Adds the voronoi module and demo

voronoi.py

@@ -0,0 +1,118 @@
+#/usr/bin/env python
+
+from utils import tour,LOG,LOGN,x,y
+import triangulation
+
+def nodes( triangles ):
+    """Compute the locations of the centers of all the circumscribed circles of the given triangles"""
+    for triangle in triangles:
+        (cx,cy),r = triangulation.circumcircle(triangle)
+        yield (cx,cy)
+
+
+def edge_in( edge, edges ):
+    """Return True if the given edge (or its symetric) is in the given polygon."""
+    n,m = edge
+    assert( len(n) == 2 )
+    assert( len(m) == 2 )
+    return (n,m) in edges or (m,n) in edges
+
+
+def neighbours( triangle, polygons ):
+    """Returns the set of triangles in candidates that have an edge in common with the given triangle."""
+    for polygon in polygons:
+        if polygon == triangle:
+            continue
+
+        # Convert list of points to list of edges, because we want to find EDGE neighbours.
+        edges_poly = list(tour(list(polygon )))
+        assert( len(list(edges_poly)) > 0 )
+        edges_tri  = list(tour(list(triangle)))
+        assert( len(list(edges_tri)) > 0 )
+
+        # If at least one of the edge that are in availables polygons are also in the given triangle.
+        # Beware the symetric edges.
+        # if any( edge_in( edge, edges_tri ) for edge in edges_poly ):
+        #     yield polygon
+        for edge in edges_poly:
+            if edge_in( edge, edges_tri ):
+                yield polygon
+                break
+
+
+def dual( triangles ):
+    graph = {}
+
+    def add_edge( current, neighbor ):
+        if current in graph:
+            if neighbor not in graph[current]:
+                graph[current].append( neighbor )
+        else:
+            graph[current] = [ neighbor ]
+
+    for triangle in triangles:
+        assert( len(triangle) == 3 )
+        current_node = triangulation.circumcircle(triangle)[0]
+        assert( len(current_node) == 2 )
+
+        for neighbor_triangle in neighbours( triangle, triangles ):
+            neighbor_node = triangulation.circumcircle(neighbor_triangle)[0]
+            assert( len(neighbor_node) == 2 )
+
+            add_edge(  current_node, neighbor_node )
+            add_edge( neighbor_node,  current_node )
+
+    return graph
+
+
+def edges_of( graph ):
+    # edges = set()
+    edges = []
+    for k in graph:
+        for n in graph[k]:
+            if k != n and (k,n) not in edges and (n,k) not in edges:
+                # edges.add( (k,n) )
+                edges.append( (k,n) )
+
+    return edges
+
+
+if __name__ == "__main__":
+    import sys
+    import random
+    import utils
+    import uberplot
+    import triangulation
+    import matplotlib.pyplot as plot
+
+    if len(sys.argv) > 1:
+        scale = 100
+        nb = int(sys.argv[1])
+        points = [ (scale*random.random(),scale*random.random()) for i in range(nb)]
+    else:
+        points = [
+                (0,40),
+                (100,60),
+                (40,0),
+                (50,100),
+                (90,10),
+                # (50,50),
+                ]
+
+    fig = plot.figure()
+
+    triangles = triangulation.delaunay_bowyer_watson( points )
+    delaunay_edges = triangulation.edges_of( triangles )
+
+    voronoi_graph = dual( triangles )
+    voronoi_edges = edges_of( voronoi_graph )
+    print voronoi_edges
+
+    ax = fig.add_subplot(111)
+    ax.set_aspect('equal')
+    uberplot.scatter_segments( ax, delaunay_edges, facecolor = "blue" )
+    uberplot.plot_segments( ax, delaunay_edges, edgecolor = "blue" )
+    uberplot.scatter_segments( ax, voronoi_edges, facecolor = "red" )
+    uberplot.plot_segments( ax, voronoi_edges, edgecolor = "red" )
+    plot.show()
+