def test_parabola_intersection():
l1 = Line(Point(1, -2), Point(-1, -2))
l2 = Line(Point(1, 2), Point(-1, 2))
l3 = Line(Point(1, 0), Point(-1, 0))
p1 = Point(0, 0)
p2 = Point(0, -2)
p3 = Point(120, -12)
parabola1 = Parabola(p1, l1)
# parabola with parabola
assert parabola1.intersection(parabola1) == [parabola1]
assert parabola1.intersection(Parabola(
p1, l2)) == [Point2D(-2, 0), Point2D(2, 0)]
assert parabola1.intersection(Parabola(p2, l3)) == [Point2D(0, -1)]
assert parabola1.intersection(Parabola(Point(16, 0),
l1)) == [Point2D(8, 15)]
assert parabola1.intersection(Parabola(Point(
0, 16), l1)) == [Point2D(-6, 8), Point2D(6, 8)]
assert parabola1.intersection(Parabola(p3, l3)) == []
# parabola with point
assert parabola1.intersection(p1) == []
assert parabola1.intersection(Point2D(0, -1)) == [Point2D(0, -1)]
assert parabola1.intersection(Point2D(4, 3)) == [Point2D(4, 3)]
# parabola with line
assert parabola1.intersection(Line(Point2D(-7, 3), Point(
12, 3))) == [Point2D(-4, 3), Point2D(4, 3)]
assert parabola1.intersection(Line(Point(-4, -1),
Point(4, -1))) == [Point(0, -1)]
assert parabola1.intersection(Line(Point(2, 0),
Point(0, -2))) == [Point2D(2, 0)]
raises(
TypeError,
lambda: parabola1.intersection(Line(Point(0, 0, 0), Point(1, 1, 1))))
# parabola with segment
assert parabola1.intersection(Segment2D(
(-4, -5), (4, 3))) == [Point2D(0, -1), Point2D(4, 3)]
assert parabola1.intersection(Segment2D((0, -5),
(0, 6))) == [Point2D(0, -1)]
assert parabola1.intersection(Segment2D((-12, -65), (14, -68))) == []
# parabola with ray
assert parabola1.intersection(Ray2D(
(-4, -5), (4, 3))) == [Point2D(0, -1), Point2D(4, 3)]
assert parabola1.intersection(Ray2D(
(0, 7), (1, 14))) == [Point2D(14 + 2 * sqrt(57), 105 + 14 * sqrt(57))]
assert parabola1.intersection(Ray2D((0, 7), (0, 14))) == []
# parabola with ellipse/circle
assert parabola1.intersection(Circle(
p1, 2)) == [Point2D(-2, 0), Point2D(2, 0)]
assert parabola1.intersection(Circle(
p2, 1)) == [Point2D(0, -1), Point2D(0, -1)]
assert parabola1.intersection(Ellipse(
p2, 2, 1)) == [Point2D(0, -1), Point2D(0, -1)]
assert parabola1.intersection(Ellipse(Point(0, 19), 5, 7)) == []
assert parabola1.intersection(Ellipse((0, 3), 12, 4)) == \
[Point2D(0, -1), Point2D(0, -1), Point2D(-4*sqrt(17)/3, Rational(59, 9)), Point2D(4*sqrt(17)/3, Rational(59, 9))]
# parabola with unsupported type
raises(TypeError, lambda: parabola1.intersection(2))
def test_all_circles_two_points(p1, p2):
"""
Check whether `all_circles` yields all expected circles with two points
"""
assume(p1 != p2)
two_circles = EuclideanWorld.all_circles([p1, p2])
assert len(two_circles) == 2
r = p1.distance(p2)
assert Circle(p1, r) in two_circles
assert Circle(p2, r) in two_circles
def test_geometry():
p1 = Point(1, 2)
p2 = Point(2, 3)
p3 = Point(0, 0)
p4 = Point(0, 1)
for c in (
GeometryEntity,
GeometryEntity(),
Point,
p1,
Circle,
Circle(p1, 2),
Ellipse,
Ellipse(p1, 3, 4),
Line,
Line(p1, p2),
LinearEntity,
LinearEntity(p1, p2),
Ray,
Ray(p1, p2),
Segment,
Segment(p1, p2),
Polygon,
Polygon(p1, p2, p3, p4),
RegularPolygon,
RegularPolygon(p1, 4, 5),
Triangle,
Triangle(p1, p2, p3),
):
check(c, check_attr=False)
def all_circles(points):
"""
Find all circles the can be made using the given points as centre and "radius"
"""
for centre in points:
radii = set(
centre.distance(other) for other in points if other != centre)
for radius in radii:
yield Circle(centre, radius)
def test_geometry():
p1 = Point(1, 2)
p2 = Point(2, 3)
p3 = Point(0, 0)
p4 = Point(0, 1)
for c in (GeometryEntity, GeometryEntity(), Point, p1, Circle,
Circle(p1, 2), Ellipse, Ellipse(p1, 3, 4), Line, Line(p1, p2),
LinearEntity, LinearEntity(p1, p2), Ray, Ray(p1, p2), Segment,
Segment(p1, p2), Polygon, Polygon(p1, p2, p3,
p4), RegularPolygon,
RegularPolygon(p1, 4, 5), Triangle):
