本文整理汇总了Python中sympy.geometry.Ellipse类的典型用法代码示例。如果您正苦于以下问题：Python Ellipse类的具体用法？Python Ellipse怎么用？Python Ellipse使用的例子？那么恭喜您, 这里精选的类代码示例或许可以为您提供帮助。
在下文中一共展示了Ellipse类的20个代码示例，这些例子默认根据受欢迎程度排序。您可以为喜欢或者感觉有用的代码点赞，您的评价将有助于我们的系统推荐出更棒的Python代码示例。
示例1: test_ellipse_random_point
def test_ellipse_random_point():
e3 = Ellipse(Point(0, 0), y1, y1)
rx, ry = Symbol("rx"), Symbol("ry")
for ind in xrange(0, 5):
r = e3.random_point()
# substitution should give zero*y1**2
assert e3.equation(rx, ry).subs(zip((rx, ry), r.args)).equals(0)
开发者ID:flacjacket，项目名称:sympy，代码行数:7，代码来源:test_geometry.py
示例2: test_reflect
def test_reflect():
b = Symbol('b')
m = Symbol('m')
l = Line((0, b), slope=m)
p = Point(x, y)
r = p.reflect(l)
dp = l.perpendicular_segment(p).length
dr = l.perpendicular_segment(r).length
assert test_numerically(dp, dr)
t = Triangle((0, 0), (1, 0), (2, 3))
assert t.area == -t.reflect(l).area
e = Ellipse((1, 0), 1, 2)
assert e.area == -e.reflect(Line((1, 0), slope=0)).area
assert e.area == -e.reflect(Line((1, 0), slope=oo)).area
raises(NotImplementedError, lambda: e.reflect(Line((1,0), slope=m)))
# test entity overrides
c = Circle((x, y), 3)
cr = c.reflect(l)
assert cr == Circle(r, -3)
assert c.area == -cr.area
pent = RegularPolygon((1, 2), 1, 5)
l = Line((0, pi), slope=sqrt(2))
rpent = pent.reflect(l)
poly_pent = Polygon(*pent.vertices)
assert rpent.center == pent.center.reflect(l)
assert str([w.n(3) for w in rpent.vertices]) == (
'[Point(-0.586, 4.27), Point(-1.69, 4.66), '
'Point(-2.41, 3.73), Point(-1.74, 2.76), '
'Point(-0.616, 3.10)]')
assert pent.area.equals(-rpent.area)
开发者ID:Acebulf，项目名称:sympy，代码行数:30，代码来源:test_geometry.py
示例3: test_auxiliary_circle
def test_auxiliary_circle():
x, y, a, b = symbols('x y a b')
e = Ellipse((x, y), a, b)
# the general result
assert e.auxiliary_circle() == Circle((x, y), Max(a, b))
# a special case where Ellipse is a Circle
assert Circle((3, 4), 8).auxiliary_circle() == Circle((3, 4), 8)
开发者ID:oscarbenjamin，项目名称:sympy，代码行数:7，代码来源:test_ellipse.py
示例4: main
def main():
O = Point(0, 0)
p0 = Point(0, 10.1)
p1 = Point(1.4, -9.6)
m = p0.midpoint(p1)
X = Line(O, Point(10, 0))
Y = Line(O, Point(0, 10))
ellipse = Ellipse(Point(0, 0), 5 , 10)
sortie = Segment(Point(-0.01, 10), Point(0.01, 10))
ray = Ray(m, p1)
reflections = 0
while not sortie.intersection(ray) and reflections < 5:
targets = ellipse.intersection(ray)
print " Targets: ", targets
origin = next_origin(ray.p1, targets)
tangents = ellipse.tangent_lines(origin)
if len(tangents) > 1:
print("Error computing intersection")
break
tangent = tangents.pop()
alpha = next_angle(ray, tangent, (X, Y))
reflections += 1
ray = Ray(origin, angle=alpha)
print "Reflections :", reflections
开发者ID:icot，项目名称:euler，代码行数:29，代码来源:p144.py
示例5: test_director_circle
def test_director_circle():
x, y, a, b = symbols('x y a b')
e = Ellipse((x, y), a, b)
# the general result
assert e.director_circle() == Circle((x, y), sqrt(a**2 + b**2))
# a special case where Ellipse is a Circle
assert Circle((3, 4), 8).director_circle() == Circle((3, 4), 8*sqrt(2))
开发者ID:oscarbenjamin，项目名称:sympy，代码行数:7，代码来源:test_ellipse.py
示例6: test_ellipse_random_point
def test_ellipse_random_point():
e3 = Ellipse(Point(0, 0), y1, y1)
rx, ry = Symbol('rx'), Symbol('ry')
for ind in xrange(0, 5):
r = e3.random_point()
# substitution should give zero*y1**2
assert e3.equation(rx, ry).subs(zip((rx, ry), r.args)
).n(3).as_coeff_Mul()[0] < 1e-10
开发者ID:Misbah6317，项目名称:sympy，代码行数:8，代码来源:test_geometry.py
示例7: test_ellipse_random_point
def test_ellipse_random_point():
y1 = Symbol('y1', real=True)
e3 = Ellipse(Point(0, 0), y1, y1)
rx, ry = Symbol('rx'), Symbol('ry')
for ind in range(0, 5):
r = e3.random_point()
# substitution should give zero*y1**2
assert e3.equation(rx, ry).subs(zip((rx, ry), r.args)).equals(0)
开发者ID:oscarbenjamin，项目名称:sympy，代码行数:8，代码来源:test_ellipse.py
