(p3, normal_vector=(1, 2, 3))
    pl6 = Plane(Point3D(2, 3, 7), normal_vector=(2, 2, 2))
    pl7 = Plane(Point3D(1, -5, -6), normal_vector=(1, -2, 1))
    pl8 = Plane(p1, normal_vector=(0, 0, 1))
    pl9 = Plane(p1, normal_vector=(0, 12, 0))
    pl10 = Plane(p1, normal_vector=(-2, 0, 0))
    pl11 = Plane(p2, normal_vector=(0, 0, 1))
    l1 = Line3D(Point3D(5, 0, 0), Point3D(1, -1, 1))
    l2 = Line3D(Point3D(0, -2, 0), Point3D(3, 1, 1))
    l3 = Line3D(Point3D(0, -1, 0), Point3D(5, -1, 9))

    raises(ValueError, lambda: Plane(p1, p1, p1))

    assert Plane(p1, p2, p3) != Plane(p1, p3, p2)
    assert Plane(p1, p2, p3).is_coplanar(Plane(p1, p3, p2))
    assert Plane(p1, p2, p3).is_coplanar(p1)
    assert Plane(p1, p2, p3).is_coplanar(Circle(p1, 1)) is False
    assert Plane(p1, normal_vector=(0, 0, 1)).is_coplanar(Circle(p1, 1))

    assert pl3 == Plane(Point3D(0, 0, 0), normal_vector=(1, -2, 1))
    assert pl3 != pl4
    assert pl4 == pl4b
    assert pl5 == Plane(Point3D(1, 2, 3), normal_vector=(1, 2, 3))

    assert pl5.equation(x, y, z) == x + 2*y + 3*z - 14
    assert pl3.equation(x, y, z) == x - 2*y + z

    assert pl3.p1 == p1
    assert pl4.p1 == p1
    assert pl5.p1 == p3

    assert pl4.normal_vector == (1, 1, 1)
    assert pl5.normal_vector == (1, 2, 3)

    assert p1 in pl3
    assert p1 in pl4
    assert p3 in pl5

    assert pl3.projection(Point(0, 0)) == p1
    p = pl3.projection(Point3D(1, 1, 0))
    assert p == Point3D(Rational(7, 6), Rational(2, 3), Rational(1, 6))
    assert p in pl3

    l = pl3.projection_line(Line(Point(0, 0), Point(1, 1)))
    assert l == Line3D(Point3D(0, 0, 0), Point3D(Rational(7, 6), Rational(2, 3), Rational(1, 6)))
    assert l in pl3
    # get a segment that does not intersect the plane which is also
    # parallel to pl3's normal veector
    t = Dummy()
    r = pl3.random_point()
    a = pl3.perpendicular_line(r).arbitrary_point(t)
    s = Segment3D(a.subs(t, 1), a.subs(t, 2))
    assert s.p1 not in pl3 and s.p2 not in pl3
    assert pl3.projection_line(s).equals(r)
    assert pl3.projection_line(Segment(Point(1, 0), Point(1, 1))) == \
               Segment3D(Point3D(Rational(5, 6), Rational(1, 3), Rational(-1, 6)), Point3D(Rational(7, 6), Rational(2, 3), Rational(1, 6)))
    assert pl6.projection_line(Ray(Point(1, 0), Point(1, 1))) == \
               Ray3D(Point3D(Rational(14, 3), Rational(11, 3), Rational(11, 3)), Point3D(Rational(13, 3), Rational(13, 3), Rational(10, 3)))
    assert pl3.perpendicular_line(r.args) == pl3.perpendicular_line(r)

    assert pl3.is_parallel(pl6) is False
    assert pl4.is_parallel(pl6)
    assert pl3.is_parallel(Line(p1, p2))
    assert pl6.is_parallel(l1) is False

    assert pl3.is_perpendicular(pl6)
    assert pl4.is_perpendicular(pl7)
    assert pl6.is_perpendicular(pl7)
    assert pl6.is_perpendicular(pl4) is False
    assert pl6.is_perpendicular(l1) is False
    assert pl6.is_perpendicular(Line((0, 0, 0), (1, 1, 1)))
    assert pl6.is_perpendicular((1, 1)) is False

