def test_bezier(self):
B = Bezier()
C = Bezier(2)
D = Bezier(2, 4)
E = Bezier(1, 3, 9)
F = Bezier(-2, 5, -1, 2)
self.assertTrue( B.is_zero() )
self.assertTrue( C.is_constant() )
self.assertTrue( D.is_finite() )
C.clear()
self.assertEqual(D.degree(), 1)
self.assertEqual(E.at0(), 1)
self.assertEqual(E.at1(), 9)
self.assertEqual(E[2], 9)
for i in range(11):
t = i/10.0
self.assertAlmostEqual( D(t), lerp(t, 2, 4) )
self.assertAlmostEqual( D(t), D.value_at(t))
self.assertAlmostEqual( D.value_and_derivatives(t, 0)[0], D(t) )
self.assertAlmostEqual( D.value_and_derivatives(t, 1)[1], Bezier.derivative(D)(t) )
self.assertAlmostEqual( Bezier.integral(D).value_and_derivatives(t, 1)[1], D(t) )
#~ self.assertAlmostEqual( D.elevate_degree().reduce_degree()(t), D(t) )
self.assertAlmostEqual( (D+2)(t), D(t)+2 )
self.assertAlmostEqual( (D-1)(t), D(t)-1 )
self.assertAlmostEqual( (D*2)(t), D(t)*2 )
self.assertAlmostEqual( (D/4)(t), D(t)/4 )
self.assertTrue( Bezier.bounds_fast(F).Interval.contains(F(t)) )
self.assertTrue( Bezier.bounds_exact(F).Interval.contains(F(t)) )
self.assertTrue( Bezier.bounds_local(F, OptInterval(t-0.05, t+0.05)).Interval.contains(F(t)) )
for r in F.roots():
self.assertAlmostEqual(F(r), 0)
#TODO: bug in 2geom?
#~ for r in F.roots(Interval(0.1, 0.8)):
#~ self.assertAlmostEqual(F(r), 0)
#~ self.assertTrue( 0.1 <= r <= 0.8 )
self.assertIsInstance(F.forward_difference(1), Bezier)
self.assertIsInstance(F.elevate_degree(), Bezier)
self.assertIsInstance(E.reduce_degree(), Bezier)
#F.reduce_degree() fails with
# *** glibc detected *** python2: malloc(): memory corruption:
self.assertIsInstance(F.elevate_to_degree(4), Bezier)
self.assertIsInstance(F.deflate(), Bezier)
S = F.to_SBasis()
self.assertIsInstance(S, SBasis)
for i in range(11):
t = i/10.0
self.assertAlmostEqual(S(t), F(t))
def test_optInterval(self):
I = OptInterval(2.2, 9.3)
J = Interval(3, 13)
K = OptInterval.from_Interval(J)
self.assertEqual(K.Interval, J)
self.interval_basic(K.Interval, I.Interval)
L = OptInterval()
self.assertFalse(L)
self.assertTrue( (L&I).is_empty() )
L.intersect_with(I)
self.assertFalse(L)
L |= I
self.assertEqual(L.Interval, I.Interval)
self.assertEqual((I & K).Interval, Interval(3, 9.3))
def test_sBasis(self):
S = SBasis()
T = SBasis(2)
U = SBasis(1, 7)
V = SBasis.from_linear( Linear(2, 8) )
self.assertEqual(V[0], Linear(2, 8))
self.assertEqual(V.back(), Linear(2, 8))
#~ self.assertTrue(S.empty())
self.assertFalse(T.empty())
T.pop_back()
self.assertTrue(T.empty())
self.assertEqual(S.size(), 0)
self.assertEqual(U.size(), 1)
self.assertEqual((U*V).size(), 2)
T.resize(1, Linear(2, 3))
self.assertEqual(T[0], Linear(2, 3))
