def __new__(cls, p1, p2, **kwargs):
if not isinstance(p1, Point) or not isinstance(p2, Point):
raise TypeError("%s.__new__ requires Point instances" % cls.__name__)
if p1 == p2:
raise RuntimeError("%s.__new__ requires two distinct points" % cls.__name__)
return GeometryEntity.__new__(cls, p1, p2, **kwargs)
def __new__(cls, center=None, hradius=None, vradius=None, eccentricity=None,
**kwargs):
hradius = sympify(hradius)
vradius = sympify(vradius)
eccentricity = sympify(eccentricity)
if len(filter(None, (hradius, vradius, eccentricity))) != 2:
raise ValueError, 'Exactly two arguments between "hradius", '\
'"vradius", and "eccentricity" must be not None."'
if eccentricity is not None:
if hradius is None:
hradius = vradius / sqrt(1 - eccentricity**2)
elif vradius is None:
vradius = hradius * sqrt(1 - eccentricity**2)
else:
if hradius is None and vradius is None:
raise ValueError("At least two arguments between hradius, "
"vradius and eccentricity must not be none.")
if center is None:
center = Point(0, 0)
if not isinstance(center, Point):
raise TypeError("center must be a Point")
if hradius == vradius:
return Circle(center, hradius, **kwargs)
return GeometryEntity.__new__(cls, center, hradius, vradius, **kwargs)
def __new__(cls, function, limits):
fun = sympify(function)
if not fun:
raise GeometryError("%s.__new__ don't know how to handle" % cls.__name__);
if not isinstance(limits, (list, tuple)) or len(limits) != 3:
raise ValueError("Limits argument has wrong syntax");
return GeometryEntity.__new__(cls, fun, limits)
def __new__(cls, center=None, hradius=None, vradius=None, eccentricity=None,
**kwargs):
hradius = sympify(hradius)
vradius = sympify(vradius)
eccentricity = sympify(eccentricity)
if center is None:
center = Point(0, 0)
else:
center = Point(center)
if len(filter(None, (hradius, vradius, eccentricity))) != 2:
raise ValueError('Exactly two arguments of "hradius", '\
'"vradius", and "eccentricity" must not be None."')
if eccentricity is not None:
if hradius is None:
hradius = vradius / sqrt(1 - eccentricity**2)
elif vradius is None:
vradius = hradius * sqrt(1 - eccentricity**2)
if hradius == vradius:
return Circle(center, hradius, **kwargs)
return GeometryEntity.__new__(cls, center, hradius, vradius, **kwargs)
def __new__(cls, *args, **kwargs):
if len(args) != 3:
raise GeometryError("Triangle.__new__ requires three points")
vertices = [Point(a) for a in args]
# remove consecutive duplicates
nodup = []
for p in vertices:
if nodup and p == nodup[-1]:
continue
nodup.append(p)
if len(nodup) > 1 and nodup[-1] == nodup[0]:
nodup.pop() # last point was same as first
# remove collinear points
i = -3
while i < len(nodup) - 3 and len(nodup) > 2:
a, b, c = sorted([nodup[i], nodup[i + 1], nodup[i + 2]])
if Point.is_collinear(a, b, c):
nodup[i] = a
nodup[i + 1] = None
nodup.pop(i + 1)
i += 1
vertices = filter(lambda x: x is not None, nodup)
if len(vertices) == 3:
return GeometryEntity.__new__(cls, *vertices, **kwargs)
elif len(vertices) == 2:
return Segment(*vertices, **kwargs)
else:
return Point(*vertices, **kwargs)
def __new__(
cls, center=None, hradius=None, vradius=None, eccentricity=None,
**kwargs):
hradius = sympify(hradius)
vradius = sympify(vradius)
eccentricity = sympify(eccentricity)
if center is None:
center = Point(0, 0)
else:
center = Point(center)
if len(filter(None, (hradius, vradius, eccentricity))) != 2:
raise ValueError('Exactly two arguments of "hradius", '
'"vradius", and "eccentricity" must not be None."')
