New example: Menger sponge, to be plotted

[linpy.git] / pypol / polyhedra.py

diff --git a/pypol/polyhedra.py b/pypol/polyhedra.py
index db99753..5d1bfa1 100644 (file)
--- a/pypol/polyhedra.py
+++ b/pypol/polyhedra.py
@@ -1,10 +1,11 @@
-

 import functools
 import functools

+import math

 import numbers
 
 from . import islhelper
 
 from .islhelper import mainctx, libisl
 import numbers
 
 from . import islhelper
 
 from .islhelper import mainctx, libisl

+from .geometry import GeometricObject, Point, Vector

 from .linexprs import Expression, Symbol, Rational
 from .domains import Domain
 
 from .linexprs import Expression, Symbol, Rational
 from .domains import Domain
 


@@ -31,11 +32,7 @@ class Polyhedron(Domain):
             if inequalities is not None:
                 raise TypeError('too many arguments')
             return cls.fromstring(equalities)
             if inequalities is not None:
                 raise TypeError('too many arguments')
             return cls.fromstring(equalities)

-        elif isinstance(equalities, Polyhedron):
-            if inequalities is not None:
-                raise TypeError('too many arguments')
-            return equalities
-        elif isinstance(equalities, Domain):
+        elif isinstance(equalities, GeometricObject):

             if inequalities is not None:
                 raise TypeError('too many arguments')
             return equalities.aspolyhedron()
             if inequalities is not None:
                 raise TypeError('too many arguments')
             return equalities.aspolyhedron()


@@ -74,9 +71,15 @@ class Polyhedron(Domain):
         return self,
 
     def disjoint(self):
         return self,
 
     def disjoint(self):

+        """
+        Return this set as disjoint.
+        """

         return self
 
     def isuniverse(self):
         return self
 
     def isuniverse(self):

+        """
+        Return true if this set is the Universe set.
+        """

         islbset = self._toislbasicset(self.equalities, self.inequalities,
             self.symbols)
         universe = bool(libisl.isl_basic_set_is_universe(islbset))
         islbset = self._toislbasicset(self.equalities, self.inequalities,
             self.symbols)
         universe = bool(libisl.isl_basic_set_is_universe(islbset))


@@ -84,8 +87,24 @@ class Polyhedron(Domain):
         return universe
 
     def aspolyhedron(self):
         return universe
 
     def aspolyhedron(self):

+        """
+        Return polyhedral hull of this set.
+        """

         return self
 
         return self
 

+    def __contains__(self, point):
+        if not isinstance(point, Point):
+            raise TypeError('point must be a Point instance')
+        if self.symbols != point.symbols:
+            raise ValueError('arguments must belong to the same space')
+        for equality in self.equalities:
+            if equality.subs(point.coordinates()) != 0:
+                return False
+        for inequality in self.inequalities:
+            if inequality.subs(point.coordinates()) < 0:
+                return False
+        return True
+

     def subs(self, symbol, expression=None):
         equalities = [equality.subs(symbol, expression)
             for equality in self.equalities]
     def subs(self, symbol, expression=None):
         equalities = [equality.subs(symbol, expression)
             for equality in self.equalities]


@@ -172,14 +191,27 @@ class Polyhedron(Domain):
         else:
             strings = []
             for equality in self.equalities:
         else:
             strings = []
             for equality in self.equalities:

-                strings.append('0 == {}'.format(equality))
+                strings.append('Eq({}, 0)'.format(equality))

             for inequality in self.inequalities:
             for inequality in self.inequalities:

-                strings.append('0 <= {}'.format(inequality))
+                strings.append('Ge({}, 0)'.format(inequality))

             if len(strings) == 1:
                 return strings[0]
             else:
                 return 'And({})'.format(', '.join(strings))
 
             if len(strings) == 1:
                 return strings[0]
             else:
                 return 'And({})'.format(', '.join(strings))
 

+    def _repr_latex_(self):
+        if self.isempty():
+            return '$\\emptyset$'
+        elif self.isuniverse():
+            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))
+

     @classmethod
     def fromsympy(cls, expr):
         domain = Domain.fromsympy(expr)
     @classmethod
     def fromsympy(cls, expr):
         domain = Domain.fromsympy(expr)


@@ -195,85 +227,201 @@ class Polyhedron(Domain):
         for inequality in self.inequalities:
             constraints.append(sympy.Ge(inequality.tosympy(), 0))
         return sympy.And(*constraints)
         for inequality in self.inequalities:
             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(self):
     def plot(self):

+        """
+        Display 3D plot of set. 
+        """

         import matplotlib.pyplot as plt
         import matplotlib.pyplot as plt

-        from matplotlib.path import Path

         import matplotlib.patches as patches
         import matplotlib.patches as patches

-        
+

         if len(self.symbols)> 3:
             raise TypeError
         if len(self.symbols)> 3:
             raise TypeError

-        
+

         elif len(self.symbols) == 2:
         elif len(self.symbols) == 2:

-            verts = self.vertices()
-            points = []
-            codes = [Path.MOVETO]   
-            for vert in verts:
-                pairs = ()
-                for sym in sorted(vert, key=Symbol.sortkey):
-                    num = vert.get(sym)
-                    pairs = pairs + (num,)
-                points.append(pairs)
-            points.append((0.0, 0.0))
-            num = len(points)
-            while num > 2:
-                codes.append(Path.LINETO)
-                num = num - 1
-            else:
-                codes.append(Path.CLOSEPOLY)
-            path = Path(points, codes)
+            import pylab
+            points = []  
+            for verts in self.vertices():
+                    pairs=()
+                    for coordinate, point in verts.coordinates():
+                        pairs = pairs + (float(point),)
+                    points.append(pairs)
+            cent=(sum([p[0] for p in points])/len(points),sum([p[1] for p in points])/len(points))
+            points.sort(key=lambda p: math.atan2(p[1]-cent[1],p[0]-cent[0]))
+            pylab.scatter([p[0] for p in points],[p[1] for p in points])
+            pylab.gca().add_patch(patches.Polygon(points,closed=True,fill=True))
+            pylab.grid()
+            pylab.show()
+
+        elif len(self.symbols)==3:
+            from mpl_toolkits.mplot3d import Axes3D
+            from mpl_toolkits.mplot3d.art3d import Poly3DCollection
+            faces = self.faces()

             fig = plt.figure()
             fig = plt.figure()

-            ax = fig.add_subplot(111)
-            patch = patches.PathPatch(path, facecolor='blue', lw=2)
-            ax.add_patch(patch)
-            ax.set_xlim(-5,5)
-            ax.set_ylim(-5,5)
+            ax = Axes3D(fig)
+            for face in faces:
+                points = []
+                vertices = Polyhedron._sort_polygon_3d(face)
+                for verts in vertices:
+                    pairs=()
+                    for coordinate, point in verts.coordinates():
+                        pairs = pairs + (float(point),)
+                    points.append(pairs)
+                collection = Poly3DCollection([points], alpha=0.7)
+                face_color = [0.5, 0.5, 1] # alternative: matplotlib.colors.rgb2hex([0.5, 0.5, 1])
+                collection.set_facecolor(face_color)
+                ax.add_collection3d(collection)
+            ax.set_xlabel('X')   
+            ax.set_xlim(0, 5)
+            ax.set_ylabel('Y')
+            ax.set_ylim(0, 5)
+            ax.set_zlabel('Z')
+            ax.set_zlim(0, 5)
+            plt.grid()      

             plt.show()
             plt.show()

-            
-        elif len(self.symbols)==3:
-            return 0
-            

         return points
         return points

-
+    
+    @classmethod
+    def limit(cls, faces, variable, lim):
+        sym = []
+        if variable is 'x':
+            n = 0
+        elif variable is 'y':
+            n = 1
+        elif variable is 'z':
+            n = 2
+        for face in faces:
+            for vert in face:
+                coordinates = vert.coordinates()
+                for point in enumerate(coordinates):
+                        coordinates.get(n)
+                        sym.append(points)
+        if lim == 0:
+            value = min(sym)
+        else:
+            value = max(sym)
+        return value

 
 def _polymorphic(func):
     @functools.wraps(func)
     def wrapper(left, right):
 
 def _polymorphic(func):
     @functools.wraps(func)
     def wrapper(left, right):

-        if isinstance(left, numbers.Rational):
-            left = Rational(left)
-        elif not isinstance(left, Expression):
-            raise TypeError('left must be a a rational number '
-                'or a linear expression')
-        if isinstance(right, numbers.Rational):
-            right = Rational(right)
-        elif not isinstance(right, Expression):
-            raise TypeError('right must be a a rational number '
-                'or a linear expression')
+        if not isinstance(left, Expression):
+            if isinstance(left, numbers.Rational):
+                left = Rational(left)
+            else:
+                raise TypeError('left must be a a rational number '
+                    'or a linear expression')
+        if not isinstance(right, Expression):
+            if isinstance(right, numbers.Rational):
+                right = Rational(right)
+            else:
+                raise TypeError('right must be a a rational number '
+                    'or a linear expression')

         return func(left, right)
     return wrapper
 
 @_polymorphic
 def Lt(left, right):
         return func(left, right)
     return wrapper
 
 @_polymorphic
 def Lt(left, right):

+    """
+    Return true if the first set is less than the second.
+    """

     return Polyhedron([], [right - left - 1])
 
 @_polymorphic
 def Le(left, right):
     return Polyhedron([], [right - left - 1])
 
 @_polymorphic
 def Le(left, right):

+    """
+    Return true the first set is less than or equal to the second.
+    """

     return Polyhedron([], [right - left])
 
 @_polymorphic
 def Eq(left, right):
     return Polyhedron([], [right - left])
 
 @_polymorphic
 def Eq(left, right):

+    """
+    Return true if the sets are equal.
+    """

     return Polyhedron([left - right], [])
 
 @_polymorphic
 def Ne(left, right):
     return Polyhedron([left - right], [])
 
 @_polymorphic
 def Ne(left, right):

+    """
+    Return true if the sets are NOT equal.
+    """

     return ~Eq(left, right)
 
 @_polymorphic
 def Gt(left, right):
     return ~Eq(left, right)
 
 @_polymorphic
 def Gt(left, right):

+    """
+    Return true if the first set is greater than the second set.
+    """

     return Polyhedron([], [left - right - 1])
 
 @_polymorphic
 def Ge(left, right):
     return Polyhedron([], [left - right - 1])
 
 @_polymorphic
 def Ge(left, right):

+    """
+    Return true if the first set is greater than or equal the second set.
+    """

     return Polyhedron([], [left - right])
 
 
     return Polyhedron([], [left - right])