from __future__ import division

from sympy import I, Rational, Symbol, pi, sqrt
from sympy.geometry import Line, Point, Point3D, Line3D
from sympy.geometry.entity import rotate, scale, translate
from sympy.matrices import Matrix
from sympy.utilities.pytest import raises

x = Symbol('x', real=True)
y = Symbol('y', real=True)
z = Symbol('z', real=True)
t = Symbol('t', real=True)
x1 = Symbol('x1', real=True)
x2 = Symbol('x2', real=True)
x3 = Symbol('x3', real=True)
y1 = Symbol('y1', real=True)
y2 = Symbol('y2', real=True)
y3 = Symbol('y3', real=True)
half = Rational(1, 2)


def test_point():
    p1 = Point(x1, x2)
    p2 = Point(y1, y2)
    p3 = Point(0, 0)
    p4 = Point(1, 1)
    p5 = Point(0, 1)

    assert p1 in p1
    assert p1 not in p2
    assert p2.y == y2
    assert (p3 + p4) == p4
    assert (p2 - p1) == Point(y1 - x1, y2 - x2)
    assert p4*5 == Point(5, 5)
    assert -p2 == Point(-y1, -y2)
    raises(ValueError, lambda: Point(3, I))
    raises(ValueError, lambda: Point(2*I, I))
    raises(ValueError, lambda: Point(3 + I, I))

    assert Point(34.05, sqrt(3)) == Point(Rational(681, 20), sqrt(3))
    assert Point.midpoint(p3, p4) == Point(half, half)
    assert Point.midpoint(p1, p4) == Point(half + half*x1, half + half*x2)
    assert Point.midpoint(p2, p2) == p2
    assert p2.midpoint(p2) == p2

    assert Point.distance(p3, p4) == sqrt(2)
    assert Point.distance(p1, p1) == 0
    assert Point.distance(p3, p2) == sqrt(p2.x**2 + p2.y**2)

    assert Point.taxicab_distance(p4, p3) == 2

    p1_1 = Point(x1, x1)
    p1_2 = Point(y2, y2)
    p1_3 = Point(x1 + 1, x1)
    assert Point.is_collinear(p3)
    assert Point.is_collinear(p3, p4)
    assert Point.is_collinear(p3, p4, p1_1, p1_2)
    assert Point.is_collinear(p3, p4, p1_1, p1_3) is False
    assert Point.is_collinear(p3, p3, p4, p5) is False
    line = Line(Point(1,0), slope = 1)
    raises(TypeError, lambda: Point.is_collinear(line))
    raises(TypeError, lambda: p1_1.is_collinear(line))

    assert p3.intersection(Point(0, 0)) == [p3]
    assert p3.intersection(p4) == []

    x_pos = Symbol('x', real=True, positive=True)
    p2_1 = Point(x_pos, 0)
    p2_2 = Point(0, x_pos)
    p2_3 = Point(-x_pos, 0)
    p2_4 = Point(0, -x_pos)
    p2_5 = Point(x_pos, 5)
    assert Point.is_concyclic(p2_1)
    assert Point.is_concyclic(p2_1, p2_2)
    assert Point.is_concyclic(p2_1, p2_2, p2_3, p2_4)
    assert Point.is_concyclic(p2_1, p2_2, p2_3, p2_5) is False
    assert Point.is_concyclic(p4, p4 * 2, p4 * 3) is False

    assert p4.scale(2, 3) == Point(2, 3)
    assert p3.scale(2, 3) == p3

    assert p4.rotate(pi, Point(0.5, 0.5)) == p3
    assert p1.__radd__(p2) == p1.midpoint(p2).scale(2, 2)
    assert (-p3).__rsub__(p4) == p3.midpoint(p4).scale(2, 2)

    assert p4 * 5 == Point(5, 5)
    assert p4 / 5 == Point(0.2, 0.2)

    raises(ValueError, lambda: Point(0, 0) + 10)

    # Point differences should be simplified
    assert Point(x*(x - 1), y) - Point(x**2 - x, y + 1) == Point(0, -1)

    a, b = Rational(1, 2), Rational(1, 3)
    assert Point(a, b).evalf(2) == \
        Point(a.n(2), b.n(2))
    raises(ValueError, lambda: Point(1, 2) + 1)

    # test transformations
    p = Point(1, 0)
    assert p.rotate(pi/2) == Point(0, 1)
    assert p.rotate(pi/2, p) == p
    p = Point(1, 1)
    assert p.scale(2, 3) == Point(2, 3)
    assert p.translate(1, 2) == Point(2, 3)
    assert p.translate(1) == Point(2, 1)
    assert p.translate(y=1) == Point(1, 2)
    assert p.translate(*p.args) == Point(2, 2)

