def test_eigen(self):
#TODO looks like bug in eigen - (1, 0) should be eigenvector too
#~ S = Scale(1, 2)
#~ E_S = Eigen(S)
#~ print E_S.vectors, E_S.values
#~ print Affine(S)
#~ for i in E_S.vectors:
#~ print i, i*S, Point(1, 0) * S
B = Affine(-2, 2, 2, 1, 0, 0)
G1 = Eigen(B)
G2 = Eigen([[-2, 2], [2, 1]])
self.assertAlmostEqual(min(G1.values), min(G2.values))
self.assertAlmostEqual(max(G1.values), max(G2.values))
if Point.are_near(G1.vectors[0] * G1.values[0], G1.vectors[0] * B):
self.assertTrue(
Point.are_near(G1.vectors[1] * G1.values[1],
G1.vectors[1] * B))
else:
self.assertTrue(
Point.are_near(G1.vectors[1] * G1.values[0],
G1.vectors[1] * B))
self.assertTrue(
Point.are_near(G1.vectors[0] * G1.values[1],
G1.vectors[0] * B))
def Nagon(N):
"""Return N-agon with side of length 1."""
side = cy2geom.LineSegment(Point(-0.5, 0), Point(0.5, 0))
angle = 2 * math.pi / N
distance_to_center = 0.5 / math.tan(math.pi / N)
return Path.fromList([
side.transformed(
cy2geom.Translate(Point(0, -distance_to_center)) *
cy2geom.Rotate(angle * i)) for i in range(N)
],
stitching=Path.STITCH_DISCONTINUOUS,
closed=True)
def test_quadraticBezier(self):
Q = QuadraticBezier(Point(2, 8), Point(1, 9), Point(-2, 3))
R = QuadraticBezier.from_beziers(Bezier(2, 8, 4), Bezier(-1, 9, 9))
self.curve(Q)
self.curve(R)
self.curve(Q.reverse())
self.curve(Q.portion(interval=Interval(0.1, 0.9)))
self.curve(Q.subdivide(0.8)[0])
self.curve(Q.subdivide(0.8)[1])
self.curve(Q.derivative())
self.curve(Q.transformed(Scale(-3)*Translate(4, 8)))
self.curve(QuadraticBezier())
def ntest_lineSegment(self):
L = LineSegment(Point(2, 8), Point(1, 9))
K = LineSegment.from_beziers(Bezier(2, 8), Bezier(-1, 9))
self.curve(L)
self.curve(K)
self.curve(L.reverse())
self.curve(L.portion(Interval(0.2, 0.4)))
self.curve(L.subdivide(0.3)[0])
self.curve(L.subdivide(0.3)[1])
self.curve(L.derivative())
self.curve(L.transformed(Scale(30)*Translate(3, 9)))
self.curve(LineSegment())
def test_cubicBezier(self):
C = CubicBezier(Point(2, 0), Point(-1, 2.9), Point(-2, 3), Point(3, 1))
D = CubicBezier.from_beziers(Bezier(2, 8, 4, 7), Bezier(-1, 9, 9, 8))
print 343
self.curve(C)
self.curve(D)
self.curve(C.reverse())
#Some kind of numerical instability imo
#~ self.curve(C.portion(Interval(0.1, 0.9)))
self.curve(C.subdivide(0.8)[0])
self.curve(C.subdivide(0.8)[1])
self.curve(C.derivative())
self.curve(C.transformed(Scale(-3)*Translate(4, 8)))
self.curve(CubicBezier())
def test_angle(self):
self.assertAlmostEqual(Angle.deg_to_rad(45), pi / 4)
self.assertAlmostEqual(Angle.rad_to_deg(pi / 6), 30)
self.assertAlmostEqual(
Angle.map_circular_arc_on_unit_interval(pi / 6, 0, pi / 2), 1 / 3.)
self.assertAlmostEqual(
Angle.map_unit_interval_on_circular_arc(0.4, 0, pi), 2 * pi / 5)
self.assertTrue(Angle.arc_contains(pi / 3, pi / 4, pi / 2, pi))
self.assertFalse(Angle.arc_contains(pi / 6, pi / 4, pi / 2, pi))
p = Point(1, sqrt(3))
alpha = Angle.from_Point(p)
self.assertAlmostEqual(alpha.degrees(), 60)
beta = Angle.from_radians(pi / 5)
gamma = Angle.from_degrees(36)
self.assertAlmostEqual(beta.radians0(), gamma.radians0())
self.assertTrue(beta == gamma)
omega = Angle.from_degrees_clock(0)
self.assertAlmostEqual(omega.radians(), pi / 2)
delta = Angle(-pi * 0.5)
self.assertAlmostEqual(delta.degrees(), -90)
self.assertAlmostEqual(delta.radians0(), 1.5 * pi)
#degreesClock roughly means [ 90 - Angle.degrees() ] mod 360
self.assertAlmostEqual(delta.degrees_clock(), 180)
self.assertAlmostEqual((beta + gamma).radians(),
beta.radians() + gamma.radians())
self.assertAlmostEqual((beta - gamma).degrees(), 0)
def test_angle(self):
self.assertAlmostEqual(Angle.rad_from_deg(45), pi/4)
self.assertAlmostEqual(Angle.deg_from_rad(pi/6), 30)
p = Point(1, sqrt(3))
alpha = Angle.from_Point(p)
self.assertAlmostEqual(alpha.degrees(), 60)
beta = Angle.from_radians(pi/5)
gamma = Angle.from_degrees(36)
self.assertAlmostEqual(beta.radians0(), gamma.radians0())
self.assertTrue(beta==gamma)
omega = Angle.from_degrees_clock(0)
self.assertAlmostEqual(omega.radians(), pi/2)
delta = Angle(-pi * 0.5)
self.assertAlmostEqual(delta.degrees(), -90)
self.assertAlmostEqual(delta.radians0(), 1.5*pi)
#degreesClock roughly means [ 90 - Angle.degrees() ] mod 360
self.assertAlmostEqual(delta.degrees_clock(), 180)
self.assertAlmostEqual(
(beta + gamma).radians(),
beta.radians()+gamma.radians() )
self.assertAlmostEqual( (beta - gamma).degrees(), 0)
def test_rotate(self):
R = Rotate()
S = Rotate(pi / 3)
T = Rotate(Point(1, 1))
U = Rotate(-1, 1)
self.assertTrue(S.vector(), Point(cos(pi / 3), sin(pi / 3)))
self.assertEqual(Point(T[0], T[1]), T.vector())
self.assertTrue(Affine.are_near(Rotate.from_degrees(60), S))
self.assertEqual(R, Rotate.identity())
self.assertTrue(
Point.are_near((S * T).vector(),
Point(cos(pi / 3 + pi / 4), sin(pi / 3 + pi / 4))))
self.affine(Affine(R), Affine(S))
self.affine(Affine(S), Affine(T))
self.affine(Affine(T), Affine(U))
self.affine(Affine(U), Affine(R))
def test_translate(self):