    assert pl6.distance(pl6.arbitrary_point(u, v)) == 0
    assert pl7.distance(pl7.arbitrary_point(u, v)) == 0
    assert pl6.distance(pl6.arbitrary_point(t)) == 0
    assert pl7.distance(pl7.arbitrary_point(t)) == 0
    assert pl6.p1.distance(pl6.arbitrary_point(t)).simplify() == 1
    assert pl7.p1.distance(pl7.arbitrary_point(t)).simplify() == 1
    assert pl3.arbitrary_point(t) == Point3D(-sqrt(30)*sin(t)/30 + \
        2*sqrt(5)*cos(t)/5, sqrt(30)*sin(t)/15 + sqrt(5)*cos(t)/5, sqrt(30)*sin(t)/6)
    assert pl3.arbitrary_point(u, v) == Point3D(2*u - v, u + 2*v, 5*v)

    assert pl7.distance(Point3D(1, 3, 5)) == 5*sqrt(6)/6
    assert pl6.distance(Point3D(0, 0, 0)) == 4*sqrt(3)
    assert pl6.distance(pl6.p1) == 0
    assert pl7.distance(pl6) == 0
    assert pl7.distance(l1) == 0
    assert pl6.distance(Segment3D(Point3D(2, 3, 1), Point3D(1, 3, 4))) == \
        pl6.distance(Point3D(1, 3, 4)) == 4*sqrt(3)/3
    assert pl6.distance(Segment3D(Point3D(1, 3, 4), Point3D(0, 3, 7))) == \
        pl6.distance(Point3D(0, 3, 7)) == 2*sqrt(3)/3
    assert pl6.distance(Segment3D(Point3D(0, 3, 7), Point3D(-1, 3, 10))) == 0
    assert pl6.distance(Segment3D(Point3D(-1, 3, 10), Point3D(-2, 3, 13))) == 0
    assert pl6.distance(Segment3D(Point3D(-2, 3, 13), Point3D(-3, 3, 16))) == \
        pl6.distance(Point3D(-2, 3, 13)) == 2*sqrt(3)/3
    assert pl6.distance(Plane(Point3D(5, 5, 5), normal_vector=(8, 8, 8))) == sqrt(3)
    assert pl6.distance(Ray3D(Point3D(1, 3, 4), direction_ratio=[1, 0, -3])) == 4*sqrt(3)/3
    assert pl6.distance(Ray3D(Point3D(2, 3, 1), direction_ratio=[-1, 0, 3])) == 0


    assert pl6.angle_between(pl3) == pi/2
    assert pl6.angle_between(pl6) == 0
    assert pl6.angle_between(pl4) == 0
    assert pl7.angle_between(Line3D(Point3D(2, 3, 5), Point3D(2, 4, 6))) == \
        -asin(sqrt(3)/6)
    assert pl6.angle_between(Ray3D(Point3D(2, 4, 1), Point3D(6, 5, 3))) == \
        asin(sqrt(7)/3)
    assert pl7.angle_between(Segment3D(Point3D(5, 6, 1), Point3D(1, 2, 4))) == \
        asin(7*sqrt(246)/246)

    assert are_coplanar(l1, l2, l3) is False
    assert are_coplanar(l1) is False
    assert are_coplanar(Point3D(2, 7, 2), Point3D(0, 0, 2),
        Point3D(1, 1, 2), Point3D(1, 2, 2))
    assert are_coplanar(Plane(p1, p2, p3), Plane(p1, p3, p2))
    assert Plane.are_concurrent(pl3, pl4, pl5) is False
    assert Plane.are_concurrent(pl6) is False
    raises(ValueError, lambda: Plane.are_concurrent(Point3D(0, 0, 0)))
    raises(ValueError, lambda: Plane((1, 2, 3), normal_vector=(0, 0, 0)))

    assert pl3.parallel_plane(Point3D(1, 2, 5)) == Plane(Point3D(1, 2, 5), \
                                                      normal_vector=(1, -2, 1))