    # Check invalid input for transform
    raises(ValueError, lambda: p3.transform(p3))
    raises(ValueError, lambda: p.transform(Matrix([[1, 0], [0, 1]])))


def test_point3D():
    p1 = Point3D(x1, x2, x3)
    p2 = Point3D(y1, y2, y3)
    p3 = Point3D(0, 0, 0)
    p4 = Point3D(1, 1, 1)
    p5 = Point3D(0, 1, 2)

    assert p1 in p1
    assert p1 not in p2
    assert p2.y == y2
    assert (p3 + p4) == p4
    assert (p2 - p1) == Point3D(y1 - x1, y2 - x2, y3 - x3)
    assert p4*5 == Point3D(5, 5, 5)
    assert -p2 == Point3D(-y1, -y2, -y3)

    assert Point(34.05, sqrt(3)) == Point(Rational(681, 20), sqrt(3))
    assert Point3D.midpoint(p3, p4) == Point3D(half, half, half)
    assert Point3D.midpoint(p1, p4) == Point3D(half + half*x1, half + half*x2,
                                         half + half*x3)
    assert Point3D.midpoint(p2, p2) == p2
    assert p2.midpoint(p2) == p2

    assert Point3D.distance(p3, p4) == sqrt(3)
    assert Point3D.distance(p1, p1) == 0
    assert Point3D.distance(p3, p2) == sqrt(p2.x**2 + p2.y**2 + p2.z**2)

    p1_1 = Point3D(x1, x1, x1)
    p1_2 = Point3D(y2, y2, y2)
    p1_3 = Point3D(x1 + 1, x1, x1)
    # according to the description in the docs, points are collinear
    # if they like on a single line.  Thus a single point should always
    # be collinear
    assert Point3D.are_collinear(p3)
    assert Point3D.are_collinear(p3, p4)
    assert Point3D.are_collinear(p3, p4, p1_1, p1_2)
    assert Point3D.are_collinear(p3, p4, p1_1, p1_3) is False
    assert Point3D.are_collinear(p3, p3, p4, p5) is False

    assert p3.intersection(Point3D(0, 0, 0)) == [p3]
    assert p3.intersection(p4) == []


    assert p4 * 5 == Point3D(5, 5, 5)
    assert p4 / 5 == Point3D(0.2, 0.2, 0.2)

    raises(ValueError, lambda: Point3D(0, 0, 0) + 10)

    # Point differences should be simplified
    assert Point3D(x*(x - 1), y, 2) - Point3D(x**2 - x, y + 1, 1) == \
        Point3D(0, -1, 1)

    a, b = Rational(1, 2), Rational(1, 3)
    assert Point(a, b).evalf(2) == \
        Point(a.n(2), b.n(2))
    raises(ValueError, lambda: Point(1, 2) + 1)

    # test transformations
    p = Point3D(1, 1, 1)
    assert p.scale(2, 3) == Point3D(2, 3, 1)
    assert p.translate(1, 2) == Point3D(2, 3, 1)
    assert p.translate(1) == Point3D(2, 1, 1)
    assert p.translate(z=1) == Point3D(1, 1, 2)
    assert p.translate(*p.args) == Point3D(2, 2, 2)

    # Test __new__
    assert Point3D(Point3D(1, 2, 3), 4, 5, evaluate=False) ==  Point3D(1, 2, 3)


    # Test length property returns correctly
    assert p.length == 0
    assert p1_1.length == 0
    assert p1_2.length == 0

    # Test are_colinear type error
    raises(TypeError, lambda: Point3D.are_collinear(p, x))

    # Test are_coplanar
    planar2 = Point3D(1, -1, 1)
    planar3 = Point3D(-1, 1, 1)
    assert Point3D.are_coplanar(p, planar2, planar3) == True
    assert Point3D.are_coplanar(p, planar2, planar3, p3) == False
    raises(ValueError, lambda: Point3D.are_coplanar(p, planar2))
    planar2 = Point3D(1, 1, 2)
    planar3 = Point3D(1, 1, 3)
    raises(ValueError, lambda: Point3D.are_coplanar(p, planar2, planar3))

    # Test Intersection
    assert planar2.intersection(Line3D(p, planar3)) == [Point3D(1, 1, 2)]

    # Test Scale
    assert planar2.scale(1, 1, 1) == planar2
    assert planar2.scale(2, 2, 2, planar3) == Point3D(1, 1, 1)
    assert planar2.scale(1, 1, 1, p3) == planar2

    # Test Transform
    identity = Matrix([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]])
    assert p.transform(identity) == p
    trans = Matrix([[1, 0, 0, 1], [0, 1, 0, 1], [0, 0, 1, 1], [0, 0, 0, 1]])
    assert p.transform(trans) == Point3D(2, 2, 2)
    raises(ValueError, lambda: p.transform(p))
    raises(ValueError, lambda: p.transform(Matrix([[1, 0], [0, 1]])))

    # Test Equals
    assert p.equals(x1) == False

    # Test __sub__
    p_2d = Point(0, 0)
    raises(ValueError, lambda: (p - p_2d))


def test_issue_9214():
    p1 = Point3D(4, -2, 6)
    p2 = Point3D(1, 2, 3)
    p3 = Point3D(7, 2, 3)

    assert Point3D.are_collinear(p1, p2, p3) is False


def test_transform():
    p = Point(1, 1)
    assert p.transform(rotate(pi/2)) == Point(-1, 1)
    assert p.transform(scale(3, 2)) == Point(3, 2)
    assert p.transform(translate(1, 2)) == Point(2, 3)


def test_concyclic_doctest_bug():
    p1, p2 = Point(-1, 0), Point(1, 0)
    p3, p4 = Point(0, 1), Point(-1, 2)
    assert Point.is_concyclic(p1, p2, p3)
    assert not Point.is_concyclic(p1, p2, p3, p4)