if eccentricity is not None:
if hradius is None:
hradius = vradius / sqrt(1 - eccentricity**2)
elif vradius is None:
vradius = hradius * sqrt(1 - eccentricity**2)
if hradius == vradius:
return Circle(center, hradius, **kwargs)
return GeometryEntity.__new__(cls, center, hradius, vradius, **kwargs)
def __new__(cls, *args, **kwargs):
if len(args) != 3:
raise GeometryError("Triangle.__new__ requires three points")
vertices = [Point(a) for a in args]
# remove consecutive duplicates
nodup = []
for p in vertices:
if nodup and p == nodup[-1]:
continue
nodup.append(p)
if len(nodup) > 1 and nodup[-1] == nodup[0]:
nodup.pop() # last point was same as first
# remove collinear points
i = -3
while i < len(nodup) - 3 and len(nodup) > 2:
a, b, c = sorted([nodup[i], nodup[i + 1], nodup[i + 2]])
if Point.is_collinear(a, b, c):
nodup[i] = a
nodup[i + 1] = None
nodup.pop(i + 1)
i += 1
vertices = filter(lambda x: x is not None, nodup)
if len(vertices) == 3:
return GeometryEntity.__new__(cls, *vertices, **kwargs)
elif len(vertices) == 2:
return Segment(*vertices, **kwargs)
else:
return Point(*vertices, **kwargs)
def __new__(cls, function, limits):
fun = sympify(function)
if not ordered_iter(fun) or len(fun) != 2:
raise ValueError("Function argument should be (x(t), y(t)) but got %s" % str(function))
if not ordered_iter(limits) or len(limits) != 3:
raise ValueError("Limit argument should be (t, tmin, tmax) but got %s" % str(limits))
return GeometryEntity.__new__(cls, tuple(sympify(fun)), tuple(sympify(limits)))
def __new__(cls,
center=None,
hradius=None,
vradius=None,
eccentricity=None,
**kwargs):
hradius = sympify(hradius)
vradius = sympify(vradius)
eccentricity = sympify(eccentricity)
if len(filter(None, (hradius, vradius, eccentricity))) != 2:
raise ValueError, 'Exactly two arguments between "hradius", '\
'"vradius", and "eccentricity" must be not None."'
if eccentricity is not None:
if hradius is None:
hradius = vradius / sqrt(1 - eccentricity**2)
elif vradius is None:
vradius = hradius * sqrt(1 - eccentricity**2)
else:
if hradius is None and vradius is None:
raise ValueError("At least two arguments between hradius, "
"vradius and eccentricity must not be none.")
if center is None:
center = Point(0, 0)
if not isinstance(center, Point):
raise TypeError("center must be a Point")
if hradius == vradius:
return Circle(center, hradius, **kwargs)
return GeometryEntity.__new__(cls, center, hradius, vradius, **kwargs)
def __new__(cls, p1, p2, **kwargs):
if not isinstance(p1, Point) or not isinstance(p2, Point):
raise TypeError("%s.__new__ requires Point instances" % cls.__name__)
if p1 == p2:
raise RuntimeError("%s.__new__ requires two distinct points" % cls.__name__)
return GeometryEntity.__new__(cls, p1, p2, **kwargs)
def __new__(cls, p1, p2, **kwargs):
p1 = Point(p1)
p2 = Point(p2)
if p1 == p2:
# Rolygon returns lower priority classes...should LinearEntity, too?
return p1 # raise ValueError("%s.__new__ requires two unique Points." % cls.__name__)
return GeometryEntity.__new__(cls, p1, p2, **kwargs)
def __new__(cls, p1, p2, **kwargs):
p1 = Point(p1)
p2 = Point(p2)
if p1 == p2:
# Rolygon returns lower priority classes...should LinearEntity, too?
return p1 # raise ValueError("%s.__new__ requires two unique Points." % cls.__name__)
return GeometryEntity.__new__(cls, p1, p2, **kwargs)
def __new__(cls, center, hradius, vradius, **kwargs):
hradius = sympify(hradius)
vradius = sympify(vradius)
if not isinstance(center, Point):
raise TypeError("center must be be a Point")
if hradius == vradius:
return Circle(center, hradius, **kwargs)
return GeometryEntity.__new__(cls, center, hradius, vradius, **kwargs)
def __new__(cls, center, hradius, vradius, **kwargs):
hradius = sympify(hradius)
vradius = sympify(vradius)
if not isinstance(center, Point):
raise TypeError("center must be be a Point")
if hradius == vradius:
return Circle(center, hradius, **kwargs)
return GeometryEntity.__new__(cls, center, hradius, vradius, **kwargs)
def __new__(cls, *args, **kwargs):
if isinstance(args[0], (tuple, list, set)):
coords = tuple([sympify(x) for x in args[0]])
else:
coords = tuple([sympify(x) for x in args])
if len(coords) != 2:
raise NotImplementedError("Only two dimensional points currently supported")
return GeometryEntity.__new__(cls, *coords)
def __new__(cls, *args, **kwargs):
vertices = GeometryEntity.extract_entities(args, remove_duplicates=False)
if len(vertices) != 3:
raise GeometryError("Triangle.__new__ requires three points")
for p in vertices:
if not isinstance(p, Point):
raise GeometryError("Triangle.__new__ requires three points")
return GeometryEntity.__new__(cls, *vertices, **kwargs)
def __new__(cls, *args, **kwargs):
vertices = GeometryEntity.extract_entities(args, remove_duplicates=False)
if len(vertices) != 3:
raise GeometryError("Triangle.__new__ requires three points")
for p in vertices:
if not isinstance(p, Point):
raise GeometryError("Triangle.__new__ requires three points")
return GeometryEntity.__new__(cls, *vertices, **kwargs)
def __new__(cls, *args, **kwargs):
if isinstance(args[0], (tuple, list, set)):
coords = tuple([sympify(x) for x in args[0]])
else:
coords = tuple([sympify(x) for x in args])
if len(coords) != 2:
raise NotImplementedError("Only two dimensional points currently supported")
return GeometryEntity.__new__(cls, *coords)
def __new__(self, c, r, n, **kwargs):
r = sympify(r)
if not isinstance(c, Point):
raise GeometryError("RegularPolygon.__new__ requires c to be a Point instance")
if not isinstance(r, Basic):
raise GeometryError("RegularPolygon.__new__ requires r to be a number or Basic instance")
if n < 3:
raise GeometryError("RegularPolygon.__new__ requires n >= 3")
obj = GeometryEntity.__new__(self, c, r, n, **kwargs)
return obj
def __new__(self, c, r, n, **kwargs):
r = sympify(r)
if not isinstance(c, Point):
raise GeometryError("RegularPolygon.__new__ requires c to be a Point instance")
if not isinstance(r, Basic):
raise GeometryError("RegularPolygon.__new__ requires r to be a number or Basic instance")
if n < 3:
raise GeometryError("RegularPolygon.__new__ requires n >= 3")
obj = GeometryEntity.__new__(self, c, r, n, **kwargs)
return obj
def __new__(cls, function, limits):
fun = sympify(function)
if not is_sequence(fun) or len(fun) != 2:
raise ValueError(
"Function argument should be (x(t), y(t)) but got %s" %
str(function))
if not is_sequence(limits) or len(limits) != 3:
raise ValueError(
"Limit argument should be (t, tmin, tmax) but got %s" %
str(limits))
return GeometryEntity.__new__(cls, tuple(sympify(fun)),
tuple(sympify(limits)))
def __new__(cls, *args, **kwargs):
if iterable(args[0]):
coords = Tuple(*args[0])
elif isinstance(args[0], Point):
coords = args[0].args
else:
coords = Tuple(*args)
if len(coords) != 2:
raise NotImplementedError("Only two dimensional points currently supported")
return GeometryEntity.__new__(cls, *coords)
def __new__(cls, *args, **kwargs):
if iterable(args[0]):
coords = Tuple(*args[0])
elif isinstance(args[0], Point):
coords = args[0].args
else:
coords = Tuple(*args)
if len(coords) != 2:
raise NotImplementedError(
"Only two dimensional points currently supported")
return GeometryEntity.__new__(cls, *coords)
def __new__(self, c, r, n, rot=0, **kwargs):
r, n, rot = sympify([r, n, rot])
c = Point(c)
if not isinstance(r, Basic):
raise GeometryError("RegularPolygon.__new__ requires r to be a number or Basic instance")
