def chk_tri_ell_hy(myck):
"""[summary]
Arguments:
myck (type): [description]
K (type): [description]
Raises:
NotImplementedError -- [description]
NotImplementedError -- [description]
"""
a1 = pg_point([33, 121, 54])
a2 = pg_point([33, 564, 34])
a3 = pg_point([34, 64, -62])
temp = myck.perp(a1)
triangle = [a1, a2, a3]
trilateral = tri_dual(triangle)
l1, _, _ = trilateral
Q = myck.tri_quadrance(triangle)
S = myck.tri_spread(trilateral)
a4 = plucker(2, a1, 3, a2)
collin = [a1, a2, a4]
Q2 = myck.tri_quadrance(collin)
assert myck.perp(temp) == a1
assert myck.perp(myck.perp(l1)) == l1
assert myck.quadrance(a1, a1) == 0
assert myck.spread(l1, l1) == 0
assert check_cross_law(S, Q[2]) == 0
assert check_cross_law(Q, S[2]) == 0
assert check_cross_TQF(Q2) == 0
def test_persp():
Ire = pg_point([0, 1, 1])
Iim = pg_point([1, 0, 0])
l_inf = pg_line([0, -1, 1])
P = persp_euclid_plane(Ire, Iim, l_inf)
chk_ck(P, pg_point)
chk_degenerate(P)
def chk_euclid(K):
"""[summary]
Arguments:
K (type): [description]
Raises:
NotImplementedError -- [description]
NotImplementedError -- [description]
"""
a1 = pg_point([31, -53, 1])
a2 = pg_point([6, 23, 21])
a3 = pg_point([5, -43, 31])
triangle = [a1, a2, a3]
trilateral = tri_dual(triangle)
l1, l2, l3 = trilateral
t1, t2, t3 = tri_altitude(triangle)
t4 = harm_conj(t1, t2, t3)
o = orthocenter(triangle)
tau = reflect(l1)
m23, m13, m12 = tri_midpoint(triangle)
mt1 = a1 * m23
mt2 = a2 * m13
mt3 = a3 * m12
q1, q2, q3 = tri_quadrance(triangle)
s1, s2, s3 = tri_spread(trilateral)
tqf = ((q1 + q2 + q3)**2) - 2 * (q1 * q1 + q2 * q2 + q3 * q3)
tsf = (s1 + s2 +
s3)**2 - 2 * (s1 * s1 + s2 * s2 + s3 * s3) - 4 * s1 * s2 * s3
c3 = ((q1 + q2 - q3)**2) / (4 * q1 * q2)
a4 = plucker(3, a1, 4, a2)
qq1, qq2, qq3 = tri_quadrance([a1, a2, a4])
tqf2 = Ar(qq1, qq2, qq3) # get 0
assert not is_parallel(l1, l2)
assert not is_parallel(l2, l3)
assert is_perpendicular(t1, l1)
assert spread(t1, l1) == 1 # get 1
assert coincident(t1, t2, t3)
assert R(t1, t2, t3, t4) == -1
assert o == meet(t2, t3)
assert a1 == orthocenter([o, a2, a3])
assert tau(tau(a1)) == a1
assert coincident(mt1, mt2, mt3)
assert spread(l1, l1) == 0
assert quadrance(a1, a1) == 0
assert cross_s(l1, l2) == c3
assert c3 + s3 == 1 # get the same
assert tqf == Ar(q1, q2, q3)
assert tsf == 0
assert tqf2 == 0
def test_special_case(px, py, pz, Lx, Ly, Lz):
p = pg_point([px, py, pz])
L = pg_line([Lx, Ly, Lz])
# L_inf = pg_line([0, 0, 1])
L_nan = pg_line([0, 0, 0])
p_nan = pg_point([0, 0, 0])
assert L_nan.is_NaN()
assert L_nan == L_nan
assert L_nan == p * p # join two equal points
assert p_nan == L * L
assert L_nan == p_nan * p
assert p_nan == L_nan * L
assert p.incident(L_nan)
assert L.incident(p_nan)
assert p_nan.incident(L_nan)
def chk_degenerate(myck):
"""[summary]
Arguments:
myck (type): [description]
K (type): [description]
Raises:
NotImplementedError -- [description]
NotImplementedError -- [description]
"""
a1 = pg_point([-1, 2, 3])
a2 = pg_point([4, -1, 1])
a3 = pg_point([0, -1, 1])
triangle = [a1, a2, a3]
trilateral = tri_dual(triangle)
l1, l2, l3 = trilateral
m23, m13, m12 = myck.tri_midpoint(triangle)
t1 = a1 * m23
t2 = a2 * m13
t3 = a3 * m12
q1, q2, q3 = myck.tri_quadrance(triangle)
s1, s2, s3 = myck.tri_spread(trilateral)
tqf = ((q1 + q2 + q3)**2) - 2 * (q1 * q1 + q2 * q2 + q3 * q3)
tsf = (s1 + s2 +
s3)**2 - 2 * (s1 * s1 + s2 * s2 + s3 * s3) - 4 * s1 * s2 * s3
a4 = plucker(3, a1, 4, a2)
qq1, qq2, qq3 = myck.tri_quadrance([a1, a2, a4])
tqf2 = Ar(qq1, qq2, qq3) # get 0
assert not myck.is_parallel(l1, l2)
assert not myck.is_parallel(l2, l3)
assert coincident(t1, t2, t3)
assert tqf == Ar(q1, q2, q3)
assert tsf == 0
assert tqf2 == 0
def no_test_symbolic():
import sympy
sympy.init_printing()
pv = sympy.symbols("p:3", integer=True)
qv = sympy.symbols("q:3", integer=True)
lambda1, mu1 = sympy.symbols("lambda1 mu1", integer=True)
p = pg_point(pv)
q = pg_point(qv)
r = plucker(lambda1, p, mu1, q)
sv = sympy.symbols("s:3", integer=True)
tv = sympy.symbols("t:3", integer=True)
lambda2, mu2 = sympy.symbols("lambda2 mu2", integer=True)
s = pg_point(sv)
t = pg_point(tv)
u = plucker(lambda2, s, mu2, t)
# Prove Pappus Theorem
G = meet(join(p, t), join(q, s))
H = meet(join(p, u), join(r, s))
J = meet(join(q, u), join(r, t))
ans = G.dot(join(H, J))
ans = sympy.simplify(ans)
assert ans == 0
# p, q, s, t
lambda3, mu3 = sympy.symbols("lambda3 mu3", integer=True)
p2 = plucker(lambda1, p, mu1, t)
q2 = plucker(lambda2, q, mu2, t)
s2 = plucker(lambda3, s, mu3, t)
# Prove Desargue Theorem
G = meet(join(p, q), join(p2, q2))
H = meet(join(q, s), join(q2, s2))
J = meet(join(s, p), join(s2, p2))
ans = G.dot(join(H, J))
ans = sympy.simplify(ans)
assert ans == 0