def _contains(self, other):
if not is_Tuple(other) or len(other) != 3:
return false
v = Mat(other)
p = v - self.center
if self.closed:
return norm(cross(p, self.direction)) <= self.slope*dot(p, self.direction)
else:
return norm(cross(p, self.direction)) < self.slope*dot(p, self.direction)
def _contains(self, other):
if not is_Tuple(other) or len(other) != 3:
return false
v = Mat(other)
p = v - self.center
if self.closed:
return norm(cross(p, self.direction))**2 <= self.radius**2
else:
return norm(cross(p, self.direction))**2 < self.radius**2
def rquat2rmat(rquat):
"""
>>> from sympy import *
>>> from symplus.strplus import init_mprinting
>>> init_mprinting()
>>> t = Symbol('t', positive=True)
>>> simplify(rquat2rmat(rquat(pi/3, i+j)))
<BLANKLINE>
[ 3/4 1/4 sqrt(6)/4]
[ 1/4 3/4 -sqrt(6)/4]
[-sqrt(6)/4 sqrt(6)/4 1/2]
>>> simplify(rquat2rmat(rquat(t, i)))
<BLANKLINE>
[1 0 0]
[0 cos(t) -sin(t)]
[0 sin(t) cos(t)]
>>> simplify(rquat2rmat(rquat(t, i+k)))
<BLANKLINE>
[ cos(t/2)**2 -sqrt(2)*sin(t)/2 sin(t/2)**2]
[sqrt(2)*sin(t)/2 cos(t) -sqrt(2)*sin(t)/2]
[ sin(t/2)**2 sqrt(2)*sin(t)/2 cos(t/2)**2]
"""
w = rquat[0]
xyz = Mat(rquat[1:])
return (1-2*norm(xyz)**2)*eye3 + 2*xyz*xyz.T + 2*w*cross(xyz)
def qmult(q1, q2):
"""
>>> from sympy import *
>>> from symplus.strplus import init_mprinting
>>> init_mprinting()
>>> q1 = rquat(pi/2, i)
>>> q2 = rquat(pi/3, j)
>>> rquat2rmat(q1) * rquat2rmat(q2)
<BLANKLINE>
[ 1/2 0 sqrt(3)/2]
[sqrt(3)/2 0 -1/2]
[ 0 1 0]
>>> rquat2rmat(qmult(q1, q2))
<BLANKLINE>
[ 1/2 0 sqrt(3)/2]
[sqrt(3)/2 0 -1/2]
[ 0 1 0]
"""
w1 = q1[0]
xyz1 = Mat(q1[1:])
w2 = q2[0]
xyz2 = Mat(q2[1:])
w = w1*w2 - dot(xyz1, xyz2)
xyz = w1*xyz2 + w2*xyz1 + cross(xyz1, xyz2)
return Mat([w] + xyz[:])
def as_abstract(self):
"""
>>> from sympy import *
>>> from symplus.strplus import init_mprinting
>>> init_mprinting()
>>> SemiInfiniteCone().as_abstract()
{(x, y, z) | sqrt(x**2 + y**2) < z}
>>> SemiInfiniteCone(5, [0,0,0], [3,4,0]).as_abstract()
{(x, y, z) | sqrt(z**2 + (4*x/5 - 3*y/5)**2) < 3*x + 4*y}
"""
p = r - self.center
if self.closed:
expr = norm(cross(p, self.direction)) <= self.slope*dot(p, self.direction)
else:
expr = norm(cross(p, self.direction)) < self.slope*dot(p, self.direction)
return AbstractSet((x,y,z), expr)
def as_abstract(self):
"""
>>> from sympy import *
>>> from symplus.strplus import init_mprinting
>>> init_mprinting()
>>> InfiniteCylinder().as_abstract()
{(x, y, z) | x**2 + y**2 < 1}
>>> InfiniteCylinder(2, [0,0,0], [0,1,1]).as_abstract()
{(x, y, z) | x**2 + (-sqrt(2)*y/2 + sqrt(2)*z/2)**2 < 4}
"""
p = r - self.center
if self.closed:
expr = norm(cross(p, self.direction))**2 <= self.radius**2
else:
expr = norm(cross(p, self.direction))**2 < self.radius**2
return AbstractSet((x,y,z), expr)
def rmat_k2d(d):
d = normalize(d)
if d == k:
rot = eye(3)
elif d == -k:
rot = diag(1,-1,-1)
else:
rot = rquat2rmat(rquat(acos(dot(k, d)), cross(k, d)))
return rot
def as_abstract(self):
"""
>>> from sympy import *
>>> from symplus.strplus import init_mprinting
>>> init_mprinting()
>>> Revolution(lambda h, s: h**2<s**2).as_abstract()
{(x, y, z) | z**2 < x**2 + y**2}
>>> Revolution(lambda h, s: h+1<s**2, [0,0,0], [3,4,0]).as_abstract()
{(x, y, z) | 3*x/5 + 4*y/5 + 1 < z**2 + (4*x/5 - 3*y/5)**2}
"""
p = r - self.center
expr = self.func(dot(p, self.direction), norm(cross(p, self.direction)))
return AbstractSet((x,y,z), expr)
def _contains(self, other):
if not is_Tuple(other) or len(other) != 3:
return false
v = Mat(other)
p = v - self.center
return self.func(dot(p, self.direction), norm(cross(p, self.direction)))