T = Translate()
U = Translate(Point(2, 4))
V = Translate(1, -9)
self.assertTrue(Affine(T).is_translation())
self.assertTrue(Affine(U).is_nonzero_translation())
self.assertEqual((U * V).vector(), U.vector() + V.vector())
self.assertEqual(U.inverse().vector(), -U.vector())
self.assertEqual(T, Translate.identity())
self.assertEqual(U.vector(), Point(U[0], U[1]))
self.affine(Affine(V), Affine(U))
self.affine(Affine(U), Affine(V))
r = Rect.from_points(Point(0, 2), Point(4, 8))
self.assertEqual((r * (U * V)).min(),
r.min() + U.vector() + V.vector())
def test_intPoint(self):
p = Point(4.89, 3.21)
self.assertEqual(p.round(), IntPoint(5, 3))
self.assertEqual(p.floor(), IntPoint(4, 3))
self.assertEqual(p.ceil(), IntPoint(5, 4))
self.assertEqual(p.ceil().x, 5)
self.assertEqual(p.floor().y, 3)
self.assertEqual(IntPoint(), p.floor() - p.floor())
a = IntPoint(2, -5)
b = IntPoint(5, 3)
self.assertEqual(IntPoint(7, -2), a + b)
self.assertEqual(IntPoint(3, 8), b - a)
self.assertGreater(b, a)
self.assertGreaterEqual(b, b)
self.assertNotEqual(a, b)
def test_eigen(self):
#TODO looks like bug in eigen - (1, 0) should be eigenvector too
#~ S = Scale(1, 2)
#~ E_S = Eigen(S)
#~ print E_S.vectors, E_S.values
#~ print Affine(S)
#~ for i in E_S.vectors:
#~ print i, i*S, Point(1, 0) * S
B = Affine(-2, 2, 2, 1, 0, 0)
G1 = Eigen(B)
G2 = Eigen( [[-2, 2], [2, 1]] )
self.assertAlmostEqual(min(G1.values), min(G2.values))
self.assertAlmostEqual(max(G1.values), max(G2.values))
if Point.are_near( G1.vectors[0]*G1.values[0], G1.vectors[0]*B ):
self.assertTrue( Point.are_near( G1.vectors[1]*G1.values[1], G1.vectors[1]*B ) )
else:
self.assertTrue( Point.are_near( G1.vectors[1]*G1.values[0], G1.vectors[1]*B ) )
self.assertTrue( Point.are_near( G1.vectors[0]*G1.values[1], G1.vectors[0]*B ) )
def test_scale(self):
S = Scale()
T = Scale(Point(3, 8))
U = Scale(-3, 1)
V = Scale(sqrt(2))
self.assertTrue(Affine(T).is_scale())
self.assertTrue(Affine(T).is_nonzero_scale())
self.assertTrue(Affine(V).is_nonzero_uniform_scale())
self.assertEqual((T * V).vector(), T.vector() * sqrt(2))
self.assertEqual((T * U)[0], T[0] * U[0])
self.assertAlmostEqual(1 / U.inverse()[1], U[1])
r = Rect.from_points(Point(0, 2), Point(4, 8))
self.assertAlmostEqual((r * V).area(), 2 * r.area())
self.assertFalse(Affine(U).preserves_area())
self.assertTrue(Affine(V).preserves_angles())
self.affine(Affine(T), Affine(U))
self.affine(Affine(U), Affine(V))
self.affine(Affine(V), Affine(T))
def test_affine(self):
al = []
for i in range(10):
al.append(
Affine(uniform(-10, 10), uniform(-10, 10), uniform(-10, 10),
uniform(-10, 10), uniform(-10, 10), uniform(-10, 10)))
for A in al:
for B in al:
self.affine(A, B)
o = Point(2, 4)
v = Point(-1, 1) / sqrt(2)
l = Line.from_origin_and_versor(o, v)
R = Affine.reflection(v, o)
for i in range(100):
p = Point(randint(0, 100), randint(0, 100))
self.assertAlmostEqual(Line.distance(p, l),
Line.distance(p * R, l))
self.assertTrue(Affine.are_near(R, R.inverse()))
self.affine(R, R.inverse())
def test_optRect(self):
P = OptRect(0.298, 2, 4, 5)
self.interval_basic(P.Rect[0], P.Rect[1])
G = Rect(sqrt(2), sqrt(2), sqrt(3), sqrt(3))
H = OptRect.from_rect(G)
self.rect_basic(P.Rect, G)
lst = [Point(randint(-100, 100), randint(-100, 100)) for i in range(10)]
R = OptRect.from_list(lst)
for p in lst:
self.assertTrue(R.Rect.contains(p))
self.assertAlmostEqual(min(lst).y, R.Rect.min().y)
self.assertAlmostEqual(max(lst).y, R.Rect.max().y)
Q = OptRect()
self.assertFalse(Q)
self.assertTrue(P)
self.assertTrue(Q.is_empty())
self.assertFalse(P.is_empty())
self.assertTrue(P.contains_rect( P ))
self.assertTrue(P.contains_rect(Q))
self.assertFalse(Q.contains_rect(P))
self.assertFalse(P.intersects(Q))
self.assertTrue(P.contains_rect(P.Rect))
self.assertTrue(P.contains(P.Rect.midpoint()))
self.assertEqual(P, OptRect.from_rect(P))
P.union_with(G)
P.union_with(H)
self.assertTrue(P.contains_rect(H))
P.intersect_with(G)
self.assertEqual(P, G)
self.assertEqual( P|H, G )
self.assertEqual( (P|R).Rect.min().x , min( P.Rect.min().x, R.Rect.min().x ))
self.assertFalse(P & Q)
self.assertEqual(P, P&P)
self.assertEqual( P & (R | H), (P & R) | (P & H) )
def test_bezierCurve(self):
B = BezierCurve.create( [ Point(0, 5), Point(3, 65), Point(-3, 2), Point(1, 9) ] )
C = BezierCurve.create( [ Point(0,1), Point(1, 0) ] )
self.curve(B)
self.curve(C)
self.curve(C.reverse())
self.curve(B.portion(0, 2))
self.curve(B.transformed(Zoom(9, Translate(3, 6))))
self.curve(B.derivative())
def test_intPoint(self):
p = Point(4.89, 3.21)
self.assertEqual(p.round(), IntPoint(5, 3))
self.assertEqual(p.floor(), IntPoint(4, 3))
self.assertEqual(p.ceil(), IntPoint(5, 4))
self.assertEqual(p.ceil().x, 5)
self.assertEqual(p.floor().y, 3)
self.assertEqual(IntPoint(), p.floor()-p.floor())
a = IntPoint(2, -5)
b = IntPoint(5, 3)
self.assertEqual(IntPoint(7, -2), a+b)
self.assertEqual(IntPoint(3, 8), b-a)
self.assertGreater(b, a)
self.assertGreaterEqual(b, b)
self.assertNotEqual(a, b)
def test_rotate(self):
