def test_fuzz_bisect():
N = 50
for data in generate_fuzz_data(N, lines=2):
l1, l2 = data.lines
if l1.null() or l2.null() or Vertex(l1, l2).parallel() or Vertex(
l1, l2).point.null():
continue
V = l1.vector()
U = l2.vector()
try:
(U.norm() / V.norm()).sqrt()
except ValueError:
continue
v0 = Vertex(l1, l2)
bisectors = v0.bisect()
s0 = v0.spread()
s1 = Vertex(l1, bisectors.line1).spread()
s2 = Vertex(l1, bisectors.line2).spread()
s3 = Vertex(l2, bisectors.line1).spread()
s4 = Vertex(l2, bisectors.line2).spread()
assert bisectors.spread() == 1
def test_fuzz_grammola():
N = 20
for data in generate_fuzz_data(N, vertices=1, spreads=1):
try:
K = data.spreads[0]
diags = data.vertices[0]
if diags.parallel():
continue
grammola = diags.grammola(K)
d1, d2 = diags.line1, diags.line2
try:
point = grammola._point_on()
except ValueError:
continue
except ZeroDivisionError:
continue
assert PointLine(point, d1).quadrance() + PointLine(
point, d2).quadrance() - K == 0
d22, K22 = grammola.co_diagonal(d1)
d11, K11 = grammola.co_diagonal(d2)
assert d22 == d2
assert d11 == d1
assert K22 == K
assert K11 == K
d1.geometry = True
assert_raises(GeometryError, grammola.co_diagonal, d1)
except NullLineError:
pass
def test_fuzz_bisect():
N = 50
for data in generate_fuzz_data(N, lines=2):
l1, l2 = data.lines
if l1.null() or l2.null() or Vertex(l1, l2).parallel() or Vertex(l1, l2).point.null():
continue
V = l1.vector()
U = l2.vector()
try:
(U.norm()/V.norm()).sqrt()
except ValueError:
continue
v0 = Vertex(l1, l2)
bisectors = v0.bisect()
s0 = v0.spread()
s1 = Vertex(l1, bisectors.line1).spread()
s2 = Vertex(l1, bisectors.line2).spread()
s3 = Vertex(l2, bisectors.line1).spread()
s4 = Vertex(l2, bisectors.line2).spread()
assert bisectors.spread() == 1
def test_fuzz_grammola():
N = 20
for data in generate_fuzz_data(N, vertices=1, spreads=1):
try:
K = data.spreads[0]
diags = data.vertices[0]
if diags.parallel():
continue
grammola = diags.grammola(K)
d1, d2 = diags.line1, diags.line2
try:
point = grammola._point_on()
except ValueError:
continue
except ZeroDivisionError:
continue
assert PointLine(point, d1).quadrance() + PointLine(point, d2).quadrance() - K == 0
d22, K22 = grammola.co_diagonal(d1)
d11, K11 = grammola.co_diagonal(d2)
assert d22 == d2
assert d11 == d1
assert K22 == K
assert K11 == K
d1.geometry = True
assert_raises(GeometryError, grammola.co_diagonal, d1)
except NullLineError:
pass
def test_fuzz_parabola():
N = 50
for data in generate_fuzz_data(N, pointlines=1):
try:
parabola = data.pointlines[0].parabola()
assert parabola.is_parabola()
except NullLineError:
pass
def test_div():
for data in generate_fuzz_data(20, points=1, spreads=1):
point = data.points[0]
x = data.spreads[0]
if x == 0:
assert_raises(ZeroDivisionError, point.__div__, x)
else:
assert x * (point / x) == point
def test_div():
for data in generate_fuzz_data(20, points=1, spreads=1):
point = data.points[0]
x = data.spreads[0]
if x == 0:
assert_raises(ZeroDivisionError, point.__div__, x)
else:
assert x*(point/x) == point
def test_fuzz_parabola():
N = 50
for data in generate_fuzz_data(N, pointlines=1):
try:
parabola = data.pointlines[0].parabola()
assert parabola.is_parabola()
except NullLineError:
pass
def test_parallel():
N = 20
for data in generate_fuzz_data(N, lines=1):
line = data.lines[0]
if line.null():
assert_raises(NullLineError, Vertex(line, line).spread)
else:
assert Vertex(line, line).spread() == 0
assert Vertex(line, line).parallel()
def test_parallel():
N = 20
for data in generate_fuzz_data(N, lines=1):
line = data.lines[0]
if line.null():
assert_raises(NullLineError, Vertex(line, line).spread)
else:
assert Vertex(line, line).spread() == 0
