MLPY/Lib/site-packages/sympy/geometry/tests/test_point.py

from sympy.core.basic import Basic
from sympy.core.numbers import (I, Rational, pi)
from sympy.core.parameters import evaluate
from sympy.core.singleton import S
from sympy.core.symbol import Symbol
from sympy.core.sympify import sympify
from sympy.functions.elementary.miscellaneous import sqrt
from sympy.geometry import Line, Point, Point2D, Point3D, Line3D, Plane
from sympy.geometry.entity import rotate, scale, translate, GeometryEntity
from sympy.matrices import Matrix
from sympy.utilities.iterables import subsets, permutations, cartes
from sympy.utilities.misc import Undecidable
from sympy.testing.pytest import raises, warns


def test_point():
    x = Symbol('x', real=True)
    y = Symbol('y', real=True)
    x1 = Symbol('x1', real=True)
    x2 = Symbol('x2', real=True)
    y1 = Symbol('y1', real=True)
    y2 = Symbol('y2', real=True)
    half = S.Half
    p1 = Point(x1, x2)
    p2 = Point(y1, y2)
    p3 = Point(0, 0)
    p4 = Point(1, 1)
    p5 = Point(0, 1)
    line = Line(Point(1, 0), slope=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 -p2 == Point(-y1, -y2)
    raises(TypeError, lambda: Point(1))
    raises(ValueError, lambda: Point([1]))
    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 p1.origin == Point(0, 0)

    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)
    raises(TypeError, lambda: Point.distance(p1, 0))
    raises(TypeError, lambda: Point.distance(p1, GeometryEntity()))

    # distance should be symmetric
    assert p1.distance(line) == line.distance(p1)
    assert p4.distance(line) == line.distance(p4)

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

    assert Point.canberra_distance(p4, p5) == 1
    raises(ValueError, lambda: Point.canberra_distance(p3, p3))

    p1_1 = Point(x1, x1)
    p1_2 = Point(y2, y2)
    p1_3 = Point(x1 + 1, x1)
    assert Point.is_collinear(p3)

    with warns(UserWarning, test_stacklevel=False):
        assert Point.is_collinear(p3, Point(p3, dim=4))
    assert p3.is_collinear()
    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

    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) == []
    assert p3.intersection(line) == []
    with warns(UserWarning, test_stacklevel=False):
        assert Point.intersection(Point(0, 0, 0), Point(0, 0)) == [Point(0, 0, 0)]

    x_pos = Symbol('x', 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)
    for pts in permutations((p2_1, p2_2, p2_3, p2_5)):
        assert Point.is_concyclic(*pts) is False
    assert Point.is_concyclic(p4, p4 * 2, p4 * 3) is False
    assert Point(0, 0).is_concyclic((1, 1), (2, 2), (2, 1)) is False
    assert Point.is_concyclic(Point(0, 0, 0, 0), Point(1, 0, 0, 0), Point(1, 1, 0, 0), Point(1, 1, 1, 0)) is False

    assert p1.is_scalar_multiple(p1)
    assert p1.is_scalar_multiple(2*p1)
    assert not p1.is_scalar_multiple(p2)
    assert Point.is_scalar_multiple(Point(1, 1), (-1, -1))
    assert Point.is_scalar_multiple(Point(0, 0), (0, -1))
    # test when is_scalar_multiple can't be determined
    raises(Undecidable, lambda: Point.is_scalar_multiple(Point(sympify("x1%y1"), sympify("x2%y2")), Point(0, 1)))

    assert Point(0, 1).orthogonal_direction == Point(1, 0)
    assert Point(1, 0).orthogonal_direction == Point(0, 1)

    assert p1.is_zero is None
    assert p3.is_zero
    assert p4.is_zero is False
    assert p1.is_nonzero is None
    assert p3.is_nonzero is False
    assert p4.is_nonzero

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

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

    # test project
    assert Point.project((0, 1), (1, 0)) == Point(0, 0)
    assert Point.project((1, 1), (1, 0)) == Point(1, 0)
    raises(ValueError, lambda: Point.project(p1, Point(0, 0)))

    # 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]])))

    # test __contains__
    assert 0 in Point(0, 0, 0, 0)
    assert 1 not in Point(0, 0, 0, 0)

    # test affine_rank
    assert Point.affine_rank() == -1


def test_point3D():
    x = Symbol('x', real=True)
    y = Symbol('y', 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 = S.Half
    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 -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)
    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)
    assert 5 * p4 == Point3D(5, 5, 5)