T.clear()
self.assertTrue(T.empty())
#TODO
#~ T.reserve(5)
#~ print T.size()
self.assertEqual(V.at(0), V[0])
self.assertEqual(V, U+1)
self.assertNotEqual(V, U)
self.assertTrue(T.is_zero())
self.assertTrue(SBasis(1).is_constant())
def f(A, B):
return (-A)*(A+B*2.2)*(A*B-B*B/3)
W = f(U, V)
self.assertAlmostEqual(W(0), W.at0())
self.assertAlmostEqual(W(1), W.at1())
for i in range(11):
t = i/10.0
self.assertAlmostEqual(W(t), W.value_at(t))
self.assertAlmostEqual(W(t), f(U(t), V(t)))
vd_UV = (U*V).value_and_derivatives(t, 1)
vd_U = U.value_and_derivatives(t, 1)
vd_V = V.value_and_derivatives(t, 1)
self.assertAlmostEqual( vd_UV[1], vd_U[1]*V(t)+U(t)*vd_V[1] )
self.assertAlmostEqual( U(V)(t), U(V(t)) )
self.assertEqual(T.degrees_of_freedom(), 0)
self.assertEqual(U.degrees_of_freedom(), 2)
self.assertEqual(T, T.to_SBasis())
U2 = SBasis(U(0), U(1))
U2.resize(10)
self.assertNotEqual(U2, U)
U2.truncate(U.size())
self.assertEqual(U2, U)
#TODO: normalize()
sL = Linear.sin(Linear(0, 1), 3)
cL = Linear.cos(Linear(0, 1), 3)
sqrtU = SBasis.sqrt( U, 3 )
rL = Linear.reciprocal(Linear(1,2), 3)
# cy2geom.inverse seems to return nans for degrees > 1
#~ asin = cy2geom.inverse( cy2geom.sqrt( SBasis(Linear(0, 1)), 3 ), 1)
for i in range(11):
t = i/10.0
self.assertAlmostEqual(sL(t), math.sin(t))
self.assertAlmostEqual(cL(t), math.cos(t))
#cy2geom.sqrt is not that precise
self.assertAlmostEqual(sqrtU(t), math.sqrt(U(t)), places = 1)
self.assertAlmostEqual(rL(t), 1/(1+t), places = 1 )
#~ self.assertAlmostEqual( asin(t), math.asin(t) )
self.assertAlmostEqual( SBasis.compose(U, V)(t), U(V)(t) )
self.assertAlmostEqual( SBasis.divide(U, V, 3)(t), U(t)/V(t), places = 1)
self.assertAlmostEqual( SBasis.derivative(SBasis.integral(W))(t), W(t))
self.assertAlmostEqual( cy2geom.reverse(W)(t), W(1-t) )
self.assertAlmostEqual( SBasis.multiply(U, V)(t), (U*V)(t))
#TODO looks like bug in 2geom
#~ print cy2geom.multiply_add(U, V, W)(t), (U*V+W)(t)
self.assertAlmostEqual( SBasis.multiply_add(U, W, V)(t), (U*W+V)(t))
self.assertTrue( SBasis.bounds_exact(U).Interval.contains(U(t)) )
self.assertTrue( SBasis.bounds_fast(U).Interval.contains(U(t)) )
self.assertTrue( SBasis.bounds_local(U, OptInterval(t-0.05, t+0.05)).Interval.contains(U(t)) )
for r in SBasis.roots(W):
self.assertAlmostEqual(W(r), 0)
for r in SBasis.roots(W, Interval(0, 0.7)):
self.assertAlmostEqual(W(r), 0)
self.assertTrue(Interval(0, 0.7).contains(r))
levels = [0, 3, 22, -21]
for i, roots in enumerate( SBasis.multi_roots(W, levels) ):
level = levels[i]
for r in roots:
self.assertAlmostEqual(W(r), level)
self.assertEqual(SBasis.valuation(W), 0)
#TODO: why is this still 0?
