index 7202bec..a5d9495 100644 (file)
@@ -5,8 +5,8 @@ import numbers
from . import islhelper

from .islhelper import mainctx, libisl
-from .geometry import GeometricObject, Point, Vector
-from .linexprs import Expression, Symbol, Rational
+from .geometry import GeometricObject, Point
+from .linexprs import Expression, Rational
from .domains import Domain

@@ -201,16 +201,16 @@ class Polyhedron(Domain):

def _repr_latex_(self):
if self.isempty():
-            return '\$\$\\emptyset\$\$'
+            return '\$\\emptyset\$'
elif self.isuniverse():
-            return '\$\$\\Omega\$\$'
+            return '\$\\Omega\$'
else:
strings = []
for equality in self.equalities:
strings.append('{} = 0'.format(equality._repr_latex_().strip('\$')))
for inequality in self.inequalities:
strings.append('{} \\ge 0'.format(inequality._repr_latex_().strip('\$')))
-            return '\$\${}\$\$'.format(' \\wedge '.join(strings))
+            return '\${}\$'.format(' \\wedge '.join(strings))

@classmethod
def fromsympy(cls, expr):
@@ -228,129 +228,6 @@ class Polyhedron(Domain):
constraints.append(sympy.Ge(inequality.tosympy(), 0))
return sympy.And(*constraints)

-    @classmethod
-    def _polygon_inner_point(cls, points):
-        symbols = points[0].symbols
-        coordinates = {symbol: 0 for symbol in symbols}
-        for point in points:
-            for symbol, coordinate in point.coordinates():
-                coordinates[symbol] += coordinate
-        for symbol in symbols:
-            coordinates[symbol] /= len(points)
-        return Point(coordinates)
-
-    @classmethod
-    def _sort_polygon_2d(cls, points):
-        if len(points) <= 3:
-            return points
-        o = cls._polygon_inner_point(points)
-        angles = {}
-        for m in points:
-            om = Vector(o, m)
-            dx, dy = (coordinate for symbol, coordinate in om.coordinates())
-            angle = math.atan2(dy, dx)
-            angles[m] = angle
-        return sorted(points, key=angles.get)
-
-    @classmethod
-    def _sort_polygon_3d(cls, points):
-        if len(points) <= 3:
-            return points
-        o = cls._polygon_inner_point(points)
-        a = points[0]
-        oa = Vector(o, a)
-        norm_oa = oa.norm()
-        for b in points[1:]:
-            ob = Vector(o, b)
-            u = oa.cross(ob)
-            if not u.isnull():
-                u = u.asunit()
-                break
-        else:
-            raise ValueError('degenerate polygon')
-        angles = {a: 0.}
-        for m in points[1:]:
-            om = Vector(o, m)
-            normprod = norm_oa * om.norm()
-            cosinus = max(oa.dot(om) / normprod, -1.)
-            sinus = u.dot(oa.cross(om)) / normprod
-            angle = math.acos(cosinus)
-            angle = math.copysign(angle, sinus)
-            angles[m] = angle
-        return sorted(points, key=angles.get)
-
-    def faces(self):
-        vertices = self.vertices()
-        faces = []
-        for constraint in self.constraints:
-            face = []
-            for vertex in vertices:
-                if constraint.subs(vertex.coordinates()) == 0:
-                    face.append(vertex)
-            faces.append(face)
-        return faces
-
-    def _plot_2d(self, plot=None, **kwargs):
-        import matplotlib.pyplot as plt
-        from matplotlib.patches import Polygon
-        vertices = self._sort_polygon_2d(self.vertices())
-        xys = [tuple(vertex.values()) for vertex in vertices]
-        if plot is None:
-            fig = plt.figure()
-            plot = fig.add_subplot(1, 1, 1)
-        xmin, xmax = plot.get_xlim()
-        ymin, ymax = plot.get_xlim()
-        xs, ys = zip(*xys)
-        xmin, xmax = min(xmin, float(min(xs))), max(xmax, float(max(xs)))
-        ymin, ymax = min(ymin, float(min(ys))), max(ymax, float(max(ys)))
-        plot.set_xlim(xmin, xmax)
-        plot.set_ylim(ymin, ymax)
-        return plot
-
-    def _plot_3d(self, plot=None, **kwargs):
-        import matplotlib.pyplot as plt
-        from mpl_toolkits.mplot3d import Axes3D
-        from mpl_toolkits.mplot3d.art3d import Poly3DCollection
-        if plot is None:
-            fig = plt.figure()
-            axes = Axes3D(fig)
-        else:
-            axes = plot
-        xmin, xmax = axes.get_xlim()
-        ymin, ymax = axes.get_xlim()
-        zmin, zmax = axes.get_xlim()
-        poly_xyzs = []
-        for vertices in self.faces():
-            if len(vertices) == 0:
-                continue
-            vertices = Polyhedron._sort_polygon_3d(vertices)
-            vertices.append(vertices[0])
-            face_xyzs = [tuple(vertex.values()) for vertex in vertices]
-            xs, ys, zs = zip(*face_xyzs)
-            xmin, xmax = min(xmin, float(min(xs))), max(xmax, float(max(xs)))
-            ymin, ymax = min(ymin, float(min(ys))), max(ymax, float(max(ys)))
-            zmin, zmax = min(zmin, float(min(zs))), max(zmax, float(max(zs)))
-            poly_xyzs.append(face_xyzs)
-        collection = Poly3DCollection(poly_xyzs, **kwargs)
-        axes.set_xlim(xmin, xmax)
-        axes.set_ylim(ymin, ymax)
-        axes.set_zlim(zmin, zmax)
-        return axes
-
-    def plot(self, plot=None, **kwargs):
-        """
-        Display 3D plot of set.
-        """
-        if self.dimension == 2:
-            return self._plot_2d(plot=plot, **kwargs)
-        elif self.dimension == 3:
-            return self._plot_3d(plot=plot, **kwargs)
-        else:
-            raise ValueError('polyhedron must be 2 or 3-dimensional')
-
-
def _polymorphic(func):
@functools.wraps(func)
def wrapper(left, right):