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 zvec2zmat(zvec):
"""
>>> from sympy import *
>>> from symplus.strplus import init_mprinting
>>> init_mprinting()
>>> zvec2zmat(j*3)
<BLANKLINE>
[1 0 0]
[0 3 0]
[0 0 1]
>>> zvec2zmat(i-j)
<BLANKLINE>
[ 1/2 + sqrt(2)/2 -sqrt(2)/2 + 1/2 0]
[-sqrt(2)/2 + 1/2 1/2 + sqrt(2)/2 0]
[ 0 0 1]
>>> t,r,p,z,s = aff2trpzs(augment(m=_))
>>> simplify(r)
[2**(1/4)*3**(3/4)*sqrt(1 + sqrt(2) + sqrt(6))/6 0 0 (-6**(3/4) + 54**(1/4))/(6*sqrt(1 + sqrt(2) + sqrt(6)))]'
>>> simplify(z)
[sqrt(6)/2 2*sqrt(3)/3 1]'
>>> simplify(s)
[-1/3 0 0]'
"""
zvec = Mat(zvec)
nvec = normalize(zvec)
zfac = norm(zvec)
return eye3 + nvec*nvec.T*(zfac-1)
def __new__(cls, func, center=[0,0,0], direction=[0,0,1], **kwargs):
center = Mat(center)
direction = Mat(direction)
if norm(direction) == 0:
raise ValueError
direction = normalize(direction)
return Basic.__new__(cls, func, center, direction)
def __new__(cls, radius=1, center=[0,0,0], direction=[0,0,1], closed=False, **kwargs):
"""
>>> from sympy import *
>>> from symplus.strplus import init_mprinting
>>> init_mprinting()
>>> InfiniteCylinder()
InfiniteCylinder(1, [0 0 0]', [0 0 1]', False)
>>> InfiniteCylinder(2, [0,0,0], [0,1,1])
InfiniteCylinder(2, [0 0 0]', [0 -sqrt(2)/2 -sqrt(2)/2]', False)
>>> InfiniteCylinder().contains((1,1,1))
False
>>> InfiniteCylinder(2, [0,0,0], [0,1,1]).contains((1,1,1))
True
"""
normalization = kwargs.pop("normalization", True)
radius = sympify(abs(radius))
direction = Mat(direction)
if normalization:
if norm(direction) == 0:
raise ValueError
direction = simplify(normalize(direction))
direction = max(direction, -direction, key=hash)
center = Mat(center)
if normalization:
center = simplify(center - project(center, direction))
closed = sympify(bool(closed))
return Basic.__new__(cls, radius, center, direction, closed)
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 __new__(cls, radius=1, height=2, center=[0,0,0], direction=[0,0,1], closed=False, **kwargs):
normalization = kwargs.pop("normalization", True)
radius = sympify(abs(radius))
height = sympify(abs(height))
center = Mat(center)
direction = Mat(direction)
if normalization:
if norm(direction) == 0:
raise ValueError
direction = simplify(normalize(direction))
direction = max(direction, -direction, key=hash)
closed = sympify(bool(closed))
return Basic.__new__(cls, radius, height, center, direction, closed)
def fvec2fmat(fvec):
"""
>>> from sympy import *
>>> from symplus.strplus import init_mprinting
>>> init_mprinting()
>>> fvec2fmat(i)
<BLANKLINE>
[-1 0 0]
[ 0 1 0]
[ 0 0 1]
>>> fvec2fmat(i-sqrt(2)*j)
<BLANKLINE>
[ 1/3 2*sqrt(2)/3 0]
[2*sqrt(2)/3 -1/3 0]
[ 0 0 1]
>>> t,r,p,z,s = aff2trpzs(augment(m=_))
>>> r
[0 sqrt(3)/3 -sqrt(6)/3 0]'
>>> p
-1
"""
fvec = normalize(Mat(fvec))
return eye3 - fvec*fvec.T*2
def __new__(cls, offset=0, direction=[0,0,1], closed=False, **kwargs):
"""
>>> from sympy import *
>>> from symplus.strplus import init_mprinting
>>> init_mprinting()
>>> Halfspace()
Halfspace(0, [0 0 1]', False)
>>> Halfspace(3, [1,2,0])
Halfspace(3, [sqrt(5)/5 2*sqrt(5)/5 0]', False)
>>> Halfspace().contains((1,2,3))
True
>>> Halfspace(3, [1,2,0]).contains((1,2,3))
False
"""
normalization = kwargs.pop("normalization", True)
offset = sympify(offset)
direction = Mat(direction)
if normalization:
if norm(direction) == 0:
raise ValueError
direction = simplify(normalize(direction))
closed = sympify(bool(closed))
return Basic.__new__(cls, offset, direction, closed)
def __new__(cls, slope=1, center=[0,0,0], direction=[0,0,1], closed=False, **kwargs):
"""
>>> from sympy import *
>>> from symplus.strplus import init_mprinting
>>> init_mprinting()
>>> SemiInfiniteCone()
SemiInfiniteCone(1, [0 0 0]', [0 0 1]', False)
>>> SemiInfiniteCone(5, [0,0,0], [3,4,0])
SemiInfiniteCone(5, [0 0 0]', [3/5 4/5 0]', False)
>>> SemiInfiniteCone().contains((-1,0,2))
True
>>> SemiInfiniteCone(5, [0,0,0], [3,4,0]).contains((-1,0,1))
False
"""
normalization = kwargs.pop("normalization", True)
slope = sympify(abs(slope))
center = Mat(center)
direction = Mat(direction)
if normalization:
if norm(direction) == 0:
raise ValueError
direction = simplify(normalize(direction))
closed = sympify(bool(closed))
return Basic.__new__(cls, slope, center, direction, closed)
def rquat(th, axis):
axis = Mat(axis)
return Mat([cos(th/2)]).col_join(sin(th/2)*normalize(axis))
