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)
pytest.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.evalf(2), b.evalf(2))
pytest.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
pytest.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) is True
assert Point3D.are_coplanar(p, planar2, planar3, p3) is False
pytest.raises(ValueError, lambda: Point3D.are_coplanar(p, planar2))
planar2 = Point3D(1, 1, 2)
planar3 = Point3D(1, 1, 3)
pytest.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)
pytest.raises(ValueError, lambda: p.transform(p))
pytest.raises(ValueError, lambda: p.transform(Matrix([[1, 0], [0, 1]])))
# Test Equals
assert p.equals(x1) is False
# Test __sub__
p_2d = Point(0, 0)
pytest.raises(ValueError, lambda: (p - p_2d))
def test_sympyissue_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_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)
pytest.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.evalf(2), b.evalf(2))
pytest.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
pytest.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) is True
assert Point3D.are_coplanar(p, planar2, planar3, p3) is False
pytest.raises(ValueError, lambda: Point3D.are_coplanar(p, planar2))
planar2 = Point3D(1, 1, 2)
planar3 = Point3D(1, 1, 3)
pytest.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)
pytest.raises(ValueError, lambda: p.transform(p))
pytest.raises(ValueError, lambda: p.transform(Matrix([[1, 0], [0, 1]])))
# Test Equals
assert p.equals(x1) is False
# Test __sub__
p_2d = Point(0, 0)
pytest.raises(ValueError, lambda: (p - p_2d))
def test_sympyissue_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