From 843dede1d98c459f9761abff5877e0b019fa0155 Mon Sep 17 00:00:00 2001 From: Danielle Bolan Date: Thu, 17 Jul 2014 11:31:44 +0200 Subject: [PATCH] Plot domain added --- pypol/domains.py | 134 +++++++++++++++++++++++++++++++++++++++++++-- pypol/polyhedra.py | 133 ++------------------------------------------ 2 files changed, 134 insertions(+), 133 deletions(-) diff --git a/pypol/domains.py b/pypol/domains.py index 5db1856..23c21af 100644 --- a/pypol/domains.py +++ b/pypol/domains.py @@ -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) + 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: @@ -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): diff --git a/pypol/polyhedra.py b/pypol/polyhedra.py index 7202bec..a5d9495 100644 --- a/pypol/polyhedra.py +++ b/pypol/polyhedra.py @@ -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) - 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') - - def _polymorphic(func): @functools.wraps(func) def wrapper(left, right): -- 2.20.1