示例8: test_reflect
def test_reflect():
b = Symbol('b')
m = Symbol('m')
l = Line((0, b), slope=m)
t1 = Triangle((0, 0), (1, 0), (2, 3))
assert t1.area == -t1.reflect(l).area
e = Ellipse((1, 0), 1, 2)
assert e.area == -e.reflect(Line((1, 0), slope=0)).area
assert e.area == -e.reflect(Line((1, 0), slope=oo)).area
raises(NotImplementedError, lambda: e.reflect(Line((1, 0), slope=m)))
开发者ID:oscarbenjamin，项目名称:sympy，代码行数:10，代码来源:test_ellipse.py
示例9: test_second_moment_of_area
def test_second_moment_of_area():
x, y = symbols('x, y')
e = Ellipse(Point(0, 0), 5, 4)
I_yy = 2*4*integrate(sqrt(25 - x**2)*x**2, (x, -5, 5))/5
I_xx = 2*5*integrate(sqrt(16 - y**2)*y**2, (y, -4, 4))/4
Y = 3*sqrt(1 - x**2/5**2)
I_xy = integrate(integrate(y, (y, -Y, Y))*x, (x, -5, 5))
assert I_yy == e.second_moment_of_area()[1]
assert I_xx == e.second_moment_of_area()[0]
assert I_xy == e.second_moment_of_area()[2]
开发者ID:oscarbenjamin，项目名称:sympy，代码行数:10，代码来源:test_ellipse.py
示例10: test_ellipse_equation_using_slope
def test_ellipse_equation_using_slope():
from sympy.abc import x, y
e1 = Ellipse(Point(1, 0), 3, 2)
assert str(e1.equation(_slope=1)) == str((-x + y + 1)**2/8 + (x + y - 1)**2/18 - 1)
e2 = Ellipse(Point(0, 0), 4, 1)
assert str(e2.equation(_slope=1)) == str((-x + y)**2/2 + (x + y)**2/32 - 1)
e3 = Ellipse(Point(1, 5), 6, 2)
assert str(e3.equation(_slope=2)) == str((-2*x + y - 3)**2/20 + (x + 2*y - 11)**2/180 - 1)
开发者ID:oscarbenjamin，项目名称:sympy，代码行数:11，代码来源:test_ellipse.py
示例11: test_ellipse
def test_ellipse():
p1 = Point(0, 0)
p2 = Point(1, 1)
p3 = Point(x1, x2)
p4 = Point(0, 1)
p5 = Point(-1, 0)
e1 = Ellipse(p1, 1, 1)
e2 = Ellipse(p2, half, 1)
e3 = Ellipse(p1, y1, y1)
c1 = Circle(p1, 1)
c2 = Circle(p2,1)
c3 = Circle(Point(sqrt(2),sqrt(2)),1)
# Test creation with three points
cen,rad = Point(3*half, 2), 5*half
assert Circle(Point(0,0), Point(3,0), Point(0,4)) == Circle(cen, rad)
raises(GeometryError, "Circle(Point(0,0), Point(1,1), Point(2,2))")
# Basic Stuff
assert e1 == c1
assert e1 != e2
assert p4 in e1
assert p2 not in e2
assert e1.area == pi
assert e2.area == pi/2
assert e3.area == pi*(y1**2)
assert c1.area == e1.area
assert c1.circumference == 2*pi
assert e2.arbitrary_point() in e2
for ind in xrange(0, 5):
assert e3.random_point() in e3
# Foci
f1,f2 = Point(sqrt(12), 0), Point(-sqrt(12), 0)
ef = Ellipse(Point(0, 0), 4, 2)
assert ef.foci in [(f1, f2), (f2, f1)]
# Tangents
v = sqrt(2) / 2
p1_1 = Point(v, v)
p1_2 = p2 + Point(half, 0)
p1_3 = p2 + Point(0, 1)
assert e1.tangent_line(p4) == c1.tangent_line(p4)
assert e2.tangent_line(p1_2) == Line(p1_2, p2 + Point(half, 1))
assert e2.tangent_line(p1_3) == Line(p1_3, p2 + Point(half, 1))
assert c1.tangent_line(p1_1) == Line(p1_1, Point(0, sqrt(2)))
assert e2.is_tangent(Line(p1_2, p2 + Point(half, 1)))
assert e2.is_tangent(Line(p1_3, p2 + Point(half, 1)))
assert c1.is_tangent(Line(p1_1, Point(0, sqrt(2))))
assert e1.is_tangent(Line(Point(0, 0), Point(1, 1))) == False
# Intersection
l1 = Line(Point(1, -5), Point(1, 5))
l2 = Line(Point(-5, -1), Point(5, -1))
l3 = Line(Point(-1, -1), Point(1, 1))
l4 = Line(Point(-10, 0), Point(0, 10))
pts_c1_l3 = [Point(sqrt(2)/2, sqrt(2)/2), Point(-sqrt(2)/2, -sqrt(2)/2)]
assert intersection(e2, l4) == []
assert intersection(c1, Point(1, 0)) == [Point(1, 0)]
assert intersection(c1, l1) == [Point(1, 0)]
assert intersection(c1, l2) == [Point(0, -1)]
assert intersection(c1, l3) in [pts_c1_l3, [pts_c1_l3[1], pts_c1_l3[0]]]
assert intersection(c1, c2) in [[(1,0), (0,1)],[(0,1),(1,0)]]
assert intersection(c1, c3) == [(sqrt(2)/2, sqrt(2)/2)]
v = sqrt(2)
t1 = Triangle(Point(0, v), Point(0, -v), Point(v, 0))
points = intersection(t1, c1)
assert len(points) == 4
assert Point(0, 1) in points
assert Point(0, -1) in points
assert Point(v/2, v/2) in points
assert Point(v/2, -v/2) in points
