def test_0():
c = Circle((0, 0), 1)
assert c.tangent(Point(0, 1)) == Line(0, 1, -1)
assert c.tangent(Point(0, -1)) == Line(0, -1, -1)
assert c.tangent(Point(1, 0)) == Line(1, 0, -1)
assert c.tangent(Point(-1, 0)) == Line(-1, 0, -1)
def test_0():
c = Circle((0, 0), 1)
assert c.normal(Point(0, 1)) == Line(1, 0, 0)
assert c.normal(Point(0, -1)) == Line(1, 0, 0)
assert c.normal(Point(1, 0)) == Line(0, 1, 0)
assert c.normal(Point(-1, 0)) == Line(0, 1, 0)
def test_1():
p1 = Point(0, 0)
p2 = Point(1, 0)
p3 = Point(1 * cmath.cos(cmath.pi / 3), 1 * cmath.sin(cmath.pi / 3))
t = triangle.Triangle(p1, p2, p3)
assert_almost_equal(t.circum_radius(), 1 / cmath.sqrt(3))
def test_0():
p1 = Point(0, 0)
p2 = Point(1, 0)
p3 = Point(0, 1)
t = triangle.Triangle(p1, p2, p3)
assert_almost_equal(t.circum_radius(), 1 / (2**0.5))
def test_1():
p1 = Point(0, 0)
p2 = Point(1, 0)
p3 = Point(0, 1)
t = triangle.Triangle(p1, p2, p3)
assert_almost_equal(t.in_radius(), 1 / (2 + cmath.sqrt(2)))
def test_0():
p1 = Point(1, 2)
p2 = Point(3, 4)
assert geometry.slope(p1, p2) == 1
p1 = Point(4, -6)
p2 = Point(-2, -5)
assert geometry.slope(p2, p1) == -1/6
def test_1():
p1 = Point(1, 2)
p2 = Point(1, 3)
assert geometry.distance(p1, p2) == 1
p1 = Point(2.0, 1)
p2 = Point(3.0, 1)
assert geometry.distance(p1, p2) == 1
def test_1():
p1 = Point(-1, 3)
p2 = Point(1, -3)
p_computed = geometry.section(p1, p2, (2, 3))
p_actual = Point(-1/5, 3/5)
assert_array_almost_equal(p_computed(), p_actual(), decimal=6)
def test_0():
p1 = Point(1, 2)
p2 = Point(3, 4)
assert geometry.line_equation(p1, p2) == Line(1, -1, 1)
p1 = Point(4, -6)
p2 = Point(-2, -5)
assert geometry.line_equation(p1, p2) == Line(1, 6, 32)
def test_1():
p1 = Point(1, 2)
p2 = Point(1, 3)
assert geometry.line_equation(p1, p2) == Line(1, 0, -1)
p1 = Point(1, 2)
p2 = Point(2, 2)
assert geometry.line_equation(p1, p2) == Line(0, 1, -2)
def test_0():
p1 = Point(0, 1)
p2 = Point(1, 0)
p3 = Point(0, 0)
t = triangle.Triangle(p1, p2, p3)
assert compare_points(
t.in_center(),
Point(1 / (2 + cmath.sqrt(2)), 1 / (2 + cmath.sqrt(2))))
def test_1():
from test import compare_lines
c = Circle((0, 0), 1)
p0 = Point(cmath.cos(cmath.pi / 4), cmath.sin(cmath.pi / 4))
p1 = Point(-cmath.cos(cmath.pi / 4), cmath.sin(cmath.pi / 4))
assert compare_lines(c.normal(p0), Line(1, -1, 0))
assert compare_lines(c.normal(p1), Line(1, 1, 0))
def test_1():
p1 = Point(2, 0)
p2 = Point(2, 4)
p = Point(0, 0)
l = Line.construct(p1, p2)
assert geometry.line_distance(p, l) == 2
assert l.distance(p) == 2
l = Line(0, 1, -3)
assert l.distance(p) == 3
def test_1():
from test import compare_lines
c = Circle((0, 0), 1)
p = Point(cmath.cos(cmath.pi / 4), cmath.sin(cmath.pi / 4))
p1 = Point(cmath.sqrt(2), 0)
p2 = Point(0, cmath.sqrt(2))
assert compare_lines(c.tangent(p), Line.construct(p1, p2))
def test_1():
p = Point(-1, 3)
l = Line(3, -4, -16)
p_actual = l.foot_perpendicular(p)
p_image = l.image(p)
p_desired = Point(68/25, -49/25)
assert_array_almost_equal(p_actual(), p_desired(), decimal=6)
assert geometry.midpoint(p, p_image) == p_actual
def test_1():
p1 = Point(1, 2)
p2 = Point(2, 2)
assert geometry.slope(p1, p2) == 0
p1 = Point(1, 2)
p2 = Point(1, 3)
try:
geometry.slope(p1, p2)
except ZeroDivisionError:
assert True
def __init__(self, center: Union[Point, tuple, list], radius: float):
"""Initialize the circle."""
