def _contains(self, other):
if not is_Tuple(other) or len(other) != 3:
return false
v = Mat(other)
if self.closed:
return dot(v, self.direction) >= self.offset
else:
return dot(v, self.direction) > self.offset
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 as_abstract(self):
"""
>>> from sympy import *
>>> from symplus.strplus import init_mprinting
>>> init_mprinting()
>>> Halfspace().as_abstract()
{(x, y, z) | z > 0}
>>> Halfspace(3, [1,2,0]).as_abstract()
{(x, y, z) | sqrt(5)*x/5 + 2*sqrt(5)*y/5 > 3}
"""
if self.closed:
expr = dot(r, self.direction) >= self.offset
else:
expr = dot(r, self.direction) > self.offset
return AbstractSet((x,y,z), expr)
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 mn2smat(mvec, nvec):
"""
>>> from sympy import *
>>> from symplus.strplus import init_mprinting
>>> init_mprinting()
>>> mn2smat(i,j)
<BLANKLINE>
[1 1 0]
[0 1 0]
[0 0 1]
>>> mn2smat(i-j+2*k,2*j+k)
<BLANKLINE>
[1 2 1]
[0 -1 -1]
[0 4 3]
>>> t,r,p,z,s = aff2trpzs(augment(m=_))
>>> simplify(r)
[sqrt(-34*sqrt(17) + 578)/34 2*sqrt(2)/sqrt(-sqrt(17) + 17) 0 0]'
>>> simplify(z)
[1 sqrt(17) sqrt(17)/17]'
>>> simplify(s)
[2 1 13/17]'
"""
mvec = Mat(mvec)
nvec = Mat(nvec)
mvec = mvec - dot(mvec, normalize(nvec)) * normalize(nvec)
return eye3 + mvec*nvec.T
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 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 _image(self, func):
if isinstance(func, EuclideanTransformation):
direction = simplify(qrotate(func.rquat, func.parity*self.direction))
offset = simplify(self.offset + dot(func.tvec, direction))
closed = self.closed
return Halfspace(
offset=offset,
direction=direction,
closed=closed,
normalization=False)
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 as_algebraic(self):
coffset = dot(self.center, self.direction)
return Intersection(
SemiInfiniteCone(
slope=self.radius/self.height,
center=self.center,
direction=self.direction,
closed=self.closed,
normalization=False),
Halfspace(
offset=-coffset - self.height,
direction=-self.direction,
closed=self.closed,
normalization=False))
def as_algebraic(self):
center = simplify(self.center - project(self.center, self.direction))
coffset = dot(self.center, self.direction)
return Intersection(
InfiniteCylinder(
radius=self.radius,
center=center,
direction=self.direction,
closed=self.closed,
normalization=False),
Halfspace(
offset= coffset - self.height/sympify(2),
direction= self.direction,
closed=self.closed,
normalization=False),
Halfspace(
offset=-coffset - self.height/sympify(2),
direction=-self.direction,
closed=self.closed,
normalization=False))
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)))