e1 = Circle(Point(0, 0), 5)
e2 = Ellipse(Point(0, 0), 5, 20)
assert intersection(e1, e2) in \
[[Point(5, 0), Point(-5, 0)], [Point(-5, 0), Point(5, 0)]]
# Combinations of above
assert e3.is_tangent(e3.tangent_line(p1 + Point(y1, 0)))
开发者ID:KevinGoodsell，项目名称:sympy，代码行数:84，代码来源:test_geometry.py
示例12: test_ellipse
def test_ellipse():
p1 = Point(0, 0)
p2 = Point(1, 1)
p4 = Point(0, 1)
e1 = Ellipse(p1, 1, 1)
e2 = Ellipse(p2, half, 1)
e3 = Ellipse(p1, y1, y1)
c1 = Circle(p1, 1)
c2 = Circle(p2, 1)
c3 = Circle(Point(sqrt(2), sqrt(2)), 1)
# Test creation with three points
cen, rad = Point(3 * half, 2), 5 * half
assert Circle(Point(0, 0), Point(3, 0), Point(0, 4)) == Circle(cen, rad)
raises(GeometryError, lambda: Circle(Point(0, 0), Point(1, 1), Point(2, 2)))
raises(ValueError, lambda: Ellipse(None, None, None, 1))
raises(GeometryError, lambda: Circle(Point(0, 0)))
# Basic Stuff
assert Ellipse(None, 1, 1).center == Point(0, 0)
assert e1 == c1
assert e1 != e2
assert p4 in e1
assert p2 not in e2
assert e1.area == pi
assert e2.area == pi / 2
assert e3.area == pi * (y1 ** 2)
assert c1.area == e1.area
assert c1.circumference == e1.circumference
assert e3.circumference == 2 * pi * y1
assert e1.plot_interval() == e2.plot_interval() == [t, -pi, pi]
assert e1.plot_interval(x) == e2.plot_interval(x) == [x, -pi, pi]
assert Ellipse(None, 1, None, 1).circumference == 2 * pi
assert c1.minor == 1
assert c1.major == 1
assert c1.hradius == 1
assert c1.vradius == 1
# Private Functions
assert hash(c1) == hash(Circle(Point(1, 0), Point(0, 1), Point(0, -1)))
assert c1 in e1
assert (Line(p1, p2) in e1) == False
assert e1.__cmp__(e1) == 0
assert e1.__cmp__(Point(0, 0)) > 0
# Encloses
assert e1.encloses(Segment(Point(-0.5, -0.5), Point(0.5, 0.5))) == True
assert e1.encloses(Line(p1, p2)) == False
assert e1.encloses(Ray(p1, p2)) == False
assert e1.encloses(e1) == False
assert e1.encloses(Polygon(Point(-0.5, -0.5), Point(-0.5, 0.5), Point(0.5, 0.5))) == True
assert e1.encloses(RegularPolygon(p1, 0.5, 3)) == True
assert e1.encloses(RegularPolygon(p1, 5, 3)) == False
assert e1.encloses(RegularPolygon(p2, 5, 3)) == False
# with generic symbols, the hradius is assumed to contain the major radius
M = Symbol("M")
m = Symbol("m")
c = Ellipse(p1, M, m).circumference
_x = c.atoms(Dummy).pop()
assert c == 4 * M * C.Integral(sqrt((1 - _x ** 2 * (M ** 2 - m ** 2) / M ** 2) / (1 - _x ** 2)), (_x, 0, 1))
assert e2.arbitrary_point() in e2
# Foci
f1, f2 = Point(sqrt(12), 0), Point(-sqrt(12), 0)
ef = Ellipse(Point(0, 0), 4, 2)
assert ef.foci in [(f1, f2), (f2, f1)]
# Tangents
v = sqrt(2) / 2
p1_1 = Point(v, v)
p1_2 = p2 + Point(half, 0)
p1_3 = p2 + Point(0, 1)
assert e1.tangent_lines(p4) == c1.tangent_lines(p4)
assert e2.tangent_lines(p1_2) == [Line(p1_2, p2 + Point(half, 1))]
assert e2.tangent_lines(p1_3) == [Line(p1_3, p2 + Point(half, 1))]
assert c1.tangent_lines(p1_1) == [Line(p1_1, Point(0, sqrt(2)))]
assert c1.tangent_lines(p1) == []
assert e2.is_tangent(Line(p1_2, p2 + Point(half, 1)))
assert e2.is_tangent(Line(p1_3, p2 + Point(half, 1)))
assert c1.is_tangent(Line(p1_1, Point(0, sqrt(2))))
assert e1.is_tangent(Line(Point(0, 0), Point(1, 1))) == False
assert c1.is_tangent(e1) == False
assert c1.is_tangent(Ellipse(Point(2, 0), 1, 1)) == True
assert c1.is_tangent(Polygon(Point(1, 1), Point(1, -1), Point(2, 0))) == True
assert c1.is_tangent(Polygon(Point(1, 1), Point(1, 0), Point(2, 0))) == False
assert Ellipse(Point(5, 5), 2, 1).tangent_lines(Point(0, 0)) == [
Line(Point(0, 0), Point(S(77) / 25, S(132) / 25)),
Line(Point(0, 0), Point(S(33) / 5, S(22) / 5)),
]
assert Ellipse(Point(5, 5), 2, 1).tangent_lines(Point(3, 4)) == [
Line(Point(3, 4), Point(4, 4)),
Line(Point(3, 4), Point(3, 5)),
]
assert Circle(Point(5, 5), 2).tangent_lines(Point(3, 3)) == [
Line(Point(3, 3), Point(4, 3)),
#.........这里部分代码省略.........