    # perpendicular_plane
    p = Plane((0, 0, 0), (1, 0, 0))
    # default
    assert p.perpendicular_plane() == Plane(Point3D(0, 0, 0), (0, 1, 0))
    # 1 pt
    assert p.perpendicular_plane(Point3D(1, 0, 1)) == \
        Plane(Point3D(1, 0, 1), (0, 1, 0))
    # pts as tuples
    assert p.perpendicular_plane((1, 0, 1), (1, 1, 1)) == \
        Plane(Point3D(1, 0, 1), (0, 0, -1))
    # more than two planes
    raises(ValueError, lambda: p.perpendicular_plane((1, 0, 1), (1, 1, 1), (1, 1, 0)))

    a, b = Point3D(0, 0, 0), Point3D(0, 1, 0)
    Z = (0, 0, 1)
    p = Plane(a, normal_vector=Z)
    # case 4
    assert p.perpendicular_plane(a, b) == Plane(a, (1, 0, 0))
    n = Point3D(*Z)
    # case 1
    assert p.perpendicular_plane(a, n) == Plane(a, (-1, 0, 0))
    # case 2
    assert Plane(a, normal_vector=b.args).perpendicular_plane(a, a + b) == \
        Plane(Point3D(0, 0, 0), (1, 0, 0))
    # case 1&3
    assert Plane(b, normal_vector=Z).perpendicular_plane(b, b + n) == \
        Plane(Point3D(0, 1, 0), (-1, 0, 0))
    # case 2&3
    assert Plane(b, normal_vector=b.args).perpendicular_plane(n, n + b) == \
        Plane(Point3D(0, 0, 1), (1, 0, 0))

    p = Plane(a, normal_vector=(0, 0, 1))
    assert p.perpendicular_plane() == Plane(a, normal_vector=(1, 0, 0))

    assert pl6.intersection(pl6) == [pl6]
    assert pl4.intersection(pl4.p1) == [pl4.p1]
    assert pl3.intersection(pl6) == [
        Line3D(Point3D(8, 4, 0), Point3D(2, 4, 6))]
    assert pl3.intersection(Line3D(Point3D(1,2,4), Point3D(4,4,2))) == [
        Point3D(2, Rational(8, 3), Rational(10, 3))]
    assert pl3.intersection(Plane(Point3D(6, 0, 0), normal_vector=(2, -5, 3))
        ) == [Line3D(Point3D(-24, -12, 0), Point3D(-25, -13, -1))]
    assert pl6.intersection(Ray3D(Point3D(2, 3, 1), Point3D(1, 3, 4))) == [
        Point3D(-1, 3, 10)]
    assert pl6.intersection(Segment3D(Point3D(2, 3, 1), Point3D(1, 3, 4))) == []
    assert pl7.intersection(Line(Point(2, 3), Point(4, 2))) == [
        Point3D(Rational(13, 2), Rational(3, 4), 0)]
    r = Ray(Point(2, 3), Point(4, 2))
    assert Plane((1,2,0), normal_vector=(0,0,1)).intersection(r) == [
        Ray3D(Point(2, 3), Point(4, 2))]
    assert pl9.intersection(pl8) == [Line3D(Point3D(0, 0, 0), Point3D(12, 0, 0))]
    assert pl10.intersection(pl11) == [Line3D(Point3D(0, 0, 1), Point3D(0, 2, 1))]
    assert pl4.intersection(pl8) == [Line3D(Point3D(0, 0, 0), Point3D(1, -1, 0))]
    assert pl11.intersection(pl8) == []
    assert pl9.intersection(pl11) == [Line3D(Point3D(0, 0, 1), Point3D(12, 0, 1))]
    assert pl9.intersection(pl4) == [Line3D(Point3D(0, 0, 0), Point3D(12, 0, -12))]
    assert pl3.random_point() in pl3
    assert pl3.random_point(seed=1) in pl3