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

    # Test coordinate properties
    assert p1.coordinates == (x1, x2, x3)
    assert p2.coordinates == (y1, y2, y3)
    assert p3.coordinates == (0, 0, 0)
    assert p4.coordinates == (1, 1, 1)
    assert p5.coordinates == (0, 1, 2)
    assert p5.x == 0
    assert p5.y == 1
    assert p5.z == 2

    # 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, c = S.Half, Rational(1, 3), Rational(1, 4)
    assert Point3D(a, b, c).evalf(2) == \
        Point(a.n(2), b.n(2), c.n(2), evaluate=False)
    raises(ValueError, lambda: Point3D(1, 2, 3) + 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(0.1, 0.2, evaluate=False, on_morph='ignore').args[0].is_Float

    # 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
    assert Point.are_coplanar()
    assert Point.are_coplanar((1, 2, 0), (1, 2, 0), (1, 3, 0))
    assert Point.are_coplanar((1, 2, 0), (1, 2, 3))
    with warns(UserWarning, test_stacklevel=False):
        raises(ValueError, lambda: Point2D.are_coplanar((1, 2), (1, 2, 3)))
    assert Point3D.are_coplanar((1, 2, 0), (1, 2, 3))
    assert Point.are_coplanar((0, 0, 0), (1, 1, 0), (1, 1, 1), (1, 2, 1)) is False
    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
    assert Point.are_coplanar(p, planar2)
    planar2 = Point3D(1, 1, 2)
    planar3 = Point3D(1, 1, 3)
    assert Point3D.are_coplanar(p, planar2, planar3)  # line, not plane
    plane = Plane((1, 2, 1), (2, 1, 0), (3, 1, 2))
    assert Point.are_coplanar(*[plane.projection(((-1)**i, i)) for i in range(4)])

    # all 2D points are coplanar
    assert Point.are_coplanar(Point(x, y), Point(x, x + y), Point(y, x + 2)) is True

    # 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_4d = Point(0, 0, 0, 1)
    with warns(UserWarning, test_stacklevel=False):
        assert p - p_4d == Point(1, 1, 1, -1)
    p_4d3d = Point(0, 0, 1, 0)
    with warns(UserWarning, test_stacklevel=False):
        assert p - p_4d3d == Point(1, 1, 0, 0)


def test_Point2D():

    # Test Distance
    p1 = Point2D(1, 5)
    p2 = Point2D(4, 2.5)
    p3 = (6, 3)
    assert p1.distance(p2) == sqrt(61)/2
    assert p2.distance(p3) == sqrt(17)/2

    # Test coordinates
    assert p1.x == 1
    assert p1.y == 5
    assert p2.x == 4
    assert p2.y == S(5)/2
    assert p1.coordinates == (1, 5)
    assert p2.coordinates == (4, S(5)/2)

    # test bounds
    assert p1.bounds == (1, 5, 1, 5)

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_issue_11617():
    p1 = Point3D(1,0,2)
    p2 = Point2D(2,0)

    with warns(UserWarning, test_stacklevel=False):
        assert p1.distance(p2) == sqrt(5)


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)
    assert Point(1, 1).scale(2, 3, (4, 5)) == \
        Point(-2, -7)
    assert Point(1, 1).translate(4, 5) == \
        Point(5, 6)


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)


def test_arguments():
    """Functions accepting `Point` objects in `geometry`
    should also accept tuples and lists and
    automatically convert them to points."""

    singles2d = ((1,2), [1,2], Point(1,2))
    singles2d2 = ((1,3), [1,3], Point(1,3))
    doubles2d = cartes(singles2d, singles2d2)
    p2d = Point2D(1,2)
    singles3d = ((1,2,3), [1,2,3], Point(1,2,3))
    doubles3d = subsets(singles3d, 2)
    p3d = Point3D(1,2,3)
    singles4d = ((1,2,3,4), [1,2,3,4], Point(1,2,3,4))
    doubles4d = subsets(singles4d, 2)
    p4d = Point(1,2,3,4)