开发者ID:flacjacket，项目名称:sympy，代码行数:101，代码来源:test_geometry.py
示例13: test_ellipse
def test_ellipse():
p1 = Point(0, 0)
p2 = Point(1, 1)
p3 = Point(x1, x2)
p4 = Point(0, 1)
p5 = Point(-1, 0)
e1 = Ellipse(p1, 1, 1)
e2 = Ellipse(p2, half, 1)
e3 = Ellipse(p1, y1, y1)
c1 = Circle(p1, 1)
c2 = Circle(p2,1)
c3 = Circle(Point(sqrt(2),sqrt(2)),1)
# Test creation with three points
cen, rad = Point(3*half, 2), 5*half
assert Circle(Point(0,0), Point(3,0), Point(0,4)) == Circle(cen, rad)
raises(GeometryError, "Circle(Point(0,0), Point(1,1), Point(2,2))")
# Basic Stuff
assert e1 == c1
assert e1 != e2
assert p4 in e1
assert p2 not in e2
assert e1.area == pi
assert e2.area == pi/2
assert e3.area == pi*(y1**2)
assert c1.area == e1.area
assert c1.circumference == e1.circumference
assert e3.circumference == 2*pi*y1
# with generic symbols, the hradius is assumed to contain the major radius
M = Symbol('M')
m = Symbol('m')
c = Ellipse(p1, M, m).circumference
_x = c.atoms(Dummy).pop()
assert c == \
4*M*C.Integral(sqrt((1 - _x**2*(M**2 - m**2)/M**2)/(1 - _x**2)), (_x, 0, 1))
assert e2.arbitrary_point() in e2
# Foci
f1, f2 = Point(sqrt(12), 0), Point(-sqrt(12), 0)
ef = Ellipse(Point(0, 0), 4, 2)
assert ef.foci in [(f1, f2), (f2, f1)]
# Tangents
v = sqrt(2) / 2
p1_1 = Point(v, v)
p1_2 = p2 + Point(half, 0)
p1_3 = p2 + Point(0, 1)
assert e1.tangent_lines(p4) == c1.tangent_lines(p4)
assert e2.tangent_lines(p1_2) == [Line(p1_2, p2 + Point(half, 1))]
assert e2.tangent_lines(p1_3) == [Line(p1_3, p2 + Point(half, 1))]
assert c1.tangent_lines(p1_1) == [Line(p1_1, Point(0, sqrt(2)))]
assert e2.is_tangent(Line(p1_2, p2 + Point(half, 1)))
assert e2.is_tangent(Line(p1_3, p2 + Point(half, 1)))
assert c1.is_tangent(Line(p1_1, Point(0, sqrt(2))))
assert e1.is_tangent(Line(Point(0, 0), Point(1, 1))) == False
assert Ellipse(Point(5, 5), 2, 1).tangent_lines(Point(0, 0)) == \
[Line(Point(0, 0), Point(S(77)/25, S(132)/25)),
Line(Point(0, 0), Point(S(33)/5, S(22)/5))]
assert Ellipse(Point(5, 5), 2, 1).tangent_lines(Point(3, 4)) == \
[Line(Point(3, 4), Point(3, 5)), Line(Point(3, 4), Point(5, 4))]
assert Circle(Point(5, 5), 2).tangent_lines(Point(3, 3)) == \
[Line(Point(3, 3), Point(3, 5)), Line(Point(3, 3), Point(5, 3))]
assert Circle(Point(5, 5), 2).tangent_lines(Point(5 - 2*sqrt(2), 5)) == \
[Line(Point(5 - 2*sqrt(2), 5), Point(5 - sqrt(2), 5 - sqrt(2))),
Line(Point(5 - 2*sqrt(2), 5), Point(5 - sqrt(2), 5 + sqrt(2))),]
# Properties
major = 3
minor = 1
e4 = Ellipse(p2, minor, major)
assert e4.focus_distance == sqrt(major**2 - minor**2)
ecc = e4.focus_distance / major
assert e4.eccentricity == ecc
assert e4.periapsis == major*(1 - ecc)
assert e4.apoapsis == major*(1 + ecc)
# independent of orientation
e4 = Ellipse(p2, major, minor)
assert e4.focus_distance == sqrt(major**2 - minor**2)
ecc = e4.focus_distance / major
assert e4.eccentricity == ecc
assert e4.periapsis == major*(1 - ecc)
assert e4.apoapsis == major*(1 + ecc)
# Intersection
l1 = Line(Point(1, -5), Point(1, 5))
l2 = Line(Point(-5, -1), Point(5, -1))
l3 = Line(Point(-1, -1), Point(1, 1))
l4 = Line(Point(-10, 0), Point(0, 10))
pts_c1_l3 = [Point(sqrt(2)/2, sqrt(2)/2), Point(-sqrt(2)/2, -sqrt(2)/2)]
assert intersection(e2, l4) == []
assert intersection(c1, Point(1, 0)) == [Point(1, 0)]
assert intersection(c1, l1) == [Point(1, 0)]
assert intersection(c1, l2) == [Point(0, -1)]
assert intersection(c1, l3) in [pts_c1_l3, [pts_c1_l3[1], pts_c1_l3[0]]]
#.........这里部分代码省略.........
