index 5db1856..23c21af 100644 (file)
@@ -1,13 +1,14 @@
import ast
import functools
import re
+import math

from fractions import Fraction

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

__all__ = [
@@ -361,8 +362,6 @@ class Domain(GeometricObject):
coordinate = -Fraction(constant, coefficient)
coordinates.append((symbol, coordinate))
else:
-
-                # horrible hack, find a cleaner solution
string = islhelper.isl_multi_aff_to_str(expr)
matches = self._RE_COORDINATE.finditer(string)
for symbol, match in zip(self.symbols, matches):
@@ -393,6 +392,131 @@ class Domain(GeometricObject):
coordinates[symbol] = coordinate
points.append(Point(coordinates))
return points
+
+    @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
+        for polyhedron in self.polyhedra:
+            vertices = polyhedron._sort_polygon_2d(polyhedron.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):
+        from .polyhedra import Polyhedron
+        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 polyhedron in self.polyhedra:
+            for vertices in polyhedron.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 plot of this 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 __contains__(self, point):
for polyhedron in self.polyhedra:
@@ -521,7 +645,7 @@ class Domain(GeometricObject):
strings = []
for polyhedron in self.polyhedra:
strings.append('({})'.format(polyhedron._repr_latex_().strip('\$')))
-        return '\$\${}\$\$'.format(' \\vee '.join(strings))
+        return '\${}\$'.format(' \\vee '.join(strings))

@classmethod
def fromsympy(cls, expr):