#~ print cy2geom.valuation(cy2geom.shift(W, 6))
self.assertEqual( U[0], SBasis.shift(U, 2)[2] )
for I in SBasis.level_set(W, 2, tol = 1e-7):
self.assertAlmostEqual( W(I.mid()), 2 )
for I in SBasis.level_set(W, Interval(0, 1), tol = 1e-7, vtol = 1e-7):
self.assertTrue( 0 <= W(I.begin()) <= 1 )
self.assertTrue( 0 <= W(I.mid()) <= 1 )
self.assertTrue( 0 <= W(I.end()) <= 1 )
def curve(self, C):
self.assertAlmostEqual(C.initial_point(), C(0))
self.assertAlmostEqual(C.final_point(), C.point_at(1))
#Doesn't have to be true
#~ if C.length() > 0.01:
#~ self.assertFalse(C.is_degenerate())
if C.is_degenerate():
#trivial special case
return
for i in range(11):
t = i/10.0
self.assertAlmostEqual(C(t).x, C.point_at(t).x)
self.assertAlmostEqual(C(t).y, C.value_at(t, 1))
self.assertEqual( C(t), C.point_and_derivatives(t, 1)[0] )
self.assertTrue( C.bounds_exact().contains(C(t)) )
self.assertTrue( C.bounds_fast().contains(C(t)) )
#TODO why this works only with degree = 0?
if C.bounds_local(OptInterval(t-0.05, t+0.05), 0
) and (
C.bounds_local(OptInterval(t-0.05, t+0.05), 0).Rect.area() > 1e-10):
#ruling out too small rectangles, they have problems with precision
self.assertTrue( C.bounds_local( OptInterval(t-0.05, t+0.05), 0 ).Rect.contains(C(t)))
D = C.duplicate()
D.set_initial(Point())
self.assertAlmostEqual(D.initial_point(), Point())
D.set_final(Point(1, 1))
self.assertAlmostEqual(D.final_point(), Point(1, 1))
A = Affine( uniform(-10, 10),
uniform(-10, 10),
uniform(-10, 10),
uniform(-10, 10),
uniform(-10, 10),
uniform(-10, 10))
E = C.transformed(A)
for i in range(11):
t = i/10.0
# self.assertAlmostEqual( E(t), C(t)*A )
G1 = C.portion(0.2, 0.8)
G2 = C.portion( interval=Interval(2, 8)/10 )
self.assertAlmostEqual( G1(0), C(0.2) )
self.assertAlmostEqual( G2(0.5), C( lerp(0.5, 0.2, 0.8) ))
self.assertAlmostEqual( G1(1), G2(1) )
for i in range(11):
t = i/10.0
self.assertAlmostEqual( C.reverse()(t), C(1-t) )
self.assertAlmostEqual( C.point_and_derivatives(0.3, 1)[1], C.derivative()(0.3) )
self.assertAlmostEqual( C.nearest_time(C(0)), 0 )
self.assertAlmostEqual( C( C.nearest_time(C(0.5), interval=Interval(0.2, 0.5)) ), C(0.5) )
self.assertAlmostEqual( C( C.nearest_time(C(0.5), 0.2, 0.5) ), C(0.5) )
for p in C.all_nearest_times( C(0), 0, 1):
self.assertEqual(C(p), C(0))
for p in C.all_nearest_times( C(1), interval=Interval(0, 1)):
self.assertEqual(C(p), C(1))
for r in C.roots(0, 0):
self.assertAlmostEqual(C.value_at(r, 0), 0)
self.assertGreaterEqual(C.length(), abs(C(1) - C(0)))
self.assertEqual(C.winding(Point()), int(C.winding(Point())) )
self.assertAlmostEqual( C.unit_tangent_at(0.5),
Point.unit_vector(C.derivative()(0.5)) )
self.assertTrue(isinstance(C.to_SBasis()[0], SBasis))