if isinstance(center, tuple) or isinstance(center, list):
assert len(center) == 2, "Center must be a 2-tuple or list"
center = Point(center[0], center[1])
self.center = center
self.radius = radius
def test_0():
p1 = Point(1, 2)
p2 = Point(3, 4)
l = Line.construct(p1, p2)
p = Point(2, 2)
assert geometry.foot_perpendicular(p, l) == Point(1.5, 2.5)
p = Point(2, 3)
assert geometry.foot_perpendicular(p, l) == Point(2, 3)
def intersetion(self, other) -> Union[Point, None]:
"""Return the intersection point of the circle and the other circle."""
if isinstance(other, Circle):
c1 = self.center
c2 = other.center
m = geometry.slope(c1, c2)
theta = cmath.atan(m)
d = geometry.distance(c1, c2)
if d == self.radius + other.radius:
"""Two circles are touching each other"""
x = c1.x + self.radius * cmath.cos(theta)
y = c1.y + self.radius * cmath.sin(theta)
return Point(x, y)
elif d < self.radius + other.radius:
"""Two circles intersect"""
r1 = self.radius
r2 = other.radius
theta = cmath.asin(r2 / d)
x = c1.x + r1 * cmath.cos(theta)
y = c1.y + r1 * cmath.sin(theta)
p1 = Point(x, y)
l = Line.construct(c1, c2)
p2 = l.image(p1)
return (p1, p2)
else:
return None
else:
raise ValueError("Can only intersect with another circle")
def test_0():
p1 = Point(1, 2)
p2 = Point(3, 4)
assert geometry.distance(p1, p2) == 2*(2**0.5)
p1 = Point(4, -6)
p2 = Point(-2, -5)
assert geometry.distance(p2, p1) == (37**0.5)
p1 = Point(1.3, 2.3)
p2 = Point(1.4, 2.4)
d_output = geometry.distance(p1, p2)
d_actual = 0.1*(2**0.5)
assert_array_almost_equal(d_output, d_actual, decimal=6)
def in_center(self):
"""Return the inCenter of the triangle."""
s = self.perimeters()
i = (self.a * self.points[2].x + self.b * self.points[0].x + self.c * self.points[1].x) / s, \
(self.a * self.points[2].y + self.b * self.points[0].y + self.c * self.points[1].y) / s
return Point(i[0], i[1])
def centroid(self):
"""Return the centroid of the triangle."""
x = (self.points[0].x + self.points[1].x + self.points[2].x) / 3
y = (self.points[0].y + self.points[1].y + self.points[2].y) / 3
return Point(x, y)
def _build_circle(a1, a2, circle_type, V, P = None, Q = None, S = None, power_factor = None, V_ref = None):
k = (abs(V)**2)*abs(a1)/abs(a2)
alpha = cmath.phase(a1)
beta = cmath.phase(a2)
if circle_type == "receiving_end":
center = Point(-k*cmath.cos(alpha - beta), -k*cmath.sin(alpha - beta))
elif circle_type == "sending_end":
center = Point(k*cmath.cos(alpha -beta), -k*cmath.sin(alpha - beta))
if V_ref != None and P != None and Q != None:
radius = abs(V)*abs(V_ref)/(abs(a2))
operation_point = Point(P, Q)
elif V_ref != None and S != None:
radius = abs(V)*abs(V_ref)/(abs(a2))
operation_point = Point(S.real, S.imag)
elif P != None and Q != None:
radius = geometry.distance(center, Point(P, Q))
operation_point = Point(P, Q)
elif S != None:
radius = geometry.distance(center, Point(S.real, S.imag))
operation_point = Point(S.real, S.imag)
elif P != None and power_factor != None:
Q = P*cmath.sqrt(1/power_factor**2 - 1).real
if power_factor < 0:
Q = -Q
radius = geometry.distance(center, Point(P, Q))
operation_point = Point(P, Q)
elif Q != None and power_factor != None:
P = Q/cmath.sqrt(1/power_factor**2 - 1).real
radius = geometry.distance(center, Point(P, Q))
operation_point = Point(P, Q)
else:
raise AttributeError("Enought attributes to calculate not found")
return radius, center, operation_point
def test_1():
p1 = Point(-3, 0)
p2 = Point(0, 3)
l = perpendicular_bisector(p1, p2)
assert l == Line(1, 1, 0)
def test_2():
p1 = Point(3, 0)
p2 = Point(5, 0)
l = perpendicular_bisector(p1, p2)
assert l == Line(1, 0, -4)
def test_3():
p1 = Point(0, 3)
p2 = Point(0, 5)
l = perpendicular_bisector(p1, p2)
assert l == Line(0, 1, -4)
def test_0():
p1 = Point(1, 2)
p2 = Point(3, 4)
p3 = Point(5, 6)
assert geometry.colinear(p1, p2, p3)
def test_1():
p1 = Point(1, 2)
p2 = Point(3, 4)
p3 = Point(5, 7)
assert not geometry.colinear(p1, p2, p3)
def test_2():
p1 = Point(1, 0)
p2 = Point(2, 0)
p3 = Point(3, 0)
assert geometry.colinear(p1, p2, p3)
def test_0():
p1 = Point(1, 2)
p2 = Point(3, 4)
p = geometry.section(p1, p2, 0.5)
assert p == Point(2, 3)