def distance(self, o):
"""Distance between the plane and another geometric entity.
Parameters
==========
Point3D, LinearEntity3D, Plane.
Returns
=======
distance
Notes
=====
This method accepts only 3D entities as it's parameter, but if you want
to calculate the distance between a 2D entity and a plane you should
first convert to a 3D entity by projecting onto a desired plane and
then proceed to calculate the distance.
Examples
========
>>> from diofant import Point, Point3D, Line, Line3D, Plane
>>> a = Plane(Point3D(1, 1, 1), normal_vector=(1, 1, 1))
>>> b = Point3D(1, 2, 3)
>>> a.distance(b)
sqrt(3)
>>> c = Line3D(Point3D(2, 3, 1), Point3D(1, 2, 2))
>>> a.distance(c)
0
"""
from diofant.geometry.line3d import LinearEntity3D
x, y, z = map(Dummy, 'xyz')
if self.intersection(o) != []:
return S.Zero
if isinstance(o, Point3D):
x, y, z = map(Dummy, 'xyz')
k = self.equation(x, y, z)
a, b, c = [k.coeff(i) for i in (x, y, z)]
d = k.xreplace({x: o.args[0], y: o.args[1], z: o.args[2]})
t = abs(d / sqrt(a**2 + b**2 + c**2))
return t
if isinstance(o, LinearEntity3D):
a, b = o.p1, self.p1
c = Matrix(a.direction_ratio(b))
d = Matrix(self.normal_vector)
e = c.dot(d)
f = sqrt(sum(i**2 for i in self.normal_vector))
return abs(e / f)
if isinstance(o, Plane):
a, b = o.p1, self.p1
c = Matrix(a.direction_ratio(b))
d = Matrix(self.normal_vector)
e = c.dot(d)
f = sqrt(sum(i**2 for i in self.normal_vector))
return abs(e / f)
def angle_between(self, o):
"""Angle between the plane and other geometric entity.
Parameters
==========
LinearEntity3D, Plane.
Returns
=======
angle : angle in radians
Notes
=====
This method accepts only 3D entities as it's parameter, but if you want
to calculate the angle between a 2D entity and a plane you should
first convert to a 3D entity by projecting onto a desired plane and
then proceed to calculate the angle.
Examples
========
>>> from diofant import Point3D, Line3D, Plane
>>> a = Plane(Point3D(1, 2, 2), normal_vector=(1, 2, 3))
>>> b = Line3D(Point3D(1, 3, 4), Point3D(2, 2, 2))
>>> a.angle_between(b)
-asin(sqrt(21)/6)
"""
from diofant.geometry.line3d import LinearEntity3D
if isinstance(o, LinearEntity3D):
a = Matrix(self.normal_vector)
b = Matrix(o.direction_ratio)
c = a.dot(b)
d = sqrt(sum(i**2 for i in self.normal_vector))
e = sqrt(sum(i**2 for i in o.direction_ratio))
return asin(c / (d * e))
if isinstance(o, Plane):
a = Matrix(self.normal_vector)
b = Matrix(o.normal_vector)
c = a.dot(b)
d = sqrt(sum(i**2 for i in self.normal_vector))
e = sqrt(sum(i**2 for i in o.normal_vector))
return acos(c / (d * e))
def is_perpendicular(self, l):
"""is the given geometric entity perpendicular to the given plane?
Parameters
==========
LinearEntity3D or Plane
Returns
=======
Boolean
Examples
========
>>> from diofant import Plane, Point3D
>>> a = Plane(Point3D(1,4,6), normal_vector=(2, 4, 6))
>>> b = Plane(Point3D(2, 2, 2), normal_vector=(-1, 2, -1))
>>> a.is_perpendicular(b)
True
"""
from diofant.geometry.line3d import LinearEntity3D
if isinstance(l, LinearEntity3D):
a = Matrix(l.direction_ratio)
b = Matrix(self.normal_vector)
if a.cross(b).is_zero:
return True
else:
return False
elif isinstance(l, Plane):
a = Matrix(l.normal_vector)
b = Matrix(self.normal_vector)
if a.dot(b) == 0:
return True
else:
return False
else:
return False