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 add_reflection(self, evt):
point = self._get_point(self.points)
line = self._get_line(self.lines)
if point and line:
point_line = PointLine(point, line)
name = self.name.GetValue()
ref = point_line.reflection(), name, "s", self.colours.GetValue()
self.parent.object_panel.add_point(ref)
def add_reflection(self, evt):
point = self._get_point(self.points)
line = self._get_line(self.lines)
if point and line:
point_line = PointLine(point, line)
name = self.name.GetValue()
ref = point_line.reflection(), name, "s", self.colours.GetValue()
self.parent.object_panel.add_point(ref)
def add_parallel(self, evt):
point_ = self._get_point(self.points)
line_ = self._get_line(self.lines)
if point_ and line_:
pl = PointLine(point_, line_)
name = self.name.GetValue()
parallel = pl.parallel(), name, "o", self.colours.GetValue()
self.parent.object_panel.add_line(parallel)
def add_parallel(self, evt):
point_ = self._get_point(self.points)
line_ = self._get_line(self.lines)
if point_ and line_:
pl = PointLine(point_, line_)
name = self.name.GetValue()
parallel = pl.parallel(), name, "o", self.colours.GetValue()
self.parent.object_panel.add_line(parallel)
def add_conick(self, evt):
k = self.k.GetValue()
focus = self._get_point(self.points)
directrix = self._get_line(self.lines)
if focus and directrix:
pl = PointLine(focus, directrix)
name = self.name.GetValue()
conic = pl.conic(k), name, "x", self.colours.GetValue()
self.parent.object_panel.add_conic(conic)
def add_conick(self, evt):
k = self.k.GetValue()
focus = self._get_point(self.points)
directrix = self._get_line(self.lines)
if focus and directrix:
pl = PointLine(focus, directrix)
name = self.name.GetValue()
conic = pl.conic(k), name, "x", self.colours.GetValue()
self.parent.object_panel.add_conic(conic)
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 focus_directrix(self):
"""
Calculate the two focus/directrix pairs for this conic as well as
the corresponding ratio K.
"""
#pylint: disable-msg=R0914
from pygeom.pairs import PointLine
a, b, c = self.geometry.form
D, E, F = self.d, self.e, self.f
a1 = a - self.a
b1 = b - self.b / 2
AA = 4 * (a * b1 * b1 - 2 * b * a1 * b1 + c * a1 * a1 -
a1 * self.geometry.det())
BB = 4 * a1 * ((a * E - b * D) * b1 + (-b * E + c * D) * a1)
CC = a1 * a1 * (a * E * E - 2 * b * E * D + c * D * D -
4 * self.geometry.det() * F)
c11 = (-BB + (BB * BB - 4 * AA * CC).sqrt()) / (2 * AA)
c12 = (-BB - (BB * BB - 4 * AA * CC).sqrt()) / (2 * AA)
direc1, direc2 = (Line(a1, b1, c11,
self.geometry), Line(a1, b1, c12,
self.geometry))
K = (a * b1 * b1 - 2 * b * a1 * b1 +
c * a1 * a1) / (a1 * self.geometry.det())
x1 = -(c * (2 * c11 + D) - b *
(2 * c11 * b1 / a1 + E)) / (2 * self.geometry.det())
y1 = -(-b * (2 * c11 + D) + a *
(2 * c11 * b1 / a1 + E)) / (2 * self.geometry.det())
x2 = -(c * (2 * c12 + D) - b *
(2 * c12 * b1 / a1 + E)) / (2 * self.geometry.det())
y2 = -(-b * (2 * c12 + D) + a *
(2 * c12 * b1 / a1 + E)) / (2 * self.geometry.det())
focus1 = Point(x1, y1, self.geometry)
focus2 = Point(x2, y2, self.geometry)
focus_direc_1 = PointLine(focus1, direc1)
focus_direc_2 = PointLine(focus2, direc2)
return (focus_direc_1, focus_direc_2, 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_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_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 random_pointline(field, geometry):
return PointLine(random_point(field, geometry),
random_line(field, geometry))
f.base = 13 geometry = red(f) # Create the points A = Point(f(3), f(7), geometry) B = Point(f(4), f(12), geometry) C = Point(f(9), f(2), geometry) # Create the lines of the triangle AB = LineSegment(A, B) AC = LineSegment(A, C) BC = LineSegment(B, C) # Create the altitudes alt_a = PointLine(A, BC.line).altitude().line alt_b = PointLine(B, AC.line).altitude().line alt_c = PointLine(C, AB.line).altitude().line # Calculate the points of intersection of the altitudes O_ab = Vertex(alt_a, alt_b).point O_bc = Vertex(alt_b, alt_c).point O_ca = Vertex(alt_c, alt_a).point # Check that the points are indeed equal assert O_ab == O_bc == O_ca print "Orthocentre:", O_ab # Find the circumcentre C_a = BC.perp_bisector() C_b = AC.perp_bisector()