开发者ID:Grahack，项目名称:geophar，代码行数:101，代码来源:test_geometry.py
示例14: test_ellipse
def test_ellipse():
p1 = Point(0, 0)
p2 = Point(1, 1)
p3 = Point(x1, x2)
p4 = Point(0, 1)
p5 = Point(-1, 0)
e1 = Ellipse(p1, 1, 1)
e2 = Ellipse(p2, half, 1)
e3 = Ellipse(p1, y1, y1)
c1 = Circle(p1, 1)
c2 = Circle(p2,1)
c3 = Circle(Point(sqrt(2),sqrt(2)),1)
# Test creation with three points
cen,rad = Point(3*half, 2), 5*half
assert Circle(Point(0,0), Point(3,0), Point(0,4)) == Circle(cen, rad)
raises(GeometryError, "Circle(Point(0,0), Point(1,1), Point(2,2))")
# Basic Stuff
assert e1 == c1
assert e1 != e2
assert p4 in e1
assert p2 not in e2
assert e1.area == pi
assert e2.area == pi/2
assert e3.area == pi*(y1**2)
assert c1.area == e1.area
assert c1.circumference == e1.circumference
assert e3.circumference == 2*pi*y1
a = Symbol('a')
b = Symbol('b')
e5 = Ellipse(p1, a, b)
assert e5.circumference == 4*a*C.Integral(((1 - x**2*Abs(b**2 - a**2)/a**2)/(1 - x**2))**(S(1)/2),\
(x, 0, 1))
assert e2.arbitrary_point() in e2
# Foci
f1,f2 = Point(sqrt(12), 0), Point(-sqrt(12), 0)
ef = Ellipse(Point(0, 0), 4, 2)
assert ef.foci in [(f1, f2), (f2, f1)]
# Tangents
v = sqrt(2) / 2
p1_1 = Point(v, v)
p1_2 = p2 + Point(half, 0)
p1_3 = p2 + Point(0, 1)
assert e1.tangent_line(p4) == c1.tangent_line(p4)
assert e2.tangent_line(p1_2) == Line(p1_2, p2 + Point(half, 1))
assert e2.tangent_line(p1_3) == Line(p1_3, p2 + Point(half, 1))
assert c1.tangent_line(p1_1) == Line(p1_1, Point(0, sqrt(2)))
assert e2.is_tangent(Line(p1_2, p2 + Point(half, 1)))
assert e2.is_tangent(Line(p1_3, p2 + Point(half, 1)))
assert c1.is_tangent(Line(p1_1, Point(0, sqrt(2))))
assert e1.is_tangent(Line(Point(0, 0), Point(1, 1))) == False
# Intersection
l1 = Line(Point(1, -5), Point(1, 5))
l2 = Line(Point(-5, -1), Point(5, -1))
l3 = Line(Point(-1, -1), Point(1, 1))
l4 = Line(Point(-10, 0), Point(0, 10))
pts_c1_l3 = [Point(sqrt(2)/2, sqrt(2)/2), Point(-sqrt(2)/2, -sqrt(2)/2)]
assert intersection(e2, l4) == []
assert intersection(c1, Point(1, 0)) == [Point(1, 0)]
assert intersection(c1, l1) == [Point(1, 0)]
assert intersection(c1, l2) == [Point(0, -1)]
assert intersection(c1, l3) in [pts_c1_l3, [pts_c1_l3[1], pts_c1_l3[0]]]
assert intersection(c1, c2) in [[(1,0), (0,1)],[(0,1),(1,0)]]
assert intersection(c1, c3) == [(sqrt(2)/2, sqrt(2)/2)]
# some special case intersections
csmall = Circle(p1, 3)
cbig = Circle(p1, 5)
cout = Circle(Point(5, 5), 1)
# one circle inside of another
assert csmall.intersection(cbig) == []
# separate circles
assert csmall.intersection(cout) == []
# coincident circles
assert csmall.intersection(csmall) == csmall
v = sqrt(2)
t1 = Triangle(Point(0, v), Point(0, -v), Point(v, 0))
points = intersection(t1, c1)
assert len(points) == 4
assert Point(0, 1) in points
assert Point(0, -1) in points
assert Point(v/2, v/2) in points
assert Point(v/2, -v/2) in points
e1 = Circle(Point(0, 0), 5)
e2 = Ellipse(Point(0, 0), 5, 20)
assert intersection(e1, e2) in \
[[Point(5, 0), Point(-5, 0)], [Point(-5, 0), Point(5, 0)]]
# FAILING ELLIPSE INTERSECTION GOES HERE
#.........这里部分代码省略.........
