+ @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)
+ plot.add_patch(Polygon(xys, closed=True, **kwargs))
+ 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.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 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')
+
projects / linpy.git / blobdiff