    # test geometrical entity using equals
    assert pl4.intersection(pl4.p1)[0].equals(pl4.p1)
    assert pl3.intersection(pl6)[0].equals(Line3D(Point3D(8, 4, 0), Point3D(2, 4, 6)))
    pl8 = Plane((1, 2, 0), normal_vector=(0, 0, 1))
    assert pl8.intersection(Line3D(p1, (1, 12, 0)))[0].equals(Line((0, 0, 0), (0.1, 1.2, 0)))
    assert pl8.intersection(Ray3D(p1, (1, 12, 0)))[0].equals(Ray((0, 0, 0), (1, 12, 0)))
    assert pl8.intersection(Segment3D(p1, (21, 1, 0)))[0].equals(Segment3D(p1, (21, 1, 0)))
    assert pl8.intersection(Plane(p1, normal_vector=(0, 0, 112)))[0].equals(pl8)
    assert pl8.intersection(Plane(p1, normal_vector=(0, 12, 0)))[0].equals(
        Line3D(p1, direction_ratio=(112 * pi, 0, 0)))
    assert pl8.intersection(Plane(p1, normal_vector=(11, 0, 1)))[0].equals(
        Line3D(p1, direction_ratio=(0, -11, 0)))
    assert pl8.intersection(Plane(p1, normal_vector=(1, 0, 11)))[0].equals(
        Line3D(p1, direction_ratio=(0, 11, 0)))
    assert pl8.intersection(Plane(p1, normal_vector=(-1, -1, -11)))[0].equals(
        Line3D(p1, direction_ratio=(1, -1, 0)))
    assert pl3.random_point() in pl3
    assert len(pl8.intersection(Ray3D(Point3D(0, 2, 3), Point3D(1, 0, 3)))) == 0
    # check if two plane are equals
    assert pl6.intersection(pl6)[0].equals(pl6)
    assert pl8.equals(Plane(p1, normal_vector=(0, 12, 0))) is False
    assert pl8.equals(pl8)
    assert pl8.equals(Plane(p1, normal_vector=(0, 0, -12)))
    assert pl8.equals(Plane(p1, normal_vector=(0, 0, -12*sqrt(3))))
    assert pl8.equals(p1) is False

    # issue 8570
    l2 = Line3D(Point3D(Rational(50000004459633, 5000000000000),
                        Rational(-891926590718643, 1000000000000000),
                        Rational(231800966893633, 100000000000000)),
                Point3D(Rational(50000004459633, 50000000000000),
                        Rational(-222981647679771, 250000000000000),
                        Rational(231800966893633, 100000000000000)))

    p2 = Plane(Point3D(Rational(402775636372767, 100000000000000),
                       Rational(-97224357654973, 100000000000000),
                       Rational(216793600814789, 100000000000000)),
               (-S('9.00000087501922'), -S('4.81170658872543e-13'),
                S('0.0')))

    assert str([i.n(2) for i in p2.intersection(l2)]) == \
           '[Point3D(4.0, -0.89, 2.3)]'


def test_dimension_normalization():
    A = Plane(Point3D(1, 1, 2), normal_vector=(1, 1, 1))
    b = Point(1, 1)
    assert A.projection(b) == Point(Rational(5, 3), Rational(5, 3), Rational(2, 3))

    a, b = Point(0, 0), Point3D(0, 1)
    Z = (0, 0, 1)
    p = Plane(a, normal_vector=Z)
    assert p.perpendicular_plane(a, b) == Plane(Point3D(0, 0, 0), (1, 0, 0))
    assert Plane((1, 2, 1), (2, 1, 0), (3, 1, 2)
        ).intersection((2, 1)) == [Point(2, 1, 0)]


def test_parameter_value():
    t, u, v = symbols("t, u v")
    p1, p2, p3 = Point(0, 0, 0), Point(0, 0, 1), Point(0, 1, 0)
    p = Plane(p1, p2, p3)
    assert p.parameter_value((0, -3, 2), t) == {t: asin(2*sqrt(13)/13)}
    assert p.parameter_value((0, -3, 2), u, v) == {u: 3, v: 2}
    assert p.parameter_value(p1, t) == p1
    raises(ValueError, lambda: p.parameter_value((1, 0, 0), t))
    raises(ValueError, lambda: p.parameter_value(Line(Point(0, 0), Point(1, 1)), t))
    raises(ValueError, lambda: p.parameter_value((0, -3, 2), t, 1))