开发者ID:pernici，项目名称:sympy，代码行数:101，代码来源:test_geometry.py
示例15: test_ellipse_geom
def test_ellipse_geom():
x = Symbol('x', real=True)
y = Symbol('y', real=True)
t = Symbol('t', real=True)
y1 = Symbol('y1', real=True)
half = Rational(1, 2)
p1 = Point(0, 0)
p2 = Point(1, 1)
p4 = Point(0, 1)
e1 = Ellipse(p1, 1, 1)
e2 = Ellipse(p2, half, 1)
e3 = Ellipse(p1, y1, y1)
c1 = Circle(p1, 1)
c2 = Circle(p2, 1)
c3 = Circle(Point(sqrt(2), sqrt(2)), 1)
l1 = Line(p1, p2)
# Test creation with three points
cen, rad = Point(3*half, 2), 5*half
assert Circle(Point(0, 0), Point(3, 0), Point(0, 4)) == Circle(cen, rad)
assert Circle(Point(0, 0), Point(1, 1), Point(2, 2)) == Segment2D(Point2D(0, 0), Point2D(2, 2))
raises(ValueError, lambda: Ellipse(None, None, None, 1))
raises(GeometryError, lambda: Circle(Point(0, 0)))
# Basic Stuff
assert Ellipse(None, 1, 1).center == Point(0, 0)
assert e1 == c1
assert e1 != e2
assert e1 != l1
assert p4 in e1
assert p2 not in e2
assert e1.area == pi
assert e2.area == pi/2
assert e3.area == pi*y1*abs(y1)
assert c1.area == e1.area
assert c1.circumference == e1.circumference
assert e3.circumference == 2*pi*y1
assert e1.plot_interval() == e2.plot_interval() == [t, -pi, pi]
assert e1.plot_interval(x) == e2.plot_interval(x) == [x, -pi, pi]
assert c1.minor == 1
assert c1.major == 1
assert c1.hradius == 1
assert c1.vradius == 1
assert Ellipse((1, 1), 0, 0) == Point(1, 1)
assert Ellipse((1, 1), 1, 0) == Segment(Point(0, 1), Point(2, 1))
assert Ellipse((1, 1), 0, 1) == Segment(Point(1, 0), Point(1, 2))
# Private Functions
assert hash(c1) == hash(Circle(Point(1, 0), Point(0, 1), Point(0, -1)))
assert c1 in e1
assert (Line(p1, p2) in e1) is False
assert e1.__cmp__(e1) == 0
assert e1.__cmp__(Point(0, 0)) > 0
# Encloses
assert e1.encloses(Segment(Point(-0.5, -0.5), Point(0.5, 0.5))) is True
assert e1.encloses(Line(p1, p2)) is False
assert e1.encloses(Ray(p1, p2)) is False
assert e1.encloses(e1) is False
assert e1.encloses(
Polygon(Point(-0.5, -0.5), Point(-0.5, 0.5), Point(0.5, 0.5))) is True
assert e1.encloses(RegularPolygon(p1, 0.5, 3)) is True
assert e1.encloses(RegularPolygon(p1, 5, 3)) is False
assert e1.encloses(RegularPolygon(p2, 5, 3)) is False
assert e2.arbitrary_point() in e2
# Foci
f1, f2 = Point(sqrt(12), 0), Point(-sqrt(12), 0)
ef = Ellipse(Point(0, 0), 4, 2)
assert ef.foci in [(f1, f2), (f2, f1)]
# Tangents
v = sqrt(2) / 2
p1_1 = Point(v, v)
p1_2 = p2 + Point(half, 0)
p1_3 = p2 + Point(0, 1)
assert e1.tangent_lines(p4) == c1.tangent_lines(p4)
assert e2.tangent_lines(p1_2) == [Line(Point(S(3)/2, 1), Point(S(3)/2, S(1)/2))]
assert e2.tangent_lines(p1_3) == [Line(Point(1, 2), Point(S(5)/4, 2))]
assert c1.tangent_lines(p1_1) != [Line(p1_1, Point(0, sqrt(2)))]
assert c1.tangent_lines(p1) == []
assert e2.is_tangent(Line(p1_2, p2 + Point(half, 1)))
assert e2.is_tangent(Line(p1_3, p2 + Point(half, 1)))
assert c1.is_tangent(Line(p1_1, Point(0, sqrt(2))))
assert e1.is_tangent(Line(Point(0, 0), Point(1, 1))) is False
assert c1.is_tangent(e1) is True
assert c1.is_tangent(Ellipse(Point(2, 0), 1, 1)) is True
assert c1.is_tangent(
Polygon(Point(1, 1), Point(1, -1), Point(2, 0))) is True
assert c1.is_tangent(
Polygon(Point(1, 1), Point(1, 0), Point(2, 0))) is False
assert Circle(Point(5, 5), 3).is_tangent(Circle(Point(0, 5), 1)) is False
assert Ellipse(Point(5, 5), 2, 1).tangent_lines(Point(0, 0)) == \
[Line(Point(0, 0), Point(S(77)/25, S(132)/25)),
#.........这里部分代码省略.........
