def eval(cls, arg):
arg = sympify(arg)
if arg.is_Number:
if arg is S.NaN:
return S.NaN
elif arg is S.Infinity:
return S.Infinity
elif arg is S.NegativeInfinity:
return S.Infinity
elif arg is S.Zero:
return S.Pi*S.ImaginaryUnit / 2
elif arg is S.One:
return S.Zero
elif arg is S.NegativeOne:
return S.Pi*S.ImaginaryUnit
if arg.is_number:
cst_table = {
S.ImaginaryUnit : C.log(S.ImaginaryUnit*(1+sqrt(2))),
-S.ImaginaryUnit : C.log(-S.ImaginaryUnit*(1+sqrt(2))),
S.Half : S.Pi/3,
-S.Half : 2*S.Pi/3,
sqrt(2)/2 : S.Pi/4,
-sqrt(2)/2 : 3*S.Pi/4,
1/sqrt(2) : S.Pi/4,
-1/sqrt(2) : 3*S.Pi/4,
sqrt(3)/2 : S.Pi/6,
-sqrt(3)/2 : 5*S.Pi/6,
(sqrt(3)-1)/sqrt(2**3) : 5*S.Pi/12,
-(sqrt(3)-1)/sqrt(2**3) : 7*S.Pi/12,
sqrt(2+sqrt(2))/2 : S.Pi/8,
-sqrt(2+sqrt(2))/2 : 7*S.Pi/8,
sqrt(2-sqrt(2))/2 : 3*S.Pi/8,
-sqrt(2-sqrt(2))/2 : 5*S.Pi/8,
(1+sqrt(3))/(2*sqrt(2)) : S.Pi/12,
-(1+sqrt(3))/(2*sqrt(2)) : 11*S.Pi/12,
(sqrt(5)+1)/4 : S.Pi/5,
-(sqrt(5)+1)/4 : 4*S.Pi/5
}
if arg in cst_table:
if arg.is_real:
return cst_table[arg]*S.ImaginaryUnit
return cst_table[arg]
if arg is S.ComplexInfinity:
return S.Infinity
i_coeff = arg.as_coefficient(S.ImaginaryUnit)
if i_coeff is not None:
if _coeff_isneg(i_coeff):
return S.ImaginaryUnit * C.acos(i_coeff)
return S.ImaginaryUnit * C.acos(-i_coeff)
else:
if _coeff_isneg(arg):
return -cls(-arg)
def angle_between(l1, l2):
"""The angle formed between the two linear entities.
Parameters
----------
l1 : LinearEntity
l2 : LinearEntity
Returns
-------
angle : angle in radians
Notes
-----
From the dot product of vectors v1 and v2 it is known that:
dot(v1, v2) = |v1|*|v2|*cos(A)
where A is the angle formed between the two vectors. We can
get the directional vectors of the two lines and readily
find the angle between the two using the above formula.
Examples
--------
>>> from sympy import Point, Line
>>> p1, p2, p3 = Point(0, 0), Point(0, 4), Point(2, 0)
>>> l1, l2 = Line(p1, p2), Line(p1, p3)
>>> l1.angle_between(l2)
pi/2
"""
v1 = l1.p2 - l1.p1
v2 = l2.p2 - l2.p1
return C.acos((v1[0] * v2[0] + v1[1] * v2[1]) / (abs(v1) * abs(v2)))
def angle_between(l1, l2):
"""The angle formed between the two linear entities.
Parameters
----------
l1 : LinearEntity
l2 : LinearEntity
Returns
-------
angle : angle in radians
Notes
-----
From the dot product of vectors v1 and v2 it is known that:
dot(v1, v2) = |v1|*|v2|*cos(A)
where A is the angle formed between the two vectors. We can
get the directional vectors of the two lines and readily
find the angle between the two using the above formula.
Examples
--------
>>> from sympy import Point, Line
>>> p1, p2, p3 = Point(0, 0), Point(0, 4), Point(2, 0)
>>> l1, l2 = Line(p1, p2), Line(p1, p3)
>>> l1.angle_between(l2)
pi/2
"""
v1 = l1.p2 - l1.p1
v2 = l2.p2 - l2.p1
return C.acos((v1[0]*v2[0] + v1[1]*v2[1]) / (abs(v1)*abs(v2)))
def angle_between(l1, l2):
"""
Returns an angle formed between the two linear entities.
Description of Method Used:
===========================
From the dot product of vectors v1 and v2 it is known that:
dot(v1, v2) = |v1|*|v2|*cos(A)
where A is the angle formed between the two vectors. We can
get the directional vectors of the two lines and readily
find the angle between the two using the above formula.
"""
v1 = l1.p2 - l1.p1
v2 = l2.p2 - l2.p1
return C.acos((v1[0] * v2[0] + v1[1] * v2[1]) / (abs(v1) * abs(v2)))
def angle_between(l1, l2):
"""
Returns an angle formed between the two linear entities.
Description of Method Used:
===========================
From the dot product of vectors v1 and v2 it is known that:
dot(v1, v2) = |v1|*|v2|*cos(A)
where A is the angle formed between the two vectors. We can
get the directional vectors of the two lines and readily
find the angle between the two using the above formula.
"""
v1 = l1.p2 - l1.p1
v2 = l2.p2 - l2.p1
return C.acos( (v1[0]*v2[0]+v1[1]*v2[1]) / (abs(v1)*abs(v2)) )
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 sympy 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 sympy.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 C.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 C.acos(c/(d*e))
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 sympy 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 sympy.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 C.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 C.acos(c/(d*e))
def angle_between(l1, l2):
"""The angle formed between the two linear entities.
Parameters
==========
l1 : LinearEntity
l2 : LinearEntity
Returns
=======
angle : angle in radians
Notes
=====
From the dot product of vectors v1 and v2 it is known that:
``dot(v1, v2) = |v1|*|v2|*cos(A)``
where A is the angle formed between the two vectors. We can
get the directional vectors of the two lines and readily
find the angle between the two using the above formula.
See Also
========
is_perpendicular
Examples
========
>>> from sympy import Point3D, Line3D
>>> p1, p2, p3 = Point3D(0, 0, 0), Point3D(1, 1, 1), Point3D(-1, 2, 0)
>>> l1, l2 = Line3D(p1, p2), Line3D(p2, p3)
>>> l1.angle_between(l2)
acos(-sqrt(2)/3)
"""
v1 = l1.p2 - l1.p1
v2 = l2.p2 - l2.p1
return C.acos(v1.dot(v2)/(abs(v1)*abs(v2)))
def angle_between(l1, l2):
"""The angle formed between the two linear entities.
Parameters
==========
l1 : LinearEntity
l2 : LinearEntity
Returns
=======
angle : angle in radians
Notes
=====
From the dot product of vectors v1 and v2 it is known that:
``dot(v1, v2) = |v1|*|v2|*cos(A)``
where A is the angle formed between the two vectors. We can
get the directional vectors of the two lines and readily
find the angle between the two using the above formula.
See Also
========
is_perpendicular
Examples
========
>>> from sympy import Point3D, Line3D
>>> p1, p2, p3 = Point3D(0, 0, 0), Point3D(1, 1, 1), Point3D(-1, 2, 0)
>>> l1, l2 = Line3D(p1, p2), Line3D(p2, p3)
>>> l1.angle_between(l2)
acos(-sqrt(2)/3)
"""
v1 = l1.p2 - l1.p1
v2 = l2.p2 - l2.p1
return C.acos(v1.dot(v2) / (abs(v1) * abs(v2)))