# XXX: Instance of Triangle hangs because of hasattr in check().
# Triangle(p1,p2,p3)
check(c)
pass
def random_lattice_neighbors(N):
''' Generate the neighbor dict for random lattice interactions constructed
using the Voronoi/Delaunay prescription. This requires a lot of
geometry and therefore is likely computationaly costly.
Parameters:
N: The number of ising sites.
'''
x_coords = np.random.rand(N)
y_coords = np.random.rand(N)
neigh_dict = dict()
# Initialize every dictionary entry to an empty set
for n in range(N):
neigh_dict[n] = set()
# Iterate through every possible combination of three points to determine
# if the circle they create contains no points.
for comb in list(combinations(range(N), 3)):
# Extract points in circle
x1, y1 = x_coords[comb[0]], y_coords[comb[0]]
x2, y2 = x_coords[comb[1]], y_coords[comb[1]]
x3, y3 = x_coords[comb[2]], y_coords[comb[2]]
# Calculate the center and radius of the circle defined by the
# three points.
try:
c = Circle(Point(x1, y1), Point(x2, y2), Point(x3, y3))
except GeometryError:
continue
c_x, c_y = c.center
c_x = float(c_x)
c_y = float(c_y)
r = float(c.radius)
# Run through all the points and see if any are within the circle
pt_in_circ = False
for n in range(N):
x, y = x_coords[n], y_coords[n]
if (c_x - x)**2 + (c_y - y)**2 < r**2 - 1e-8:
pt_in_circ = True
break
if pt_in_circ == False:
neigh_dict[comb[0]].update(set([comb[1], comb[2]]))
neigh_dict[comb[1]].update(set([comb[0], comb[2]]))
neigh_dict[comb[2]].update(set([comb[0], comb[1]]))
return neigh_dict, x_coords, y_coords
def test_all_circles_two_points(p1, p2, p3):
"""
Check whether `all_circles` yields all expected circles with three points
"""
assume(p1 != p2)
assume(p2 != p3)
assume(p3 != p1)
two_circles = list(EuclideanWorld.all_circles([p1, p2, p3]))
assert len(two_circles) <= 6
assert len(two_circles) >= 3
assert Circle(p1, p1.distance(p2)) in two_circles
assert Circle(p1, p1.distance(p3)) in two_circles
assert Circle(p2, p2.distance(p1)) in two_circles
assert Circle(p2, p2.distance(p3)) in two_circles
assert Circle(p3, p3.distance(p1)) in two_circles
assert Circle(p3, p3.distance(p2)) in two_circles
from sympy.geometry.ellipse import Circle
from sympy.geometry.polygon import Point, Polygon, Triangle
import numpy as np
from scipy.optimize import fsolve
from sympy.solvers import solve
from sympy import Symbol
from sympy.solvers import linsolve
from sympy.geometry import Line
from sympy import Eq
import matplotlib.pyplot as plt
import matplotlib.patches as mpatches
from matplotlib.collections import PatchCollection
c1 = Circle(Point(0, 0), 0.08462309706809855)
c2 = Circle(Point(1, 0), 0.5516666664845306)
c3 = Circle(Point(0, 1), 0.5778696787291522)
x = Symbol('x')
y = Symbol('y')
f = solve(c1.equation(x, y) - c2.equation(x, y), [x, y], dict=True)
print(f[0][x].evalf(5))
#l = Line(Eq(y - 0.15, 0))
#print(l.equation())
# o = c2.intersection(c3)
# print(o.)
# print(inters)
a = tuple(Point(0.14, 0.15).evalf(4))
print(a)
p1, p2, p3 = Point(0.35, 0.335), Point(0.35, 0.34), Point(0.355, 0.34)