code: 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)
  
imports: 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
label_desc: Use image node_id 2 for calling a global function with example usage: test_point3D() without return types