R = Rotate()
S = Rotate(pi/3)
T = Rotate(Point( 1, 1 ))
U = Rotate( -1, 1 )
self.assertTrue(S.vector(), Point(cos(pi/3), sin(pi/3)) )
self.assertEqual( Point(T[0], T[1]), T.vector() )
self.assertTrue( Affine.are_near( Rotate.from_degrees(60), S ) )
self.assertEqual(R, Rotate.identity())
self.assertTrue( Point.are_near( ( S * T ).vector(),
Point( cos( pi/3 + pi/4 ), sin( pi/3 + pi/4 ) ) ) )
self.affine( Affine(R), Affine(S))
self.affine( Affine(S), Affine(T))
self.affine( Affine(T), Affine(U))
self.affine( Affine(U), Affine(R))
def test_zoom(self):
Z = Zoom(3)
Y = Zoom(translate=Translate(3, 2))
X = Zoom(sqrt(3), Translate(-1, 3))
self.assertEqual(Zoom(Z.scale(), Translate(Y.translation())), Y * Z)
Z.set_translation(Y.translation())
Y.set_scale(Z.scale())
self.assertEqual(Z, Y)
self.assertEqual(Y.inverse().scale(), 1 / Y.scale())
r = Rect.from_xywh(1, 1, 3, 6)
q = Rect.from_xywh(0, -1, 1, 2)
W = Zoom.map_rect(r, q)
self.assertAlmostEqual(W.scale() * r.width(), q.width())
self.assertTrue(Point.are_near(r.min() + W.translation(), q.min()))
def test_rect(self):
P = Rect(0.298, 2, 4, 5)
self.interval_basic(P[0], P[1])
G = Rect(sqrt(2), sqrt(2), sqrt(3), sqrt(3))
H = Rect.from_xywh(3.43232, 9.23214, 21.523, -0.31232)
self.rect_basic(P, G)
self.rect_basic(G, H)
lst = [Point(randint(-100, 100), randint(-100, 100)) for i in range(10)]
R = Rect.from_list(lst)
for p in lst:
self.assertTrue(R.contains(p))
self.assertAlmostEqual(min(lst).y, R.min().y)
self.assertAlmostEqual(max(lst).y, R.max().y)
def test_sVGEllipticalArc(self):
F1 = EllipticalArc(Point(), 1, 2, math.pi/6, True, True, Point(1, 1))
F2 = SVGEllipticalArc(Point(), 1, 2, math.pi/6, True, True, Point(1, 1))
for i in range(11):
t = i/10.0
self.assertAlmostEqual(F1(t), F2(t))
#degenerate ellipse
D = SVGEllipticalArc(Point(0, 0), 0.5, 0, 0, False, False, Point(1, 0))
self.assertTrue(D.is_degenerate())
for i in range(11):
t = i/10.0
self.assertAlmostEqual(D(t), D.chord()(t))
self.assertAlmostEqual(D.value_at(t, 0), t)
self.assertAlmostEqual(D.roots(t, 0)[0], t)
self.assertIsInstance(D.derivative(), LineSegment)
def test_hLineSegment(self):
H = HLineSegment(Point(3, 9), Point(9, 9))
I = HLineSegment(Point(1, 3), Point(92, 3))
J = HLineSegment.from_point_length( Point(2, 4), 1)
self.curve( H )
self.curve( I )
self.curve( J )
self.curve( H.portion(0, .25) )
self.curve( H.derivative() )
self.curve( H.transformed(Rotate(20)) )
self.curve( HLineSegment() )
self.curve( I.reverse() )
map(self.curve, I.subdivide(0.8))
self.assertAlmostEqual(I.get_Y(), 3)
J.set_Y(2)
J.set_initial_X(0)
J.set_final_X(1)
self.assertAlmostEqual( J(0), Point(0, 2) )
self.assertAlmostEqual( J(1), Point(1, 2) )
def test_zoom(self):
Z = Zoom(3)
Y = Zoom(translate=Translate(3,2))
X = Zoom(sqrt(3), Translate(-1, 3))
self.assertEqual(
Zoom(Z.scale(), Translate(Y.translation())),
Y*Z )
Z.set_translation(Y.translation())
Y.set_scale(Z.scale())
self.assertEqual(Z, Y)
self.assertEqual(Y.inverse().scale(), 1/Y.scale())
r = Rect.from_xywh( 1, 1, 3, 6)
q = Rect.from_xywh( 0, -1, 1, 2)
W = Zoom.map_rect(r, q)
self.assertAlmostEqual(W.scale()*r.width(), q.width())
self.assertTrue(Point.are_near(
r.min()+W.translation(),
q.min()))
def path(self, P):
for curve in P:
self.assertIsInstance(curve, Curve)
self.assertAlmostEqual(P(0), P.front()(0))
self.curves_equal(P.front(), P[0])
self.curves_equal(P.back_default(), P[P.size_default() - 1])
self.curves_equal(P.back_open(), P.back())
self.assertEqual(P.size_open(), P.size())
self.assertFalse(P.empty() ^ (P.size() == 0))
exact = P.bounds_exact().Rect
exact.expand_by(1e-5)
fast = P.bounds_fast().Rect
fast.expand_by(1e-5)
A1 = Affine(3, 1, 8, 3, 9, 9)
A2 = Rotate(0.231)
for i in range(100 * P.size_open() + 1):
t = i / 100.0
self.assertTrue(exact.contains(P(t)))
self.assertTrue(fast.contains(P(t)))
self.assertAlmostEqual((P * A1)(t), P(t) * A1)
self.assertAlmostEqual((P * A2)(t), P(t) * A2)
self.assertAlmostEqual(P(t), P.point_at(t))
self.assertAlmostEqual(P(t).x, P.value_at(t, 0))
self.assertAlmostEqual(P(t).y, P.value_at(t, 1))
if P.closed():
self.curves_equal(P.back_default(), P.back_closed())
self.assertEqual(P.size_default(), P.size_closed())
else:
self.curves_equal(P.back_default(), P.back_open())
self.assertEqual(P.size_default(), P.size_open())
for i in range(10):
for root in P.roots(i, 0):
if root < P.size_default():
self.assertAlmostEqual(P.value_at(root, 0), i)
for root in P.roots(i, 1):
if root < P.size_default():
self.assertAlmostEqual(P.value_at(root, 1), i)
for t in P.all_nearest_times(P(0)):
self.assertAlmostEqual(P(t), P(0))
self.assertAlmostEqual(min(P.all_nearest_times(P(0))), 0)
self.assertAlmostEqual(P.nearest_time(P(0), 0, 0.2), 0)
self.assertEqual(len(P.nearest_time_per_curve(Point())),
P.size_default())
t, distSq = P.nearest_time_and_dist_sq(Point(-1, -1), 0, P.size())
self.assertAlmostEqual(distSq**0.5, abs(P(t) - Point(-1, -1)))
self.assertAlmostEqual(P.portion(0.3, 0.4)(0), P(0.3))
self.assertAlmostEqual(