assert Vertex(line, line).parallel()
def test_sub():
for data in generate_fuzz_data(20, points=2):
point1, point2 = data.points
p1 = point1 - point1
p2 = point2 - point2
p3 = (point1 - point2) + (point2 - point1)
assert p1.x == p1.y == 0
assert p2.x == p2.y == 0
assert p3.x == p3.y == 0
def test_sub():
for data in generate_fuzz_data(20, points=2):
point1, point2 = data.points
p1 = point1 - point1
p2 = point2 - point2
p3 = (point1 - point2) + (point2 - point1)
assert p1.x == p1.y == 0
assert p2.x == p2.y == 0
assert p3.x == p3.y == 0
def test_fuzz_pole_polar():
N = 50
for data in generate_fuzz_data(N, points=1, conics=1):
conic = data.conics[0]
pole = data.points[0]
try:
polar = conic.polar(pole)
assert pole == conic.pole(polar)
except ZeroDivisionError:
pass
def test_fuzz_pole_polar():
N = 50
for data in generate_fuzz_data(N, points=1, conics=1):
conic = data.conics[0]
pole = data.points[0]
try:
polar = conic.polar(pole)
assert pole == conic.pole(polar)
except ZeroDivisionError:
pass
def test_fuzz_altitude():
N = 20
for data in generate_fuzz_data(N, pointlines=1):
pl = data.pointlines[0]
if pl.line.null():
assert_raises(NullLineError, pl.altitude)
else:
alt = pl.altitude()
assert PointLine(pl.point, alt.line).on()
assert Vertex(alt.line, pl.line).perpendicular()
assert PointLine(alt.point, pl.line).on()
def test_fuzz_altitude():
N = 20
for data in generate_fuzz_data(N, pointlines=1):
pl = data.pointlines[0]
if pl.line.null():
assert_raises(NullLineError, pl.altitude)
else:
alt = pl.altitude()
assert PointLine(pl.point, alt.line).on()
assert Vertex(alt.line, pl.line).perpendicular()
assert PointLine(alt.point, pl.line).on()
def test_fuzz_circle():
N = 50
for data in generate_fuzz_data(N, points=1, spreads=1):
centre = data.points[0]
K = data.spreads[0]
circle = centre.circle(K)
assert circle.is_circle()
new_centre, new_K = circle.centre_quadrance()
assert new_centre == centre
assert new_K == K
def test_fuzz_reflection():
N = 20
for data in generate_fuzz_data(N, pointlines=1):
pl = data.pointlines[0]
if pl.line.null():
assert_raises(NullLineError, pl.reflection)
else:
ref = pl.reflection()
assert pl == ref.reflection()
assert pl.altitude().point == ref.altitude().point
assert pl.line == ref.line
assert ref.quadrance() == pl.quadrance()
def test_fuzz_reflection():
N = 20
for data in generate_fuzz_data(N, pointlines=1):
pl = data.pointlines[0]
if pl.line.null():
assert_raises(NullLineError, pl.reflection)
else:
ref = pl.reflection()
assert pl == ref.reflection()
assert pl.altitude().point == ref.altitude().point
assert pl.line == ref.line
assert ref.quadrance() == pl.quadrance()
def test_fuzz_circle():
N = 50
for data in generate_fuzz_data(N, points=1, spreads=1):
centre = data.points[0]
K = data.spreads[0]
circle = centre.circle(K)
assert circle.is_circle()
new_centre, new_K = circle.centre_quadrance()
assert new_centre == centre
assert new_K == K
def test_construct_quadrance():
f = FiniteField
f.base = 37
geom = blue(f)
line = Line(f(1), f(1), f(10), geom)
point = Point(f(0), f(1), geom)
pl = PointLine(point, line)
X = pl.construct_quadrance(f(10))
v = pl.construct_spread(f(1) / f(5))
N = 20
for data in generate_fuzz_data(N, pointlines=1, spreads=1):
pl = data.pointlines[0]
s = data.spreads[0]
try:
ls = pl.construct_quadrance(s)
except ValueError:
pass
def test_eval():
for data in generate_fuzz_data(20, points=2, lines=1):
point1, point2 = data.points
line = data.lines[0]
x1, y1 = point1.form()
x2, y2 = point2.form()
a, b, c = line.form()
assert point1.eval(x1, y1) == 0
assert point2.eval(x2, y2) == 0
if point1 != point2:
assert point1.eval(x2, y2) == 1
assert point2.eval(x1, y1) == 1
else:
assert point1.eval(x2, y2) == 0