if n < 3:
raise GeometryError("RegularPolygon.__new__ requires n >= 3")
obj = GeometryEntity.__new__(self, c, r, n, **kwargs)
obj._n = n
obj._center = c
obj._radius = r
obj._rot = rot
return obj
def __new__(cls, *args, **kwargs):
if iterable(args[0]):
coords = Tuple(*args[0])
elif isinstance(args[0], Point):
coords = args[0].args
else:
coords = Tuple(*args)
if len(coords) != 2:
raise NotImplementedError("Only two dimensional points currently supported")
if kwargs.get('evaluate', True):
coords = [nsimplify(c) for c in coords]
return GeometryEntity.__new__(cls, *coords)
def __new__(cls, *args, **kwargs):
if iterable(args[0]):
coords = Tuple(*args[0])
elif isinstance(args[0], Point):
coords = args[0].args
else:
coords = Tuple(*args)
if len(coords) != 2:
raise NotImplementedError(
"Only two dimensional points currently supported")
if kwargs.get('evaluate', True):
coords = [simplify(nsimplify(c, rational=True)) for c in coords]
return GeometryEntity.__new__(cls, *coords)
def __new__(self, c, r, n, rot=0, **kwargs):
r, n, rot = sympify([r, n, rot])
c = Point(c)
if not isinstance(r, Basic):
raise GeometryError(
"RegularPolygon.__new__ requires r to be a number or Basic instance"
)
if n < 3:
raise GeometryError("RegularPolygon.__new__ requires n >= 3")
obj = GeometryEntity.__new__(self, c, r, n, **kwargs)
obj._n = n
obj._center = c
obj._radius = r
obj._rot = rot
return obj
def __new__(cls, *args, **kwargs):
c, r = None, None
if len(args) == 3 and isinstance(args[0], Point):
from polygon import Triangle
t = Triangle(args[0], args[1], args[2])
if t.area == 0:
raise GeometryError("Cannot construct a circle from three collinear points")
c = t.circumcenter
r = t.circumradius
elif len(args) == 2:
# Assume (center, radius) pair
c = args[0]
r = sympify(args[1])
if not (c is None or r is None):
return GeometryEntity.__new__(cls, c, r, **kwargs)
raise GeometryError("Circle.__new__ received unknown arguments")
def __new__(cls, *args, **kwargs):
c, r = None, None
if len(args) == 3 and isinstance(args[0], Point):
from polygon import Triangle
t = Triangle(args[0], args[1], args[2])
if t.area == 0:
raise GeometryError("Cannot construct a circle from three collinear points")
c = t.circumcenter
r = t.circumradius
elif len(args) == 2:
# Assume (center, radius) pair
c = args[0]
r = sympify(args[1])
if not (c is None or r is None):
return GeometryEntity.__new__(cls, c, r, **kwargs)
raise GeometryError("Circle.__new__ received unknown arguments")
def __new__(cls, *args, **kwargs):
c, r = None, None
if len(args) == 3:
args = [Point(a) for a in args]
if Point.is_collinear(*args):
raise GeometryError("Cannot construct a circle from three collinear points")
from polygon import Triangle
t = Triangle(*args)
c = t.circumcenter
r = t.circumradius
elif len(args) == 2:
# Assume (center, radius) pair
c = Point(args[0])
r = sympify(args[1])
if not (c is None or r is None):
return GeometryEntity.__new__(cls, c, r, **kwargs)
raise GeometryError("Circle.__new__ received unknown arguments")
def __new__(cls, *args, **kwargs):
if kwargs.get('n', 0):
n = kwargs.pop('n')
args = list(args)
# return a virtual polygon with n sides
if len(args) == 2: # center, radius
args.append(n)
elif len(args) == 3: # center, radius, rotation
args.insert(2, n)
return RegularPolygon(*args, **kwargs)
vertices = [Point(a) for a in args]
# remove consecutive duplicates
nodup = []
for p in vertices:
if nodup and p == nodup[-1]:
continue
nodup.append(p)
if len(nodup) > 1 and nodup[-1] == nodup[0]:
nodup.pop() # last point was same as first
# remove collinear points unless they are shared points
got = set()
shared = set()
for p in nodup:
if p in got:
shared.add(p)
else:
got.add(p)
i = -3
while i < len(nodup) - 3 and len(nodup) > 2:
a, b, c = sorted([nodup[i], nodup[i + 1], nodup[i + 2]])
if b not in shared and Point.is_collinear(a, b, c):
nodup[i] = a
nodup[i + 1] = None
nodup.pop(i + 1)
i += 1
vertices = filter(lambda x: x is not None, nodup)
if len(vertices) > 3:
rv = GeometryEntity.__new__(cls, *vertices, **kwargs)
elif len(vertices) == 3:
return Triangle(*vertices, **kwargs)
elif len(vertices) == 2:
return Segment(*vertices, **kwargs)
else:
return Point(*vertices, **kwargs)