P.portion(interval=Interval(P.size(),
P.size() * 2) / 3)(0),
P(P.size() / 3.0))
self.assertAlmostEqual(P(0.23), P.reverse()(P.size() - 0.23))
self.assertAlmostEqual(P.initial_point(), P(0))
self.assertAlmostEqual(P.final_point(), P(P.size()))
def test_path(self):
a = Path()
a.append_curve(
CubicBezier(Point(-7, -3), Point(2, 8), Point(2, 1), Point(-2, 0)))
self.assertEqual(a.size(), 1)
self.assertFalse(a.closed())
self.path(a)
a.close(True)
self.assertTrue(a.closed())
self.path(a)
a.close(False)
a.append_curve(LineSegment(a.final_point(), Point(3, 5)))
self.assertEqual(a.size(), 2)
self.path(a)
a.append_SBasis(SBasis(3, 6) * SBasis(1, 0), SBasis(5, 2))
self.path(a)
a.append_curve(
EllipticalArc(Point(), 1, 2, math.pi / 6, True, True, Point(1, 1)),
Path.STITCH_DISCONTINUOUS)
#Stitching adds new segment
self.assertEqual(a.size(), 5)
b = Path()
for c in a:
b.append_curve(c)
#TODO: This fails with STITCH_DISCONTINUOUS, but also does so in C++, so
#it's either correct behaviour or bug in 2geom
#~ self.path(b)
b.insert(2, LineSegment(b[2 - 1](1),
b[2](0))) #, Path.STITCH_DISCONTINUOUS)
self.curves_equal(LineSegment(b[2 - 1](1), b[2](0)), b[2])
#TODO! fails on root finding
#self.path(b)
b.set_initial(a[2](1))
b.set_final(a[3](0))
a.insert_slice(3, b, 0, b.size())
self.assertEqual(a.size(), b.size() * 2 - 1)
for i in range(b.size()):
self.curves_equal(a[3 + i], b[i])
#Looks like bug:
# A = Path()
# A.append_curve( CubicBezier( Point(-7, -3), Point(2, 8), Point(2, 1), Point(-2, 0) ) )
# A.append_curve(EllipticalArc(Point(), 1, 2, math.pi/6, True, True, Point(1, 1)), Path.STITCH_DISCONTINUOUS)
# print A.roots(0, 1)
#Roots are [1.0, 2.768305708350847, 3.25], Point at second root is
#Point (2.32, -0.48)
#and third root is > 3 - it corresponds to root on closing segment, but A is open,
#and computing A(3.25) results in RangeError - this might be bug or feature.
self.path(a.portion(0.232, 3.12))
self.path(a.portion(interval=Interval(0.1, 4.7)))
self.path(a.portion(0.232, 3.12).reverse())
b.clear()
self.assertTrue(b.empty())
aa = Path()
for c in a:
aa.append_curve(c)
a.erase(0)
self.assertEqual(a.size(), aa.size() - 1)
self.assertAlmostEqual(a(0), aa(1))
a.erase_last()
self.assertEqual(a.size(), aa.size() - 2)
self.assertAlmostEqual(a.final_point(), aa[aa.size() - 2](1))
a.replace(3, QuadraticBezier(a(3), Point(), a(4)))
self.assertEqual(a.size(), aa.size() - 2)
cs = [
LineSegment(Point(-0.5, 0), Point(0.5, 0)).transformed(
Rotate(-math.pi / 3 * i) * Translate(
Point(0,
math.sqrt(3) / 2) * Rotate(-math.pi / 3 * i)))
for i in range(6)
]
hexagon = Path.fromList(cs,
stitching=Path.STITCH_DISCONTINUOUS,
closed=True)
if draw:
utils.draw(hexagon, scale=100)
#to = 5 because each corner contains one stitching segment
half_hexagon = Path.fromPath(hexagon, fr=0, to=5)
if draw:
utils.draw(half_hexagon, scale=100)
half_hexagon.replace_slice(
1, 5, LineSegment(half_hexagon(1), half_hexagon(5)))
self.assertEqual(half_hexagon.size(), 2)
self.assertAlmostEqual(half_hexagon(1.5), Point(0.5, 0))
half_hexagon.stitch_to(half_hexagon(0))
self.assertAlmostEqual(half_hexagon(2.5), Point())
a.start(Point(2, 2))
a.append_SBasis(SBasis(2, 6), SBasis(1, 5) * SBasis(2, 9))
self.assertAlmostEqual(a(1), Point(6, 5 * 9))
l = Path.fromList(
[QuadraticBezier(Point(6, 5 * 9), Point(1, 2), Point(-2, .21))])
a.append_path(l)
self.assertAlmostEqual(a.final_point(), l.final_point())
k = Path.fromList(
[QuadraticBezier(Point(), Point(2, 1), Point(-2, .21)).reverse()])
k.append_portion_to(l, 0, 0.3)
self.assertAlmostEqual(l.final_point(), k(0.3))
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))
def test_point(self):
p = Point(3, 4)
q = Point(8, 16)
p_inf = Point(float('inf'), 1)
#y axis points downwards
p_ccw = Point(4, -3)
self.assertAlmostEqual(p.length(), 5)
self.assertAlmostEqual(p.ccw(), p_ccw)
self.assertAlmostEqual(p_ccw.cw(), p)
self.assertAlmostEqual(p[0], 3)
self.assertAlmostEqual(p[1], 4)
self.assertFalse(p_inf.isFinite())
self.assertTrue(p.isFinite())
self.assertFalse(p.isNormalized())
self.assertTrue((p / p.length()).isNormalized())
self.assertFalse(p.isZero())
self.assertTrue((p * 0).isZero())
self.assertTrue((p + p.ccw().ccw()).isZero)
self.assertAlmostEqual((q - p).length(), 13)
self.assertGreater(q, p)
self.assertGreaterEqual(q, p)
self.assertEqual(p, p)
self.assertNotEqual(p, q)
self.assertLess(Point(1, 1), Point(1, 2))
self.assertLessEqual(p, p)
self.assertTrue(
Point.are_near(Point.polar(pi / 4, sqrt(2)), Point(1, 1)))
self.assertAlmostEqual(sqrt(2), Point.L2(Point(1, 1)))
self.assertAlmostEqual(2, Point.L2sq(Point(1, 1)))
self.assertAlmostEqual(Point.middle_point(Point(), q), q / 2)
self.assertAlmostEqual(Point.rot90(p), p.cw())
self.assertAlmostEqual(
Point.lerp(0.2, Point(), Point(3, 4)).length(), 1)
self.assertAlmostEqual(Point.dot(p, p_ccw), 0)
self.assertAlmostEqual(Point.dot(p, p_inf), float('inf'))
self.assertAlmostEqual(Point.dot(p, q), 88)
#TODO this might be implemented incorrectly in lib2geom!
