def __new__(cls, focus=None, directrix=None, **kwargs):
if focus:
focus = Point(focus, dim=2)
else:
focus = Point(0, 0)
directrix = Line(directrix)
if directrix.contains(focus):
raise ValueError('The focus must not be a point of directrix')
return GeometryEntity.__new__(cls, focus, directrix, **kwargs)
def __new__(cls, focus=None, directrix=None, **kwargs):
if focus:
focus = Point(focus, dim=2)
else:
focus = Point(0, 0)
directrix = Line(directrix)
if (directrix.slope != 0 and directrix.slope != S.Infinity):
raise NotImplementedError('The directrix must be a horizontal'
' or vertical line')
if directrix.contains(focus):
raise ValueError('The focus must not be a point of directrix')
return GeometryEntity.__new__(cls, focus, directrix, **kwargs)
def __new__(cls, focus=None, directrix=None, **kwargs):
if focus:
focus = Point(focus, dim=2)
else:
focus = Point(0, 0)
directrix = Line(directrix)
if (directrix.slope != 0 and directrix.slope != S.Infinity):
raise NotImplementedError('The directrix must be a horizontal'
' or vertical line')
if directrix.contains(focus):
raise ValueError('The focus must not be a point of directrix')
return GeometryEntity.__new__(cls, focus, directrix, **kwargs)
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 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_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 test_parabola_geom():
a, b = symbols('a b')
p1 = Point(0, 0)
p2 = Point(3, 7)
p3 = Point(0, 4)
p4 = Point(6, 0)
p5 = Point(a, a)
d1 = Line(Point(4, 0), Point(4, 9))
d2 = Line(Point(7, 6), Point(3, 6))
d3 = Line(Point(4, 0), slope=oo)
d4 = Line(Point(7, 6), slope=0)
d5 = Line(Point(b, a), slope=oo)
d6 = Line(Point(a, b), slope=0)
half = S.Half
pa1 = Parabola(None, d2)
pa2 = Parabola(directrix=d1)
pa3 = Parabola(p1, d1)
pa4 = Parabola(p2, d2)
pa5 = Parabola(p2, d4)
pa6 = Parabola(p3, d2)
pa7 = Parabola(p2, d1)
pa8 = Parabola(p4, d1)
pa9 = Parabola(p4, d3)
pa10 = Parabola(p5, d5)
pa11 = Parabola(p5, d6)
d = Line(Point(3, 7), Point(2, 9))
pa12 = Parabola(Point(7, 8), d)
pa12r = Parabola(Point(7, 8).reflect(d), d)
raises(ValueError,
lambda: Parabola(Point(7, 8, 9), Line(Point(6, 7), Point(7, 7))))
raises(ValueError,
lambda: Parabola(Point(0, 2), Line(Point(7, 2), Point(6, 2))))
raises(ValueError, lambda: Parabola(Point(7, 8), Point(3, 8)))
# Basic Stuff
assert pa1.focus == Point(0, 0)
assert pa1.ambient_dimension == S(2)
assert pa2 == pa3
assert pa4 != pa7
assert pa6 != pa7
assert pa6.focus == Point2D(0, 4)
assert pa6.focal_length == 1
assert pa6.p_parameter == -1
assert pa6.vertex == Point2D(0, 5)
assert pa6.eccentricity == 1
assert pa7.focus == Point2D(3, 7)
assert pa7.focal_length == half
assert pa7.p_parameter == -half
assert pa7.vertex == Point2D(7 * half, 7)
assert pa4.focal_length == half
assert pa4.p_parameter == half
assert pa4.vertex == Point2D(3, 13 * half)
assert pa8.focal_length == 1
assert pa8.p_parameter == 1
assert pa8.vertex == Point2D(5, 0)
assert pa4.focal_length == pa5.focal_length
assert pa4.p_parameter == pa5.p_parameter
assert pa4.vertex == pa5.vertex
assert pa4.equation() == pa5.equation()
assert pa8.focal_length == pa9.focal_length
