From 45951a9f688b1a3dda02979cacb93747b1422709 Mon Sep 17 00:00:00 2001
From: Vivien Maisonneuve <v.maisonneuve@gmail.com>
Date: Fri, 11 Jul 2014 15:41:26 +0200
Subject: [PATCH] Private methods to sort points in a polygon, untested

---
 pypol/coordinates.py |  2 +-
 pypol/polyhedra.py   | 49 ++++++++++++++++++++++++++++++++++++++------
 2 files changed, 44 insertions(+), 7 deletions(-)

diff --git a/pypol/coordinates.py b/pypol/coordinates.py
index eb8e78c..9e46673 100644
--- a/pypol/coordinates.py
+++ b/pypol/coordinates.py
@@ -171,7 +171,7 @@ class Vector(Coordinates):
         """
         if not isinstance(other, Vector):
             raise TypeError('argument must be a Vector instance')
-        cosinus = self.dot(other) / (self.norm() * other.norm())
+        cosinus = self.dot(other) / (self.norm()*other.norm())
         return math.acos(cosinus)
 
     def cross(self, other):
diff --git a/pypol/polyhedra.py b/pypol/polyhedra.py
index db99753..3db8f40 100644
--- a/pypol/polyhedra.py
+++ b/pypol/polyhedra.py
@@ -1,5 +1,6 @@
 
 import functools
+import math
 import numbers
 
 from . import islhelper
@@ -195,19 +196,55 @@ class Polyhedron(Domain):
         for inequality in self.inequalities:
             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]   
+            codes = [Path.MOVETO]
             for vert in verts:
                 pairs = ()
                 for sym in sorted(vert, key=Symbol.sortkey):
@@ -229,10 +266,10 @@ class Polyhedron(Domain):
             ax.set_xlim(-5,5)
             ax.set_ylim(-5,5)
             plt.show()
-            
+
         elif len(self.symbols)==3:
             return 0
-            
+
         return points
 
 
-- 
2.20.1