self.assertAlmostEqual(Point.cross(p, q), -16)
self.assertAlmostEqual(Point.distance(p, q), 13)
self.assertAlmostEqual(Point.distanceSq(p, p_ccw), 50)
self.assertAlmostEqual(Point.unit_vector(p), p / 5)
self.assertAlmostEqual(Point.L1(p), 7)
self.assertAlmostEqual(Point.L1(p_inf), float('inf'))
self.assertAlmostEqual(Point.LInfty(q), 16)
self.assertAlmostEqual(Point.LInfty(p_inf), float('inf'))
self.assertTrue(Point.is_zero(Point()))
self.assertFalse(Point.is_zero(p))
self.assertTrue(Point.is_unit_vector(p / 5))
self.assertFalse(Point.is_unit_vector(q))
self.assertAlmostEqual(Point.atan2(Point(1, 1)), pi / 4)
self.assertAlmostEqual(Point.angle_between(p, p_ccw), -pi / 2)
self.assertAlmostEqual(Point.abs(-p), p)
def test_ray(self):
r = Ray(Point(1, 1), pi / 4)
self.assertAlmostEqual(r.origin(), Point(1, 1))
self.assertAlmostEqual(r.versor(), Point(1, 1) / sqrt(2))
self.assertAlmostEqual(r.angle(), pi / 4)
r.set_origin(Point(4, 3))
#TODO this should maybe normalize the versor!
r.set_versor(Point(1, -1) / sqrt(2))
self.assertAlmostEqual(r.origin(), Point(4, 3))
self.assertAlmostEqual(r.versor(), Point(1, -1) / sqrt(2))
self.assertAlmostEqual(r.angle(), -pi / 4)
r.set_points(Point(1, 1), Point(1, 3))
self.assertFalse(r.is_degenerate())
self.assertFalse(Ray().is_degenerate())
self.assertAlmostEqual(r.point_at(4), Point(1, 5))
#TODO I think this should be expected behaviour
# self.assertAlmostEqual(
# r.pointAt(-3),
# Point(1, 1)))
self.assertAlmostEqual(r.value_at(4, 0), 1)
self.assertAlmostEqual(r.value_at(4, 1), 5)
roots = r.roots(3, 1)
for root in roots:
self.assertAlmostEqual(r.value_at(root, 1), 3)
self.assertAlmostEqual(
r.point_at(3) - r.origin(),
r.origin() - r.reverse().point_at(3))
self.assertAlmostEqual(Ray.distance(Point(), r), sqrt(2))
self.assertAlmostEqual(Ray.distance(Point() + r.versor(), r), 1)
self.assertTrue(Ray.are_near(Point(), r, 2))
self.assertFalse(Ray.are_near(Point(), r))
self.assertTrue(Ray.are_same(r, r))
q = Ray(r.origin(), r.angle())
self.assertTrue(Ray.are_same(r, q))
q.set_origin(r.origin() + Point(0, 1))
self.assertFalse(Ray.are_same(r, q))
#TODO shouldn't this really be 0?
self.assertAlmostEqual(Ray.angle_between(r, q), 2 * pi)
q.set_versor(Point(1, 0))
q.set_origin(r.origin())
self.assertAlmostEqual(
Point(1, 1) / sqrt(2),
Ray.make_angle_bisector_ray(q, r).versor())
q.set_angle(pi / 7)
self.assertAlmostEqual(q.angle(), pi / 7)
self.assertIsInstance(q.portion(2, 4), Curve)
self.assertAlmostEqual(q.portion(2, 4)(0), q.point_at(2))
self.assertIsInstance(q.segment(1, 5), LineSegment)
self.assertAlmostEqual(q.segment(1, 5)(1), q.point_at(5))
def test_line(self):
l = Line(Point(), pi / 4)
self.assertAlmostEqual(l.origin(), Point())
self.assertAlmostEqual(l.versor(), Point(1, 1) / sqrt(2))
self.assertAlmostEqual(l.angle(), pi / 4)
k = Line.from_points(Point(), Point(2, 1))
self.assertFalse(k.is_degenerate())
self.assertFalse(Line().is_degenerate())
self.assertAlmostEqual(l.point_at(sqrt(2)), Point(1, 1))
self.assertAlmostEqual(k.point_at(43),
Point(k.value_at(43, 0), k.value_at(43, 1)))
self.assertAlmostEqual(k.time_at(Point(4, 2)), sqrt(20))
self.assertAlmostEqual(
k.time_at_projection(Point(4, 2) + Point(2, -4)), sqrt(20))
self.assertAlmostEqual(
k.point_at(k.nearest_point(Point(4, 2) + Point(2, -4))),
Point(4, 2))
self.assertAlmostEqual(k.time_at_projection(Point(3, 3)),
-k.reverse().time_at_projection(Point(3, 3)))
self.assertAlmostEqual(k.derivative().origin(), k.versor())
self.assertAlmostEqual(k.normal(), k.versor().cw())
roots = k.roots(3, 0)
for root in roots:
self.assertAlmostEqual(k.value_at(root, 0), 3)
self.assertAlmostEqual(l.normal(), l.normal_and_dist()[0])
self.assertAlmostEqual(Line.distance(Point(), l),
l.normal_and_dist()[1])
self.assertAlmostEqual(Line.distance(Point(-1, 1), l), sqrt(2))
self.assertTrue(Line.are_near(Point(0), l))
self.assertFalse(Line.are_near(Point(1, 1), k))
self.assertTrue(Line.are_near(Point(1, 1), k, 2))
p = Line(Point(1, 1))
p_orto = Line(Point(2, 3), pi / 2)
p_para = Line(Point(2, 3))
p_same = Line.from_points(Point(1, 1), Point(5, 1))
self.assertTrue(Line.are_orthogonal(p, p_orto))
self.assertFalse(Line.are_orthogonal(p, p_para))
self.assertTrue(Line.are_parallel(p, p_para))
self.assertFalse(Line.are_parallel(p, p_orto))
self.assertTrue(Line.are_same(p, p_same))
self.assertFalse(Line.are_same(p, p_para))
self.assertTrue(
Line.are_collinear(Point(1, 1), Point(2, 3), Point(4, 7)))
self.assertAlmostEqual(Line.angle_between(p, p_orto), pi / 2)
m = Line.from_normal_distance(Point(1, -1), 1)