assert point2.eval(x1, y1) == 0
assert line.eval(x1, y1) == a * x1 + b * y1 + c
assert line.eval(x2, y2) == a * x2 + b * y2 + c
def test_construct_quadrance():
f = FiniteField
f.base = 37
geom = blue(f)
line = Line(f(1), f(1), f(10), geom)
point = Point(f(0), f(1), geom)
pl = PointLine(point, line)
X = pl.construct_quadrance(f(10))
v = pl.construct_spread(f(1)/f(5))
N = 20
for data in generate_fuzz_data(N, pointlines=1, spreads=1):
pl = data.pointlines[0]
s = data.spreads[0]
try:
ls = pl.construct_quadrance(s)
except ValueError:
pass
def test_eval():
for data in generate_fuzz_data(20, points=2, lines=1):
point1, point2 = data.points
line = data.lines[0]
x1, y1 = point1.form()
x2, y2 = point2.form()
a, b, c = line.form()
assert point1.eval(x1, y1) == 0
assert point2.eval(x2, y2) == 0
if point1 != point2:
assert point1.eval(x2, y2) == 1
assert point2.eval(x1, y1) == 1
else:
assert point1.eval(x2, y2) == 0
assert point2.eval(x1, y1) == 0
assert line.eval(x1, y1) == a*x1 + b*y1 + c
assert line.eval(x2, y2) == a*x2 + b*y2 + c
def test_fuzz_midpoint():
N = 20
for data in generate_fuzz_data(N, points=2):
X0, X1 = data.points
l0 = LineSegment(X0, X1)
l1 = LineSegment(X1, X0)
if l0.line.null():
assert l1.line.null()
assert_raises(ValueError, l0.midpoint)
assert_raises(ValueError, l1.midpoint)
continue
M0 = l0.midpoint()
M1 = l1.midpoint()
quadrance = LineSegment(X0, M0).quadrance()
assert LineSegment(X0, M0).quadrance() == quadrance
assert LineSegment(X1, M0).quadrance() == quadrance
assert LineSegment(X0, M1).quadrance() == quadrance
assert LineSegment(X1, M1).quadrance() == quadrance
def test_fuzz_init():
N = 20
for data in generate_fuzz_data(N, geoms=2, lines=2, points=2):
g0, g1 = data.geoms
l0, l1 = data.lines
p0, p1 = data.points
ls0 = LineSegment(p0, p1)
ls1 = LineSegment(p0, p1)
assert ls0 == ls1
v0 = Vertex(l0, l1)
v1 = Vertex(l1, l0)
assert v0 == v1
if g0 != g1:
l0.geometry = p0.geometry = g0
l1.geometry = p1.geometry = g1
assert_raises(GeometryError, Vertex, l0, l1)
assert_raises(GeometryError, PointLine, p0, l1)
assert_raises(GeometryError, LineSegment, p0, p1)
def test_fuzz_init():
N = 20
for data in generate_fuzz_data(N, geoms=2, lines=2, points=2):
g0, g1 = data.geoms
l0, l1 = data.lines
p0, p1 = data.points
ls0 = LineSegment(p0, p1)
ls1 = LineSegment(p0, p1)
assert ls0 == ls1
v0 = Vertex(l0, l1)
v1 = Vertex(l1, l0)
assert v0 == v1
if g0 != g1:
l0.geometry = p0.geometry = g0
l1.geometry = p1.geometry = g1
assert_raises(GeometryError, Vertex, l0, l1)
assert_raises(GeometryError, PointLine, p0, l1)
assert_raises(GeometryError, LineSegment, p0, p1)
def test_fuzz_tangent():
N = 50
for data in generate_fuzz_data(N, points=1, conics=1):
conic = data.conics[0]
point = data.points[0]
try:
tangent = conic.tangent(point)
assert conic.is_tangent(tangent)
except ValueError:
assert not conic.through(point)
try:
point = conic._point_on()
except ValueError:
continue
except ZeroDivisionError:
continue
tangent = conic.tangent(point)
assert conic.is_tangent(tangent)
def test_construct_spread():
f = FiniteField
f.base = 7
geom = blue(f)
line = Line(f(0), f(1), f(0), geom)
point = Point(f(1), f(2), geom)
pl = PointLine(point, line)
v = pl.construct_spread(f(1)/f(5))
N = 20
for data in generate_fuzz_data(N, pointlines=1, spreads=1):
pl = data.pointlines[0]
s = data.spreads[0]
if pl.line.null():
assert_raises(NullLineError, pl.construct_spread, s)
else:
try:
v = pl.construct_spread(s)
except ValueError:
pass
def test_construct_spread():
f = FiniteField
f.base = 7
geom = blue(f)
line = Line(f(0), f(1), f(0), geom)
point = Point(f(1), f(2), geom)
pl = PointLine(point, line)
v = pl.construct_spread(f(1) / f(5))
