Private methods to sort points in a polygon, untested

[linpy.git] / pypol / polyhedra.py

diff --git a/pypol/polyhedra.py b/pypol/polyhedra.py
index f93f31e..3db8f40 100644 (file)
--- a/pypol/polyhedra.py
+++ b/pypol/polyhedra.py
@@ -1,10 +1,12 @@
+
 import functools
+import math
 import numbers
 
 from . import islhelper
 
 from .islhelper import mainctx, libisl
-from .linexprs import Expression, Rational
+from .linexprs import Expression, Symbol, Rational
 from .domains import Domain
 
 
@@ -37,7 +39,7 @@ class Polyhedron(Domain):
         elif isinstance(equalities, Domain):
             if inequalities is not None:
                 raise TypeError('too many arguments')
-            return equalities.polyhedral_hull()
+            return equalities.aspolyhedron()
         if equalities is None:
             equalities = []
         else:
@@ -82,9 +84,16 @@ class Polyhedron(Domain):
         libisl.isl_basic_set_free(islbset)
         return universe
 
-    def polyhedral_hull(self):
+    def aspolyhedron(self):
         return self
 
+    def subs(self, symbol, expression=None):
+        equalities = [equality.subs(symbol, expression)
+            for equality in self.equalities]
+        inequalities = [inequality.subs(symbol, expression)
+            for inequality in self.inequalities]
+        return Polyhedron(equalities, inequalities)
+
     @classmethod
     def _fromislbasicset(cls, islbset, symbols):
         islconstraints = islhelper.isl_basic_set_constraints(islbset)
@@ -188,6 +197,81 @@ class Polyhedron(Domain):
             constraints.append(sympy.Ge(inequality.tosympy(), 0))
         return sympy.And(*constraints)
 
+    @classmethod
+    def _sort_polygon_2d(cls, points):
+        if len(points) <= 3:
+            return points
+        o = sum((Vector(point) for point in points)) / len(points)
+        o = Point(o.coordinates())
+        angles = {}
+        for m in points:
+            om = Vector(o, m)
+            dx, dy = (coordinate for symbol, coordinates 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 = sum((Vector(point) for point in points)) / len(points)
+        o = Point(o.coordinates())
+        a, b = points[:2]
+        oa = Vector(o, a)
+        ob = Vector(o, b)
+        norm_oa = oa.norm()
+        u = (oa.cross(ob)).asunit()
+        angles = {a: 0.}
+        for m in points[1:]:
+            om = Vector(o, m)
+            normprod = norm_oa * om.norm()
+            cosinus = oa.dot(om) / normprod
+            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 plot(self):
+        import matplotlib.pyplot as plt
+        from matplotlib.path import Path
+        import matplotlib.patches as patches
+
+        if len(self.symbols)> 3:
+            raise TypeError
+
+        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)
+            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)
+            plt.show()
+
+        elif len(self.symbols)==3:
+            return 0
+
+        return points
+
 
 def _polymorphic(func):
     @functools.wraps(func)