assert pa8.p_parameter == pa9.p_parameter
assert pa8.vertex == pa9.vertex
assert pa8.equation() == pa9.equation()
assert pa10.focal_length == pa11.focal_length == sqrt(
(a - b)**2) / 2 # if a, b real == abs(a - b)/2
assert pa11.vertex == Point(*pa10.vertex[::-1]) == Point(
a, a - sqrt(
(a - b)**2) * sign(a - b) / 2) # change axis x->y, y->x on pa10
aos = pa12.axis_of_symmetry
assert aos == Line(Point(7, 8), Point(5, 7))
assert pa12.directrix == Line(Point(3, 7), Point(2, 9))
assert pa12.directrix.angle_between(aos) == S.Pi / 2
assert pa12.eccentricity == 1
assert pa12.equation(
x, y) == (x - 7)**2 + (y - 8)**2 - (-2 * x - y + 13)**2 / 5
assert pa12.focal_length == 9 * sqrt(5) / 10
assert pa12.focus == Point(7, 8)
assert pa12.p_parameter == 9 * sqrt(5) / 10
assert pa12.vertex == Point2D(S(26) / 5, S(71) / 10)
assert pa12r.focal_length == 9 * sqrt(5) / 10
assert pa12r.focus == Point(-S(1) / 5, S(22) / 5)
assert pa12r.p_parameter == -9 * sqrt(5) / 10
assert pa12r.vertex == Point(S(8) / 5, S(53) / 10)
def test_parabola_geom():
a, b = symbols('a b')
p1 = Point(0, 0)
p2 = Point(3, 7)
p3 = Point(0, 4)
p4 = Point(6, 0)
p5 = Point(a, a)
d1 = Line(Point(4, 0), Point(4, 9))
d2 = Line(Point(7, 6), Point(3, 6))
d3 = Line(Point(4, 0), slope=oo)
d4 = Line(Point(7, 6), slope=0)
d5 = Line(Point(b, a), slope=oo)
d6 = Line(Point(a, b), slope=0)
half = S.Half
pa1 = Parabola(None, d2)
pa2 = Parabola(directrix=d1)
pa3 = Parabola(p1, d1)
pa4 = Parabola(p2, d2)
pa5 = Parabola(p2, d4)
pa6 = Parabola(p3, d2)
pa7 = Parabola(p2, d1)
pa8 = Parabola(p4, d1)
pa9 = Parabola(p4, d3)
pa10 = Parabola(p5, d5)
pa11 = Parabola(p5, d6)
raises(ValueError,
lambda: Parabola(Point(7, 8, 9), Line(Point(6, 7), Point(7, 7))))
raises(NotImplementedError,
lambda: Parabola(Point(7, 8), Line(Point(3, 7), Point(2, 9))))
raises(ValueError,
lambda: Parabola(Point(0, 2), Line(Point(7, 2), Point(6, 2))))
raises(ValueError, lambda: Parabola(Point(7, 8), Point(3, 8)))
# Basic Stuff
assert pa1.focus == Point(0, 0)
assert pa1.ambient_dimension == S(2)
assert pa2 == pa3
assert pa4 != pa7
assert pa6 != pa7
assert pa6.focus == Point2D(0, 4)
assert pa6.focal_length == 1
assert pa6.p_parameter == -1
assert pa6.vertex == Point2D(0, 5)
assert pa6.eccentricity == 1
assert pa7.focus == Point2D(3, 7)
assert pa7.focal_length == half
assert pa7.p_parameter == -half
assert pa7.vertex == Point2D(7 * half, 7)
assert pa4.focal_length == half
assert pa4.p_parameter == half
assert pa4.vertex == Point2D(3, 13 * half)
assert pa8.focal_length == 1
assert pa8.p_parameter == 1
assert pa8.vertex == Point2D(5, 0)
assert pa4.focal_length == pa5.focal_length
assert pa4.p_parameter == pa5.p_parameter
assert pa4.vertex == pa5.vertex
assert pa4.equation() == pa5.equation()
assert pa8.focal_length == pa9.focal_length
assert pa8.p_parameter == pa9.p_parameter
assert pa8.vertex == pa9.vertex
assert pa8.equation() == pa9.equation()
assert pa10.focal_length == pa11.focal_length == sqrt(
(a - b)**2) / 2 # if a, b real == abs(a - b)/2
assert pa11.vertex == Point(*pa10.vertex[::-1]) == Point(
a, a - sqrt(
(a - b)**2) * sign(a - b) / 2) # change axis x->y, y->x on pa10