N = 20
for data in generate_fuzz_data(N, pointlines=1, spreads=1):
pl = data.pointlines[0]
s = data.spreads[0]
if pl.line.null():
assert_raises(NullLineError, pl.construct_spread, s)
else:
try:
v = pl.construct_spread(s)
except ValueError:
pass
def test_fuzz_midpoint():
N = 20
for data in generate_fuzz_data(N, points=2):
X0, X1 = data.points
l0 = LineSegment(X0, X1)
l1 = LineSegment(X1, X0)
if l0.line.null():
assert l1.line.null()
assert_raises(ValueError, l0.midpoint)
assert_raises(ValueError, l1.midpoint)
continue
M0 = l0.midpoint()
M1 = l1.midpoint()
quadrance = LineSegment(X0, M0).quadrance()
assert LineSegment(X0, M0).quadrance() == quadrance
assert LineSegment(X1, M0).quadrance() == quadrance
assert LineSegment(X0, M1).quadrance() == quadrance
assert LineSegment(X1, M1).quadrance() == quadrance
def test_fuzz_tangent():
N = 50
for data in generate_fuzz_data(N, points=1, conics=1):
conic = data.conics[0]
point = data.points[0]
try:
tangent = conic.tangent(point)
assert conic.is_tangent(tangent)
except ValueError:
assert not conic.through(point)
try:
point = conic._point_on()
except ValueError:
continue
except ZeroDivisionError:
continue
tangent = conic.tangent(point)
assert conic.is_tangent(tangent)
def test_fuzz_conic():
N = 50
for data in generate_fuzz_data(N, pointlines=1, spreads=1):
try:
focus_direc = data.pointlines[0]
K = data.spreads[0]
conic = focus_direc.conic(K)
v1, v2, KK = conic.focus_directrix()
dir = focus_direc.line
focus = focus_direc.point
assert K == KK
assert v1 == focus_direc or v2 == focus_direc
assert Vertex(v1.line, v2.line).parallel()
except NullLineError:
pass
except ZeroDivisionError:
#FIXME
pass
def test_fuzz_conic():
N = 50
for data in generate_fuzz_data(N, pointlines=1, spreads=1):
try:
focus_direc = data.pointlines[0]
K = data.spreads[0]
conic = focus_direc.conic(K)
v1, v2, KK = conic.focus_directrix()
dir = focus_direc.line
focus = focus_direc.point
assert K == KK
assert v1 == focus_direc or v2 == focus_direc
assert Vertex(v1.line, v2.line).parallel()
except NullLineError:
pass
except ZeroDivisionError:
#FIXME
pass
def test_fuzz_quadrola():
N = 20
for data in generate_fuzz_data(N, line_segments=1, spreads=1):
try:
K = data.spreads[0]
points = data.line_segments[0]
quadrola = points.quadrola(K)
try:
point = quadrola._point_on()
except ValueError:
continue
except ZeroDivisionError:
continue
assert quadrola.through(point)
Q1 = LineSegment(point, points.point1).quadrance()
Q2 = LineSegment(point, points.point2).quadrance()
assert (Q1 + Q2 + K)*(Q1 + Q2 + K) - 2*(Q1*Q1 + Q2*Q2 + K*K) == 0
except NullLineError:
pass
def test_fuzz_quadrola():
N = 20
for data in generate_fuzz_data(N, line_segments=1, spreads=1):
try:
K = data.spreads[0]
points = data.line_segments[0]
quadrola = points.quadrola(K)
try:
point = quadrola._point_on()
except ValueError:
continue
except ZeroDivisionError:
continue
assert quadrola.through(point)
Q1 = LineSegment(point, points.point1).quadrance()
Q2 = LineSegment(point, points.point2).quadrance()
assert (Q1 + Q2 + K) * (Q1 + Q2 + K) - 2 * (Q1 * Q1 + Q2 * Q2 +
K * K) == 0
except NullLineError:
pass
def test_mul():
for data in generate_fuzz_data(20, points=1, spreads=1):
point = data.points[0]
x = data.spreads[0]
assert point*x == x*point
def test_add():
for data in generate_fuzz_data(20, points=2):
point1, point2 = data.points
assert point1 + point2 == point2 + point1
def test_add():
for data in generate_fuzz_data(20, points=2):
point1, point2 = data.points
assert point1 + point2 == point2 + point1
def test_mul():
for data in generate_fuzz_data(20, points=1, spreads=1):
point = data.points[0]
x = data.spreads[0]
assert point * x == x * point