    # test 2D
    test_single = ['distance', 'is_scalar_multiple', 'taxicab_distance', 'midpoint', 'intersection', 'dot', 'equals', '__add__', '__sub__']
    test_double = ['is_concyclic', 'is_collinear']
    for p in singles2d:
        Point2D(p)
    for func in test_single:
        for p in singles2d:
            getattr(p2d, func)(p)
    for func in test_double:
        for p in doubles2d:
            getattr(p2d, func)(*p)

    # test 3D
    test_double = ['is_collinear']
    for p in singles3d:
        Point3D(p)
    for func in test_single:
        for p in singles3d:
            getattr(p3d, func)(p)
    for func in test_double:
        for p in doubles3d:
            getattr(p3d, func)(*p)

    # test 4D
    test_double = ['is_collinear']
    for p in singles4d:
        Point(p)
    for func in test_single:
        for p in singles4d:
            getattr(p4d, func)(p)
    for func in test_double:
        for p in doubles4d:
            getattr(p4d, func)(*p)

    # test evaluate=False for ops
    x = Symbol('x')
    a = Point(0, 1)
    assert a + (0.1, x) == Point(0.1, 1 + x, evaluate=False)
    a = Point(0, 1)
    assert a/10.0 == Point(0, 0.1, evaluate=False)
    a = Point(0, 1)
    assert a*10.0 == Point(0.0, 10.0, evaluate=False)

    # test evaluate=False when changing dimensions
    u = Point(.1, .2, evaluate=False)
    u4 = Point(u, dim=4, on_morph='ignore')
    assert u4.args == (.1, .2, 0, 0)
    assert all(i.is_Float for i in u4.args[:2])
    # and even when *not* changing dimensions
    assert all(i.is_Float for i in Point(u).args)

    # never raise error if creating an origin
    assert Point(dim=3, on_morph='error')

    # raise error with unmatched dimension
    raises(ValueError, lambda: Point(1, 1, dim=3, on_morph='error'))
    # test unknown on_morph
    raises(ValueError, lambda: Point(1, 1, dim=3, on_morph='unknown'))
    # test invalid expressions
    raises(TypeError, lambda: Point(Basic(), Basic()))

def test_unit():
    assert Point(1, 1).unit == Point(sqrt(2)/2, sqrt(2)/2)


def test_dot():
    raises(TypeError, lambda: Point(1, 2).dot(Line((0, 0), (1, 1))))


def test__normalize_dimension():
    assert Point._normalize_dimension(Point(1, 2), Point(3, 4)) == [
        Point(1, 2), Point(3, 4)]
    assert Point._normalize_dimension(
        Point(1, 2), Point(3, 4, 0), on_morph='ignore') == [
        Point(1, 2, 0), Point(3, 4, 0)]


def test_issue_22684():
    # Used to give an error
    with evaluate(False):
        Point(1, 2)


def test_direction_cosine():
    p1 = Point3D(0, 0, 0)
    p2 = Point3D(1, 1, 1)

    assert p1.direction_cosine(Point3D(1, 0, 0)) == [1, 0, 0]
    assert p1.direction_cosine(Point3D(0, 1, 0)) == [0, 1, 0]
    assert p1.direction_cosine(Point3D(0, 0, pi)) == [0, 0, 1]

    assert p1.direction_cosine(Point3D(5, 0, 0)) == [1, 0, 0]
    assert p1.direction_cosine(Point3D(0, sqrt(3), 0)) == [0, 1, 0]
    assert p1.direction_cosine(Point3D(0, 0, 5)) == [0, 0, 1]

    assert p1.direction_cosine(Point3D(2.4, 2.4, 0)) == [sqrt(2)/2, sqrt(2)/2, 0]
    assert p1.direction_cosine(Point3D(1, 1, 1)) == [sqrt(3) / 3, sqrt(3) / 3, sqrt(3) / 3]
    assert p1.direction_cosine(Point3D(-12, 0 -15)) == [-4*sqrt(41)/41, -5*sqrt(41)/41, 0]

    assert p2.direction_cosine(Point3D(0, 0, 0)) == [-sqrt(3) / 3, -sqrt(3) / 3, -sqrt(3) / 3]
    assert p2.direction_cosine(Point3D(1, 1, 12)) == [0, 0, 1]
    assert p2.direction_cosine(Point3D(12, 1, 12)) == [sqrt(2) / 2, 0, sqrt(2) / 2]