from sympy import Rational, oo, sqrt, S
from sympy import Line, Point, Point2D, Parabola, Segment2D, Ray2D
from sympy import Circle, Ellipse, symbols, sign
from sympy.testing.pytest import raises


def test_parabola_geom():
    a, b = symbols('a b')
    p1 = Point(0, 0)
    p2 = Point(3, 7)
    p3 = Point(0, 4)
    p4 = Point(6, 0)
    p5 = Point(a, a)
    d1 = Line(Point(4, 0), Point(4, 9))
    d2 = Line(Point(7, 6), Point(3, 6))
    d3 = Line(Point(4, 0), slope=oo)
    d4 = Line(Point(7, 6), slope=0)
    d5 = Line(Point(b, a), slope=oo)
    d6 = Line(Point(a, b), slope=0)

    half = S.Half

    pa1 = Parabola(None, d2)
    pa2 = Parabola(directrix=d1)
    pa3 = Parabola(p1, d1)
    pa4 = Parabola(p2, d2)
    pa5 = Parabola(p2, d4)
    pa6 = Parabola(p3, d2)
    pa7 = Parabola(p2, d1)
    pa8 = Parabola(p4, d1)
    pa9 = Parabola(p4, d3)
    pa10 = Parabola(p5, d5)
    pa11 = Parabola(p5, d6)

    raises(ValueError, lambda:
           Parabola(Point(7, 8, 9), Line(Point(6, 7), Point(7, 7))))
    raises(NotImplementedError, lambda:
           Parabola(Point(7, 8), Line(Point(3, 7), Point(2, 9))))
    raises(ValueError, lambda:
           Parabola(Point(0, 2), Line(Point(7, 2), Point(6, 2))))
    raises(ValueError, lambda: Parabola(Point(7, 8), Point(3, 8)))

    # Basic Stuff
    assert pa1.focus == Point(0, 0)
    assert pa1.ambient_dimension == S(2)
    assert pa2 == pa3
    assert pa4 != pa7
    assert pa6 != pa7
    assert pa6.focus == Point2D(0, 4)
    assert pa6.focal_length == 1
    assert pa6.p_parameter == -1
    assert pa6.vertex == Point2D(0, 5)
    assert pa6.eccentricity == 1
    assert pa7.focus == Point2D(3, 7)
    assert pa7.focal_length == half
    assert pa7.p_parameter == -half
    assert pa7.vertex == Point2D(7*half, 7)
    assert pa4.focal_length == half
    assert pa4.p_parameter == half
    assert pa4.vertex == Point2D(3, 13*half)
    assert pa8.focal_length == 1
    assert pa8.p_parameter == 1
    assert pa8.vertex == Point2D(5, 0)
    assert pa4.focal_length == pa5.focal_length
    assert pa4.p_parameter == pa5.p_parameter
    assert pa4.vertex == pa5.vertex
    assert pa4.equation() == pa5.equation()
    assert pa8.focal_length == pa9.focal_length
    assert pa8.p_parameter == pa9.p_parameter
    assert pa8.vertex == pa9.vertex
    assert pa8.equation() == pa9.equation()
    assert pa10.focal_length == pa11.focal_length == sqrt((a - b) ** 2) / 2 # if a, b real == abs(a - b)/2
    assert pa11.vertex == Point(*pa10.vertex[::-1]) == Point(a,
                            a - sqrt((a - b)**2)*sign(a - b)/2) # change axis x->y, y->x on pa10


def test_parabola_intersection():
    l1 = Line(Point(1, -2), Point(-1,-2))
    l2 = Line(Point(1, 2), Point(-1,2))
    l3 = Line(Point(1, 0), Point(-1,0))

    p1 = Point(0,0)
    p2 = Point(0, -2)
    p3 = Point(120, -12)
    parabola1 = Parabola(p1, l1)

    # parabola with parabola
    assert parabola1.intersection(parabola1) == [parabola1]
    assert parabola1.intersection(Parabola(p1, l2)) == [Point2D(-2, 0), Point2D(2, 0)]
    assert parabola1.intersection(Parabola(p2, l3)) == [Point2D(0, -1)]
    assert parabola1.intersection(Parabola(Point(16, 0), l1)) == [Point2D(8, 15)]
    assert parabola1.intersection(Parabola(Point(0, 16), l1)) == [Point2D(-6, 8), Point2D(6, 8)]
    assert parabola1.intersection(Parabola(p3, l3)) == []
    # parabola with point
    assert parabola1.intersection(p1) == []
    assert parabola1.intersection(Point2D(0, -1)) == [Point2D(0, -1)]
    assert parabola1.intersection(Point2D(4, 3)) == [Point2D(4, 3)]
    # parabola with line
    assert parabola1.intersection(Line(Point2D(-7, 3), Point(12, 3))) == [Point2D(-4, 3), Point2D(4, 3)]
    assert parabola1.intersection(Line(Point(-4, -1), Point(4, -1))) == [Point(0, -1)]
    assert parabola1.intersection(Line(Point(2, 0), Point(0, -2))) == [Point2D(2, 0)]
    raises(TypeError, lambda: parabola1.intersection(Line(Point(0, 0, 0), Point(1, 1, 1))))
    # parabola with segment
    assert parabola1.intersection(Segment2D((-4, -5), (4, 3))) == [Point2D(0, -1), Point2D(4, 3)]
    assert parabola1.intersection(Segment2D((0, -5), (0, 6))) == [Point2D(0, -1)]
    assert parabola1.intersection(Segment2D((-12, -65), (14, -68))) == []
    # parabola with ray
    assert parabola1.intersection(Ray2D((-4, -5), (4, 3))) == [Point2D(0, -1), Point2D(4, 3)]
    assert parabola1.intersection(Ray2D((0, 7), (1, 14))) == [Point2D(14 + 2*sqrt(57), 105 + 14*sqrt(57))]
    assert parabola1.intersection(Ray2D((0, 7), (0, 14))) == []
    # parabola with ellipse/circle
    assert parabola1.intersection(Circle(p1, 2)) == [Point2D(-2, 0), Point2D(2, 0)]
    assert parabola1.intersection(Circle(p2, 1)) == [Point2D(0, -1), Point2D(0, -1)]
    assert parabola1.intersection(Ellipse(p2, 2, 1)) == [Point2D(0, -1), Point2D(0, -1)]
    assert parabola1.intersection(Ellipse(Point(0, 19), 5, 7)) == []
    assert parabola1.intersection(Ellipse((0, 3), 12, 4)) == \
           [Point2D(0, -1), Point2D(0, -1), Point2D(-4*sqrt(17)/3, Rational(59, 9)), Point2D(4*sqrt(17)/3, Rational(59, 9))]
    # parabola with unsupported type
    raises(TypeError, lambda: parabola1.intersection(2))