self.assertAlmostEqual(m.angle(), pi / 4)
m = Line.from_LineSegment(LineSegment(Point(2, 2), Point(4, 4)))
self.assertAlmostEqual(m.angle(), pi / 4)
m = Line.from_Ray(Ray(Point(2, 3), 0.2))
self.assertAlmostEqual(m.angle(), 0.2)
self.assertAlmostEqual(m.origin(), Point(2, 3))
self.assertIsInstance(m.portion(2, 4), Curve)
self.assertAlmostEqual(m.portion(2, 4)(0), m.point_at(2))
self.assertIsInstance(m.segment(1, 5), LineSegment)
self.assertAlmostEqual(m.segment(1, 5)(1), m.point_at(5))
self.assertAlmostEqual(m.ray(4).origin(), m.point_at(4))
m.set_origin(Point())
self.assertAlmostEqual(m.origin(), Point())
m.set_angle(0.2)
self.assertAlmostEqual(m.angle(), 0.2)
m.set_versor(Point())
self.assertTrue(m.is_degenerate())
m.set_points(Point(2, 9), Point(1, 8))
self.assertAlmostEqual(m.versor(),
Point.unit_vector(Point(1, 8) - Point(2, 9)))
def get_curve(ellipse):
p = Point(ellipse.ray(0), 0) * Rotate(ellipse.rot_angle())
return ellipse.arc(ellipse.center() + p,
ellipse.center() - p,
ellipse.center() + p * (1 - 1e-7))
def test_ellipse(self):
#TODO: maybe a bug in arc? get_curve(F) returns different ellipse than F
def get_curve(ellipse):
p = Point(ellipse.ray(0), 0) * Rotate(ellipse.rot_angle())
return ellipse.arc(ellipse.center() + p,
ellipse.center() - p,
ellipse.center() + p * (1 - 1e-7))
E = Ellipse()
self.assertAlmostEqual(E.center(), Point())
self.assertAlmostEqual(E.ray(0), 0)
self.assertAlmostEqual(E.ray(1), 0)
F = Ellipse(Point(), 3, 2, 0)
self.assertAlmostEqual(F.center(), Point())
self.assertAlmostEqual(F.ray(0), 3)
self.assertAlmostEqual(F.ray(1), 2)
self.assertAlmostEqual(F.rot_angle(), 0)
# x**2/9 + y**2/4 = 1
self.assertAlmostEqual(F.implicit_form_coefficients()[0], 1 / 9.0)
self.assertAlmostEqual(F.implicit_form_coefficients()[2], 1 / 4.0)
self.assertAlmostEqual(F.implicit_form_coefficients()[5], -1)
coeffs = (1 / 3.0, 0, 1 / 16.0, 1, 0, -1 / 4.0)
G = Ellipse.from_coefficients(*coeffs)
self.assertAlmostEqual(G.center(), Point(-3 / 2.0, 0))
self.assertAlmostEqual(G.ray(0), math.sqrt(3))
self.assertAlmostEqual(G.ray(1), 4)
self.assertAlmostEqual(G.rot_angle(), 0)
points = [
Point(1, 2),
Point(2, 9),
Point(0, 3),
Point(-3, 8),
Point(5, 8)
]
G.set_points(points)
coeffs_G = tuple(G.implicit_form_coefficients())
def paramG(x, y):
A, B, C, D, E, F = coeffs_G
return A * x**2 + B * x * y + C * y**2 + D * x + E * y + F
for p in points:
self.assertAlmostEqual(paramG(p.x, p.y), 0)
G2 = Ellipse.from_points(points)
coeffs_G2 = tuple(G.implicit_form_coefficients())
def paramG2(x, y):
A, B, C, D, E, F = coeffs_G2
return A * x**2 + B * x * y + C * y**2 + D * x + E * y + F
for p in points:
self.assertAlmostEqual(paramG2(p.x, p.y), 0)
E.set_coefficients(*coeffs_G2)
for a1, a2 in zip(E.implicit_form_coefficients(),
G2.implicit_form_coefficients()):
self.assertAlmostEqual(a1, a2)
H = Ellipse.from_circle(Circle(Point(2, 8), 5))
self.assertAlmostEqual(H.center(), Point(2, 8))
self.assertAlmostEqual(H.ray(0), 5)
self.assertAlmostEqual(H.ray(1), 5)
Ft = F.transformed(Rotate(math.pi / 2))
self.assertAlmostEqual(F.ray(0), Ft.ray(1))
self.assertAlmostEqual(F.ray(1), Ft.ray(0))
def test_circle(self):
C = Circle()
self.assertEqual(C.center(), Point())
D = Circle(Point(2, 4), 2)
Dp = D.getPath()
self.assertEqual(D.center(), Point(2, 4))
self.assertEqual(D.ray(), 2)
for i in range(11):
t = i / 10.0
#Circle approximated by SBasis is not perfect
self.assertAlmostEqual(abs(D.center() - Dp(t)), D.ray(), delta=0.1)
half_circle = D.arc(Dp(0), Dp(0.3), Dp(0.5))
self.assertTrue(half_circle.is_SVG_compliant())
self.assertAlmostEqual(Dp(0.25), half_circle(0.5), delta=0.1)
points = [Point(2, 5), Point(1, 4), Point(9, 0)]
D.set_points(points)
for p in points:
self.assertAlmostEqual(abs(p - D.center()), D.ray())
Dc = Circle.from_points(points)
self.assertAlmostEqual(Dc.center(), D.center())
self.assertAlmostEqual(Dc.ray(), D.ray())
coeffs = (2, 4, 1, -4)
E = Circle.from_coefficients(*coeffs)
def param(x, y):
A, B, C, D = coeffs
return A * x**2 + A * y**2 + B * x + C * y + D
Ec = E.arc(E.center() + Point(E.ray(), 0),
E.center() - Point(E.ray(), 0),
E.center() + Point(E.ray(), 0))
for i in range(11):
t = i / 10.0
self.assertAlmostEqual(param(Ec.value_at(t, 0), Ec.value_at(t, 1)),
0)
E.set(3, 5, 9)
self.assertAlmostEqual(E.center(), Point(3, 5))
self.assertAlmostEqual(E.ray(), 9)
E.set_coefficients(*coeffs)
#radius and center from parametric equation
ca = float(coeffs[1]) / coeffs[0]
cb = float(coeffs[2]) / coeffs[0]
cc = float(coeffs[3]) / coeffs[0]
self.assertAlmostEqual(4 * E.ray()**2, ca**2 + cb**2 - 4 * cc)