# reject polygons that have intersecting sides unless the
# intersection is a shared point or a generalized intersection.
# A self-intersecting polygon is easier to detect than a
# random set of segments since only those sides that are not
# part of the convex hull can possibly intersect with other
# sides of the polygon...but for now we use the n**2 algorithm
# and check all sides with intersection with any preceding sides
hit = _symbol('hit')
if not rv.is_convex:
sides = rv.sides
for i, si in enumerate(sides):
pts = si[0], si[1]
ai = si.arbitrary_point(hit)
for j in xrange(i):
sj = sides[j]
if sj[0] not in pts and sj[1] not in pts:
aj = si.arbitrary_point(hit)
tx = (solve(ai[0] - aj[0]) or [S.Zero])[0]
if tx.is_number and 0 <= tx <= 1:
ty = (solve(ai[1] - aj[1]) or [S.Zero])[0]
if (tx or ty) and ty.is_number and 0 <= ty <= 1:
print ai, aj
raise GeometryError("Polygon has intersecting sides.")
return rv
def __new__(cls, *args, **kwargs):
if kwargs.get('n', 0):
n = kwargs.pop('n')
args = list(args)
# return a virtual polygon with n sides
if len(args) == 2: # center, radius
args.append(n)
elif len(args) == 3: # center, radius, rotation
args.insert(2, n)
return RegularPolygon(*args, **kwargs)
vertices = [Point(a) for a in args]
# remove consecutive duplicates
nodup = []
for p in vertices:
if nodup and p == nodup[-1]:
continue
nodup.append(p)
if len(nodup) > 1 and nodup[-1] == nodup[0]:
nodup.pop() # last point was same as first
# remove collinear points unless they are shared points
got = set()
shared = set()
for p in nodup:
if p in got:
shared.add(p)
else:
got.add(p)
i = -3
while i < len(nodup) - 3 and len(nodup) > 2:
a, b, c = sorted([nodup[i], nodup[i + 1], nodup[i + 2]])
if b not in shared and Point.is_collinear(a, b, c):
nodup[i] = a
nodup[i + 1] = None
nodup.pop(i + 1)
i += 1
vertices = filter(lambda x: x is not None, nodup)
if len(vertices) > 3:
rv = GeometryEntity.__new__(cls, *vertices, **kwargs)
elif len(vertices) == 3:
return Triangle(*vertices, **kwargs)
elif len(vertices) == 2:
return Segment(*vertices, **kwargs)
else:
return Point(*vertices, **kwargs)
# reject polygons that have intersecting sides unless the
# intersection is a shared point or a generalized intersection.
# A self-intersecting polygon is easier to detect than a
# random set of segments since only those sides that are not
# part of the convex hull can possibly intersect with other
# sides of the polygon...but for now we use the n**2 algorithm
# and check all sides with intersection with any preceding sides
hit = _symbol('hit')
if not rv.is_convex:
sides = rv.sides
for i, si in enumerate(sides):
pts = si[0], si[1]
ai = si.arbitrary_point(hit)
for j in xrange(i):
sj = sides[j]
if sj[0] not in pts and sj[1] not in pts:
aj = si.arbitrary_point(hit)
tx = (solve(ai[0] - aj[0]) or [S.Zero])[0]
if tx.is_number and 0 <= tx <= 1:
ty = (solve(ai[1] - aj[1]) or [S.Zero])[0]
if (tx or ty) and ty.is_number and 0 <= ty <= 1:
print ai, aj
raise GeometryError(
"Polygon has intersecting sides.")
return rv