def test_repr():
x = Point(1, 2, 3)
assert str(x) == "(1.00, 2.00, 3.00)"
y = Point(0, 4 + 3j, 7)
assert str(y) == "(0.00, 4.00 + 3.00j, 7.00)"
def test_dimension():
x = Point(1, 2, 3)
assert x.dimension == 3
y = Point(1, 2, z=3, x=4, n=5)
assert y.dimension == 5
def test_point_initialization():
x = Point(1, 2, 3)
assert (str(type(x))) == "<class 'geometry.base.3D Point'>"
y = Point(4, 1, 2, 3)
assert (str(type(y))) == "<class 'geometry.base.4D Point'>"
def test_point_key_lookup_set():
x = Point(x=1, y=2, z=3)
x.x = 4
x.y = 5
x.z = 6
assert x.x == 4
assert x.y == 5
assert x.z == 6
def generatePoints(dim):
""" generate base points for dodecaeder """
pm = (-1, 1)
PHI=(1+math.sqrt(5))/2
phi = [0, 1/PHI, PHI]
for i in range(8):
yield Point(pm[(i>>j)&1] for j in range(3))
for j in range(3):
for i in range(4):
yield Point(pm[(i>>((k+j-1)%3))&1]*phi[(k+j)%3] for k in range(3))
def test_signature():
x = Point(1, 2, 3)
y = Point(x=1, y=2, z=3)
assert x.signature != y.signature
z = Point(4, 5, 6)
w = Point(x=4, y=5, z=6)
assert x.signature == z.signature
assert y.signature == w.signature
def generatePoints(dim):
"""
Generate base points for n-octaeder
The points are the set of +1, -1 points on each axis.
Points are yielded such that p[2*i] and p[2*i+1] are on the
same axis.
"""
for i in range(dim):
yield Point(1 if i==j else 0 for j in range(dim))
yield Point(-1 if i==j else 0 for j in range(dim))
def generatePoints(dim):
""" generate base points for n-tetraeder """
CENTER = (1.0+dim+math.sqrt(1.0+dim))/((1.0+dim)*dim)
p0= Point(CENTER for _ in range(dim))
# first points along axis
for i in range(dim):
yield Point(1 if i==j else 0 for j in range(dim))-p0
# and a single point at equal distance from others
yield Point((1+math.sqrt(dim+1))/dim for j in range(dim))-p0
def generatePoints1(dim):
assert(dim==4)
def bit(x,i):
return -1.0 if x&(1<<i) else 1.0
# (0,0,0,1) -> 4 * 2
for i in range(4):
for b in range(2):
yield Point(bit(b,0) if i==j else 0 for j in range(4))
# (0.5,0.5,0.5,0.5) -> 1 * 16
for i in range(16):
yield Point(0.5*bit(i,j) for j in range(4))
def generatePoints(dim):
""" generate base points for icosaeder """
pm = (-0.5, 0.5)
PHI=(1+math.sqrt(5))/2
phi = [0, 1.0, PHI]
for j in range(3):
for i in range(4):
yield Point(pm[(i>>((k+j-1)%3))&1]*phi[(k+j)%3] for k in range(3))
def doshape(self, cls, dim, npoints, nlines, edgelen):
""" count nr points, lines, edge size for shape """
t = cls(Point(0 for x in range(dim)))
self.assertEqual(len(t.points), npoints)
count = 0
for a, b in t.generateLines():
count += 1
self.assertAlmostEqual(t.points[a].distance(t.points[b]), edgelen)
self.assertEqual(count, nlines)
def test_point_mixed_addressing():
x = Point(1, y=2, z=3)
assert x[2] == x.z == 3
x[1] = 4
assert x.y == 4
assert x[0] == 1
def test_vector_initialization():
x = Point(1, 2, 3)
x_v = Vector(x)
assert (str(type(x_v))) == "<class 'geometry.base.3D Vector'>"
y = Vector(4, 1, 2, 3)
assert (str(type(y))) == "<class 'geometry.base.4D Vector'>"
def test_point_indexing_set():
x = Point(1, 2, 3)
x[0] = 4
x[1] = 5
x[2] = 6
assert x[0] == 4
assert x[1] == 5
assert x[2] == 6
def generatePoints(dim):
"""
Generate base points for n-cube.
Each point is assigned a binary number,
the bits form the coordinates.