self.assertAlmostEqual(E.center(), -Point(ca, cb) / 2)
def test_vLineSegment(self):
V = VLineSegment(Point(2, 9), Point(2, 6))
W = VLineSegment(Point(1, 2), Point(1, 8))
X = VLineSegment.from_point_length( Point(2, 4), 1)
def test_ellipticalArc(self):
E = EllipticalArc()
self.curve(E)
F = EllipticalArc(Point(), 1, 2, math.pi/6, True, True, Point(1, 1))
self.assertTrue(F.sweep())
self.assertTrue(F.large_arc())
self.assertAlmostEqual(F.chord()(0), Point())
self.assertAlmostEqual(F.chord()(1), Point(1, 1))
F.set_extremes(Point(1, 1), Point(-1, 1))
self.assertAlmostEqual(F.initial_point(), Point(1, 1))
self.assertAlmostEqual(F.final_point(), Point(-1, 1))
self.assertEqual(F.initial_angle(), F.angle_at(0))
self.assertEqual(F.final_angle(), F.angle_at(1))
self.assertTrue(F.contains(F.angle_at(0.5)))
G = EllipticalArc(Point(), 1, 1, 0, True, True, Point(2, 0))
for i in range(11):
t = i/10.0
print G(t)
self.assertAlmostEqual(G.extent(), math.pi)
self.assertAlmostEqual(G.extent(), G.sweep_angle())
self.assertAlmostEqual(float(G.angle_at(0.5)), -math.pi/2)
self.assertAlmostEqual(Point(1, 1), G.rays())
self.assertAlmostEqual(1, G.ray(1))
self.assertAlmostEqual(0, float(G.rotation_angle()))
self.assertAlmostEqual(G.extent(), G.angle_interval().extent())
self.assertAlmostEqual(G.center(), Point(1, 0))
#unit half-circle
U = EllipticalArc(Point(1, 0), 1, 1, 0, True, True, Point(-1, 0))
G.set(Point(), 1, 1, 0, True, False, Point(1, 0))
A = G.unit_circle_transform()
self.assertAlmostEqual( G(0.5), U.transformed(A)(0.5) )
self.assertAlmostEqual( G.value_at_angle(G.angle_at(0.32), 0), G.value_at(0.32, 0) )
self.assertTrue(G.contains_angle(Angle(math.pi/4)))
self.assertFalse(G.is_SVG_compliant())
def rect_basic(self, P, Q):
pmin = P.min()
pmax = P.max()
#for simplicity
self.assertTrue(pmin.x > 0)
self.assertTrue(pmin.y > 0)
self.assertAlmostEqual(pmin.x, P[0].min())
self.assertAlmostEqual(pmax.y, P[1].max())
self.assertEqual(pmin, P.corner(0))
self.assertEqual(pmin, Point(P.left(), P.top()))
self.assertEqual(pmax, Point(P.right(), P.bottom()))
self.assertAlmostEqual( P.width(), P[0].extent() )
self.assertAlmostEqual( P.height(), P[1].extent() )
self.assertAlmostEqual( P.aspect_ratio(), P.width()/P.height() )
self.assertEqual( P.dimensions(), Point( P.width(), P.height() ) )
self.assertEqual( P.midpoint(), (P.min() + P.max())/2 )
self.assertAlmostEqual(P.area(), P.width()*P.height())
#TODO export EPSILON from 2geom
if P.area() > 1e-7:
self.assertFalse(P.has_zero_area())
self.assertTrue(P.has_zero_area(P.area()))
else:
self.assertTrue(P.has_zero_area())
self.assertAlmostEqual(P.max_extent(), max(P.width(), P.height()))
self.assertGreaterEqual(P.max_extent(), P.min_extent())
qmin = Q.min()
qmax = Q.max()
pdiag = (pmax-pmin).length()
Q.set_min(P.midpoint())
Q.set_max(P.midpoint())
self.assertTrue(Q.has_zero_area())
#print P,Q
Q.expand_by(P.min_extent()/3.0)
#print P, Q
self.assertTrue(P.contains_rect(Q))
self.assertTrue(P.intersects(Q))
self.assertTrue(Q.intersects(P))
self.assertFalse(Q.contains_rect(P))
self.assertTrue(P.interior_contains_rect(Q))
self.assertFalse(P.interior_contains_rect(P))
self.assertTrue(P.interior_intersects(Q))
self.assertTrue(P.interior_intersects(P))
self.assertTrue(P.contains(P.midpoint()))
self.assertFalse(P.contains(P.midpoint()*3))
P.union_with(Q)
self.assertEqual( P.min(), pmin )
Q.set_left(qmin.x)
Q.set_top(qmin.y)
Q.set_right(qmax.x)
Q.set_bottom(qmax.y)
self.assertEqual(Q.min(), qmin)
self.assertEqual(Q.max(), qmax)
Q.expand_to( Point() )
self.assertEqual(Point(), Q.min())
Q.expand_by(qmax)
self.assertEqual(qmax, -Q.min())
Q.expand_by(-qmax.x, -qmax.y)
self.assertEqual(Q.max(), qmax)
self.assertEqual( (P+Q.min()).max(), P.max() + Q.min() )
self.assertEqual( (P-Q.max()).min(), P.min() - Q.max() )
self.assertEqual( P|P, P )
self.assertFalse( P != P )
Q.set_left(qmin.x)
Q.set_top(qmin.y)
Q.set_right(qmax.x)
Q.set_bottom(qmax.y)
self.assertAlmostEqual(Rect.distance(Point(), P), P.min().length())
self.assertAlmostEqual(Rect.distanceSq(Q.min(), P), Rect.distance(Q.min(), P)**2 )
self.assertEqual(P.round_outwards()[0], P[0].round_outwards())
if P.round_inwards():
self.assertEqual(P.round_inwards().Rect[1], P[1].round_inwards().Interval)
def test_line(self):
l = Line(Point(), pi/4)
self.assertAlmostEqual( l.origin(), Point() )
self.assertAlmostEqual( l.versor(), Point(1, 1)/sqrt(2) )
self.assertAlmostEqual( l.angle(), pi/4 )
k = Line.from_points(Point(), Point(2, 1))
self.assertFalse(k.is_degenerate())
self.assertFalse(Line().is_degenerate())
