def is_concyclic(*points):
"""Is a sequence of points concyclic?
Test whether or not a sequence of points are concyclic (i.e., they lie
on a circle).
Parameters
----------
points : sequence of Points
Returns
-------
is_concyclic : boolean
True if points are concyclic, False otherwise.
Notes
-----
No points are not considered to be concyclic. One or two points
are definitely concyclic and three points are conyclic iff they
are not collinear.
For more than three points, create a circle from the first three
points. If the circle cannot be created (i.e., they are collinear)
then all of the points cannot be concyclic. If the circle is created
successfully then simply check the remaining points for containment
in the circle.
Examples
--------
>>> from sympy.geometry import Point
>>> p1, p2 = Point(-1, 0), Point(1, 0)
>>> p3, p4 = Point(0, 1), Point(-1, 2)
>>> Point.is_concyclic(p1, p2, p3)
True
>>> Point.is_concyclic(p1, p2, p3, p4)
False
"""
if len(points) == 0:
return False
if len(points) <= 2:
return True
points = [Point(p) for p in points]
if len(points) == 3:
return (not Point.is_collinear(*points))
try:
from ellipse import Circle
c = Circle(points[0], points[1], points[2])
for point in points[3:]:
if point not in c:
return False
return True
except GeometryError, e:
# Circle could not be created, because of collinearity of the
# three points passed in, hence they are not concyclic.
return False
def is_concyclic(*points):
"""
Test whether or not a set of points are concyclic (i.e., on the same
circle). Returns True if they are concyclic, or False otherwise.
Example:
========
>>> from sympy.geometry import Point
>>> p1,p2 = Point(-1, 0), Point(1, 0)
>>> p3,p4 = Point(0, 1), Point(-1, 2)
>>> Point.is_concyclic(p1, p2, p3)
True
>>> Point.is_concyclic(p1, p2, p3, p4)
False
Description of method used:
===========================
No points are not considered to be concyclic. One or two points
are definitely concyclic and three points are conyclic iff they
are not collinear.
For more than three points, we pick the first three points and
attempt to create a circle. If the circle cannot be created
(i.e., they are collinear) then all of the points cannot be
concyclic. If the circle is created successfully then simply
check all of the other points for containment in the circle.
"""
points = GeometryEntity.extract_entities(points)
if len(points) == 0: return False
if len(points) <= 2: return True
if len(points) == 3: return (not Point.is_collinear(*points))
try:
from ellipse import Circle
c = Circle(points[0], points[1], points[2])
for point in points[3:]:
if point not in c:
return False
return True
except GeometryError, e:
# Circle could not be created, because of collinearity of the
# three points passed in, hence they are not concyclic.
return False
def incircle(self):
"""The incircle of the RegularPolygon.
Returns
-------
incircle : Circle
See Also
--------
Circle
Examples
--------
>>> from sympy.geometry import RegularPolygon, Point
>>> rp = RegularPolygon(Point(0, 0), 4, 8)
>>> rp.incircle
Circle(Point(0, 0), 4*cos(pi/8))
"""
return Circle(self.center, self.apothem)
def circumcircle(self):
"""The circumcircle of the RegularPolygon.
Returns
-------
circumcircle : Circle
See Also
--------
Circle
Examples
--------
>>> from sympy.geometry import RegularPolygon, Point
>>> rp = RegularPolygon(Point(0, 0), 4, 8)
>>> rp.circumcircle
Circle(Point(0, 0), 4)
"""
return Circle(self.center, self.radius)
def circumcircle(self):
"""The circle which passes through the three vertices of the triangle.
Returns
-------
circumcircle : Circle
See Also
--------
Circle
Examples
--------
>>> from sympy.geometry import Point, Triangle
>>> p1, p2, p3 = Point(0, 0), Point(1, 0), Point(0, 1)
>>> t = Triangle(p1, p2, p3)
>>> t.circumcircle
Circle(Point(1/2, 1/2), sqrt(2)/2)
"""
return Circle(self.circumcenter, self.circumradius)
def incircle(self):
"""The incircle of the triangle.
The incircle is the circle which lies inside the triangle and touches
all three sides.
Returns
-------
incircle : Circle
See Also
--------
Circle
Examples
--------
>>> from sympy.geometry import Point, Triangle
>>> p1, p2, p3 = Point(0, 0), Point(2, 0), Point(0, 2)
>>> t = Triangle(p1, p2, p3)
>>> t.incircle
Circle(Point(-sqrt(2) + 2, -sqrt(2) + 2), -sqrt(2) + 2)
"""
return Circle(self.incenter, self.inradius)
def incircle(self):
"""The incircle of the triangle."""
return Circle(self.incenter, self.inradius)
def circumcircle(self):
"""The circumcircle of the triangle."""
return Circle(self.circumcenter, self.circumradius)
def incircle(self):
"""Returns a Circle instance describing the inscribed circle."""
return Circle(self.center, self.apothem)
def circumcircle(self):
"""Returns a Circle instance describing the circumcircle."""
return Circle(self.center, self.radius)