+ _RE_COORDINATE = re.compile(r'\((?P<num>\-?\d+)\)(/(?P<den>\d+))?')
+
+ def vertices(self):
+ """
+ Return a list of vertices for this Polygon.
+ """
+ from .polyhedra import Polyhedron
+ if not self.isbounded():
+ raise ValueError('domain must be bounded')
+ islbset = self._toislbasicset(self.equalities, self.inequalities, self.symbols)
+ vertices = libisl.isl_basic_set_compute_vertices(islbset);
+ vertices = islhelper.isl_vertices_vertices(vertices)
+ points = []
+ for vertex in vertices:
+ expr = libisl.isl_vertex_get_expr(vertex)
+ coordinates = []
+ if islhelper.isl_version < '0.13':
+ constraints = islhelper.isl_basic_set_constraints(expr)
+ for constraint in constraints:
+ constant = libisl.isl_constraint_get_constant_val(constraint)
+ constant = islhelper.isl_val_to_int(constant)
+ for index, symbol in enumerate(self.symbols):
+ coefficient = libisl.isl_constraint_get_coefficient_val(constraint,
+ libisl.isl_dim_set, index)
+ coefficient = islhelper.isl_val_to_int(coefficient)
+ if coefficient != 0:
+ coordinate = -Fraction(constant, coefficient)
+ coordinates.append((symbol, coordinate))
+ else:
+ string = islhelper.isl_multi_aff_to_str(expr)
+ matches = self._RE_COORDINATE.finditer(string)
+ for symbol, match in zip(self.symbols, matches):
+ numerator = int(match.group('num'))
+ denominator = match.group('den')
+ denominator = 1 if denominator is None else int(denominator)
+ coordinate = Fraction(numerator, denominator)
+ coordinates.append((symbol, coordinate))
+ points.append(Point(coordinates))
+ return points
+
+ def points(self):
+ """
+ Returns the points contained in the set.
+ """
+ if not self.isbounded():
+ raise ValueError('domain must be bounded')
+ from .polyhedra import Universe, Eq
+ islset = self._toislset(self.polyhedra, self.symbols)
+ islpoints = islhelper.isl_set_points(islset)
+ points = []
+ for islpoint in islpoints:
+ coordinates = {}
+ for index, symbol in enumerate(self.symbols):
+ coordinate = libisl.isl_point_get_coordinate_val(islpoint,
+ libisl.isl_dim_set, index)
+ coordinate = islhelper.isl_val_to_int(coordinate)
+ 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)
+ plot.add_patch(Polygon(xys, closed=True, **kwargs))
+ 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.add_collection3d(collection)
+ 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:
+ if point in polyhedron:
+ return True
+ return False
+
+ def subs(self, symbol, expression=None):
+ polyhedra = [polyhedron.subs(symbol, expression)
+ for polyhedron in self.polyhedra]
+ return Domain(*polyhedra)
+
projects / linpy.git / blobdiff