self.assertAlmostEqual( l.point_at(sqrt(2)), Point(1,1) )
self.assertAlmostEqual(
k.point_at(43),
Point(k.value_at(43, 0), k.value_at(43, 1)))
self.assertAlmostEqual(k.time_at(Point(4, 2)), sqrt(20))
self.assertAlmostEqual(
k.time_at_projection(Point(4, 2) + Point(2, -4)),
sqrt(20))
self.assertAlmostEqual(
k.point_at(k.nearest_point(Point(4, 2) + Point(2, -4))),
Point(4,2))
self.assertAlmostEqual(
k.time_at_projection(Point(3, 3)),
-k.reverse().time_at_projection(Point(3, 3)))
self.assertAlmostEqual( k.derivative().origin(), k.versor())
self.assertAlmostEqual(k.normal(), k.versor().cw())
roots = k.roots( 3, 0 )
for root in roots:
self.assertAlmostEqual( k.value_at(root, 0), 3)
self.assertAlmostEqual(l.normal(), l.normal_and_dist()[0])
self.assertAlmostEqual(Line.distance(Point(), l), l.normal_and_dist()[1])
self.assertAlmostEqual(Line.distance(Point(-1, 1), l), sqrt(2))
self.assertTrue(Line.are_near(Point(0), l))
self.assertFalse(Line.are_near(Point(1, 1), k))
self.assertTrue(Line.are_near(Point(1, 1), k, 2))
p = Line(Point(1, 1))
p_orto = Line(Point(2, 3), pi/2)
p_para = Line(Point(2, 3))
p_same = Line.from_points(Point(1, 1), Point(5, 1))
self.assertTrue(Line.are_orthogonal(p, p_orto))
self.assertFalse(Line.are_orthogonal(p, p_para))
self.assertTrue(Line.are_parallel(p, p_para))
self.assertFalse(Line.are_parallel(p, p_orto))
self.assertTrue(Line.are_same(p, p_same))
self.assertFalse(Line.are_same(p, p_para))
self.assertTrue(Line.are_collinear(
Point(1,1),
Point(2, 3),
Point(4, 7)))
self.assertAlmostEqual(Line.angle_between(p, p_orto), pi/2)
m = Line.from_normal_distance(Point(1, -1), 1)
self.assertAlmostEqual(m.angle(), pi/4)
m = Line.from_LineSegment( LineSegment( Point(2, 2), Point(4, 4) ) )
self.assertAlmostEqual(m.angle(), pi/4)
m = Line.from_Ray( Ray(Point(2, 3), 0.2) )
self.assertAlmostEqual(m.angle(), 0.2)
self.assertAlmostEqual(m.origin(), Point(2, 3))
self.assertIsInstance(m.portion(2, 4), Curve)
self.assertAlmostEqual(m.portion(2, 4)(0), m.point_at(2))
self.assertIsInstance(m.segment(1, 5), LineSegment)
self.assertAlmostEqual(m.segment(1, 5)(1), m.point_at(5))
self.assertAlmostEqual(m.ray(4).origin(), m.point_at(4))
m.set_origin(Point())
self.assertAlmostEqual(m.origin(), Point())
m.set_angle(0.2)
self.assertAlmostEqual(m.angle(), 0.2)
m.set_versor(Point())
self.assertTrue(m.is_degenerate())
m.set_points(Point(2, 9), Point(1, 8))
self.assertAlmostEqual(m.versor(), Point.unit_vector(Point(1, 8) - Point(2, 9)))
def test_point(self):
p = Point(3, 4)
q = Point(8, 16)
p_inf = Point(float('inf'), 1)
#y axis points downwards
p_ccw = Point(4, -3)
self.assertAlmostEqual(p.length(), 5)
self.assertAlmostEqual(p.ccw(), p_ccw)
self.assertAlmostEqual(p_ccw.cw(), p)
self.assertAlmostEqual(p[0], 3)
self.assertAlmostEqual(p[1], 4)
self.assertFalse(p_inf.isFinite())
self.assertTrue(p.isFinite())
self.assertFalse(p.isNormalized())
self.assertTrue((p/p.length()).isNormalized())
self.assertFalse(p.isZero())
self.assertTrue((p*0).isZero())
self.assertTrue( (p + p.ccw().ccw()).isZero)
self.assertAlmostEqual( (q-p).length(), 13)
self.assertGreater(q, p)
self.assertGreaterEqual(q, p)
self.assertEqual(p, p)
self.assertNotEqual(p, q)
self.assertLess( Point(1, 1), Point(1, 2) )
self.assertLessEqual(p, p)
self.assertTrue( Point.are_near(
Point.polar(pi/4, sqrt(2)),
Point(1, 1) ))
self.assertAlmostEqual(sqrt(2), Point.L2(Point(1, 1)))
self.assertAlmostEqual(2, Point.L2sq(Point(1, 1)))
self.assertAlmostEqual( Point.middle_point(Point(), q), q/2 )
self.assertAlmostEqual( Point.rot90(p), p.cw() )
self.assertAlmostEqual(
Point.lerp(0.2, Point(), Point(3,4)).length(),
1)
self.assertAlmostEqual(Point.dot(p, p_ccw), 0)
self.assertAlmostEqual(Point.dot(p, p_inf), float('inf'))
self.assertAlmostEqual(Point.dot(p, q), 88)
#TODO this might be implemented incorrectly in lib2geom!
self.assertAlmostEqual(Point.cross(p, q), -16)
self.assertAlmostEqual(Point.distance(p, q), 13)
self.assertAlmostEqual(Point.distanceSq(p, p_ccw), 50)
self.assertAlmostEqual(Point.unit_vector(p), p/5)
self.assertAlmostEqual(Point.L1(p), 7)
self.assertAlmostEqual(Point.L1(p_inf), float('inf'))
self.assertAlmostEqual(Point.LInfty(q), 16)
self.assertAlmostEqual(Point.LInfty(p_inf), float('inf'))
self.assertTrue(Point.is_zero(Point()))
self.assertFalse(Point.is_zero(p))
self.assertTrue(Point.is_unit_vector(p/5))
self.assertFalse(Point.is_unit_vector(q))
self.assertAlmostEqual(Point.atan2(Point(1, 1)), pi/4)
self.assertAlmostEqual(Point.angle_between(p, p_ccw), -pi/2)
self.assertAlmostEqual(Point.abs(-p), p)