开发者ID:oscarbenjamin，项目名称:sympy，代码行数:101，代码来源:test_ellipse.py
示例16: test_parameter_value
def test_parameter_value():
t = Symbol('t')
e = Ellipse(Point(0, 0), 3, 5)
assert e.parameter_value((3, 0), t) == {t: 0}
raises(ValueError, lambda: e.parameter_value((4, 0), t))
开发者ID:oscarbenjamin，项目名称:sympy，代码行数:5，代码来源:test_ellipse.py
示例17: test_is_tangent
def test_is_tangent():
e1 = Ellipse(Point(0, 0), 3, 5)
c1 = Circle(Point(2, -2), 7)
assert e1.is_tangent(Point(0, 0)) is False
assert e1.is_tangent(Point(3, 0)) is False
assert e1.is_tangent(e1) is True
assert e1.is_tangent(Ellipse((0, 0), 1, 2)) is False
assert e1.is_tangent(Ellipse((0, 0), 3, 2)) is True
assert c1.is_tangent(Ellipse((2, -2), 7, 1)) is True
assert c1.is_tangent(Circle((11, -2), 2)) is True
assert c1.is_tangent(Circle((7, -2), 2)) is True
assert c1.is_tangent(Ray((-5, -2), (-15, -20))) is False
assert c1.is_tangent(Ray((-3, -2), (-15, -20))) is False
assert c1.is_tangent(Ray((-3, -22), (15, 20))) is False
assert c1.is_tangent(Ray((9, 20), (9, -20))) is True
assert e1.is_tangent(Segment((2, 2), (-7, 7))) is False
assert e1.is_tangent(Segment((0, 0), (1, 2))) is False
assert c1.is_tangent(Segment((0, 0), (-5, -2))) is False
assert e1.is_tangent(Segment((3, 0), (12, 12))) is False
assert e1.is_tangent(Segment((12, 12), (3, 0))) is False
assert e1.is_tangent(Segment((-3, 0), (3, 0))) is False
assert e1.is_tangent(Segment((-3, 5), (3, 5))) is True
assert e1.is_tangent(Line((0, 0), (1, 1))) is False
assert e1.is_tangent(Line((-3, 0), (-2.99, -0.001))) is False
assert e1.is_tangent(Line((-3, 0), (-3, 1))) is True
assert e1.is_tangent(Polygon((0, 0), (5, 5), (5, -5))) is False
assert e1.is_tangent(Polygon((-100, -50), (-40, -334), (-70, -52))) is False
assert e1.is_tangent(Polygon((-3, 0), (3, 0), (0, 1))) is False
assert e1.is_tangent(Polygon((-3, 0), (3, 0), (0, 5))) is False
assert e1.is_tangent(Polygon((-3, 0), (0, -5), (3, 0), (0, 5))) is False
assert e1.is_tangent(Polygon((-3, -5), (-3, 5), (3, 5), (3, -5))) is True
assert c1.is_tangent(Polygon((-3, -5), (-3, 5), (3, 5), (3, -5))) is False
assert e1.is_tangent(Polygon((0, 0), (3, 0), (7, 7), (0, 5))) is False
assert e1.is_tangent(Polygon((3, 12), (3, -12), (6, 5))) is True
assert e1.is_tangent(Polygon((3, 12), (3, -12), (0, -5), (0, 5))) is False
assert e1.is_tangent(Polygon((3, 0), (5, 7), (6, -5))) is False
raises(TypeError, lambda: e1.is_tangent(Point(0, 0, 0)))
raises(TypeError, lambda: e1.is_tangent(Rational(5)))
开发者ID:oscarbenjamin，项目名称:sympy，代码行数:38，代码来源:test_ellipse.py
示例18: test_ellipse_intersection_fail
def test_ellipse_intersection_fail():