"""
def bit(x,i):
return -1.0 if x&(1<<i) else 1.0
for i in range(1<<dim):
yield Point(bit(i,j)*0.5 for j in range(dim))
def dumppolar(dim, cls):
""" dump named points and polar representations of shape """
center = Point(0 for _ in range(dim))
count = 0
for pt in cls.generatePoints(dim):
center += pt
count += 1
center /= count
print("center = %.16f" % center.coord[0], namedpt(center), cls)
for pt in cls.generatePoints(dim):
pt -= center
print("%-40s -- %-40s" % (namedpt(pt), namedpt(pt.toNSpherical())))
def generatePoints(dim):
assert(dim==4)
def bit(x,i):
return -1.0 if x&(1<<i) else 1.0
# (1,1,0,0) -> 4 * 6
for a in range(1,4):
for b in range(a):
for i in range(4):
p= [0 for _ in range(4)]
p[a]= bit(i,0)/math.sqrt(2.0)
p[b]= bit(i,1)/math.sqrt(2.0)
yield Point(p)
def test_equality():
x = Point(1, 2, 3)
y = Point(1, 2, 3)
q = Point(4, 5, 6)
z = Point(x=1, y=2, z=3)
w = Point(x=1, y=2, z=3)
assert x == y
assert z == w
assert x != q
caught_exception = None
try:
assert x == z
except TypeError as e:
caught_exception = e
finally:
assert caught_exception is not None
def generatePoints(dim):
assert(dim==4)
SQ5 = math.sqrt(5.0)
PHI = (1.0+SQ5)/2.0
def bit(x,i):
return -1.0 if x&(1<<i) else 1.0
# (0.5,0.5,0.5,0.5) -> 1 * 16
for i in range(16):
yield Point(0.5*bit(i,j) for j in range(4))
# (0,0,0,1) -> 4 * 2
for i in range(4):
for b in range(2):
yield Point(bit(b,0) if i==j else 0 for j in range(4))
# even perms of:
# (PHI, 1, 1/PHI, 0)/2 -> 12 * 8
for a in range(8):
p0= (0, bit(a,2)*PHI/2.0, bit(a,1)/2.0, bit(a,0)/2.0/PHI)
for perm in ( (0,1,2,3), (0,2,3,1), (0,3,1,2), (1,0,3,2), (1,2,0,3), (1,3,2,0), (2,0,1,3), (2,1,3,0), (2,3,0,1), (3,0,2,1), (3,1,0,2), (3,2,1,0)):
yield Point(p0[perm[0]], p0[perm[1]], p0[perm[2]], p0[perm[3]])
def generatePoints(dim):
assert(dim==4)
SQ5 = math.sqrt(5.0)
PHI = (1.0+SQ5)/2.0
def bit(x,i):
return -1.0 if x&(1<<i) else 1.0
# perms of:
# 0022 0202 0220 2020 2200 2002
# (0,0,2, 2) -> 4*6
for a in range(1,4):
for b in range(a):
for i in range(4):
p= [0 for _ in range(4)]
p[a]= 2.0*bit(i,0)
p[b]= 2.0*bit(i,1)
yield Point(p)
# 0001 0010 0100 1000
# (1,1,1,SQ5) -> 16*4
# (PHI**-2, PHI,PHI,PHI) -> 16*4
# (PHI**-1, PHI**-1,PHI**-1, PHI**2) -> 16*4
for a in range(16):
for i in range(4):
yield Point(bit(a,j)*(SQ5 if i==j else 1.0) for j in range(4))
yield Point(bit(a,j)*(PHI**-2 if i==j else PHI) for j in range(4))
yield Point(bit(a,j)*(PHI**2 if i==j else PHI**-1) for j in range(4))
# even perms of:
# 0123 0231 0312 1032 1203 1320 2013 2130 2301 3021 3102 3210
# (0, PHI**-2, 1, PHI**2) -> 12*8
# (0, PHI**-1, PHI, SQ5) -> 12*8
# (PHI**-1, 1, PHI, 2) -> 12*16
for a in range(16):
p0= (0, bit(a,2)*PHI**-2, bit(a,1), bit(a,0)*PHI**2)
p1= (0, bit(a,2)*PHI**-1, bit(a,1)*PHI, bit(a,0)*SQ5)
p2= (bit(a,3)*PHI**-1, bit(a,2), bit(a,1)*PHI, bit(a,0)*2.0)
for perm in ( (0,1,2,3), (0,2,3,1), (0,3,1,2), (1,0,3,2), (1,2,0,3), (1,3,2,0), (2,0,1,3), (2,1,3,0), (2,3,0,1), (3,0,2,1), (3,1,0,2), (3,2,1,0)):
if a<8:
yield Point(p0[perm[0]], p0[perm[1]], p0[perm[2]], p0[perm[3]])
yield Point(p1[perm[0]], p1[perm[1]], p1[perm[2]], p1[perm[3]])
yield Point(p2[perm[0]], p2[perm[1]], p2[perm[2]], p2[perm[3]])
def test_point_key_lookup_get():
x = Point(x=1, y=2, z=3)
assert x.x == 1
assert x.y == 2
assert x.z == 3
def test_hash():
x = Point(1, 2, 3)
y = Point(1, 2, 3)
w = Point(3, 4, 5, 6)
z = Point(x=1, y=2, z=3)
assert x.__hash__() == y.__hash__()
assert x.__hash__() != z.__hash__()
assert x.__hash__() != w.__hash__()
def test_point_indexing_get():
x = Point(1, 2, 3)
assert x[0] == 1
assert x[1] == 2
assert x[2] == 3