# these need the upgrade to the solver; when this works, move
# these lines to the FAILING ELLIPSE INTERSECTION GOES HERE line in test_ellipse above.
e1 = Ellipse(Point(0, 0), 5, 10)
e2 = Ellipse(Point(2, 1), 4, 8)
assert e1.intersection(e2) # when this no longer fails, supply the answer
开发者ID:pernici，项目名称:sympy，代码行数:6，代码来源:test_geometry.py
示例19: test_ellipse_geom
def test_ellipse_geom():
p1 = Point(0, 0)
p2 = Point(1, 1)
p4 = Point(0, 1)
e1 = Ellipse(p1, 1, 1)
e2 = Ellipse(p2, half, 1)
e3 = Ellipse(p1, y1, y1)
c1 = Circle(p1, 1)
c2 = Circle(p2, 1)
c3 = Circle(Point(sqrt(2), sqrt(2)), 1)
# Test creation with three points
cen, rad = Point(3*half, 2), 5*half
assert Circle(Point(0, 0), Point(3, 0), Point(0, 4)) == Circle(cen, rad)
raises(
GeometryError, lambda: Circle(Point(0, 0), Point(1, 1), Point(2, 2)))
raises(ValueError, lambda: Ellipse(None, None, None, 1))
raises(GeometryError, lambda: Circle(Point(0, 0)))
# Basic Stuff
assert Ellipse(None, 1, 1).center == Point(0, 0)
assert e1 == c1
assert e1 != e2
assert p4 in e1
assert p2 not in e2
assert e1.area == pi
assert e2.area == pi/2
assert e3.area == pi*y1*abs(y1)
assert c1.area == e1.area
assert c1.circumference == e1.circumference
assert e3.circumference == 2*pi*y1
assert e1.plot_interval() == e2.plot_interval() == [t, -pi, pi]
assert e1.plot_interval(x) == e2.plot_interval(x) == [x, -pi, pi]
assert Ellipse(None, 1, None, 1).circumference == 2*pi
assert c1.minor == 1
assert c1.major == 1
assert c1.hradius == 1
assert c1.vradius == 1
# Private Functions
assert hash(c1) == hash(Circle(Point(1, 0), Point(0, 1), Point(0, -1)))
assert c1 in e1
assert (Line(p1, p2) in e1) is False
assert e1.__cmp__(e1) == 0
assert e1.__cmp__(Point(0, 0)) > 0
# Encloses
assert e1.encloses(Segment(Point(-0.5, -0.5), Point(0.5, 0.5))) is True
assert e1.encloses(Line(p1, p2)) is False
assert e1.encloses(Ray(p1, p2)) is False
assert e1.encloses(e1) is False
assert e1.encloses(
Polygon(Point(-0.5, -0.5), Point(-0.5, 0.5), Point(0.5, 0.5))) is True
assert e1.encloses(RegularPolygon(p1, 0.5, 3)) is True
assert e1.encloses(RegularPolygon(p1, 5, 3)) is False
assert e1.encloses(RegularPolygon(p2, 5, 3)) is False
# with generic symbols, the hradius is assumed to contain the major radius
M = Symbol('M')
m = Symbol('m')
c = Ellipse(p1, M, m).circumference
_x = c.atoms(Dummy).pop()
assert c == 4*M*Integral(
sqrt((1 - _x**2*(M**2 - m**2)/M**2)/(1 - _x**2)), (_x, 0, 1))
assert e2.arbitrary_point() in e2
# Foci
f1, f2 = Point(sqrt(12), 0), Point(-sqrt(12), 0)
ef = Ellipse(Point(0, 0), 4, 2)
assert ef.foci in [(f1, f2), (f2, f1)]
# Tangents
v = sqrt(2) / 2
p1_1 = Point(v, v)
p1_2 = p2 + Point(half, 0)
p1_3 = p2 + Point(0, 1)
assert e1.tangent_lines(p4) == c1.tangent_lines(p4)
assert e2.tangent_lines(p1_2) == [Line(Point(3/2, 1), Point(3/2, 1/2))]
assert e2.tangent_lines(p1_3) == [Line(Point(1, 2), Point(5/4, 2))]
assert c1.tangent_lines(p1_1) != [Line(p1_1, Point(0, sqrt(2)))]
assert c1.tangent_lines(p1) == []
assert e2.is_tangent(Line(p1_2, p2 + Point(half, 1)))
assert e2.is_tangent(Line(p1_3, p2 + Point(half, 1)))
assert c1.is_tangent(Line(p1_1, Point(0, sqrt(2))))
assert e1.is_tangent(Line(Point(0, 0), Point(1, 1))) is False
assert c1.is_tangent(e1) is False
assert c1.is_tangent(Ellipse(Point(2, 0), 1, 1)) is True
assert c1.is_tangent(
Polygon(Point(1, 1), Point(1, -1), Point(2, 0))) is True
assert c1.is_tangent(
Polygon(Point(1, 1), Point(1, 0), Point(2, 0))) is False
assert Circle(Point(5, 5), 3).is_tangent(Circle(Point(0, 5), 1)) is False
assert Ellipse(Point(5, 5), 2, 1).tangent_lines(Point(0, 0)) == \
[Line(Point(0, 0), Point(77/25, 132/25)),
Line(Point(0, 0), Point(33/5, 22/5))]
assert Ellipse(Point(5, 5), 2, 1).tangent_lines(Point(3, 4)) == \
#.........这里部分代码省略.........
开发者ID:ec-m，项目名称:sympy，代码行数:101，代码来源:test_ellipse.py
示例20: test_ellipse_random_point
def test_ellipse_random_point():
e3 = Ellipse(Point(0, 0), y1, y1)
for ind in xrange(0, 5):
assert e3.random_point() in e3
开发者ID:pernici，项目名称:sympy，代码行数:4，代码来源:test_geometry.py
注：本文中的sympy.geometry.Ellipse类示例由纯净天空整理自Github/MSDocs等源码及文档管理平台，相关代码片段筛选自各路编程大神贡献的开源项目，源码版权归原作者所有，传播和使用请参考对应项目的License；未经允许，请勿转载。 |
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