Adds the voronoi module and demo
This commit is contained in:
Johann Dreo
parent
e8fdfbfa04
commit
ca985518b0
3 changed files with 144 additions and 18 deletions
41
run_all.py
41
run_all.py
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@ -159,23 +159,26 @@ else:
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hull_edges = list(utils.tour(hull))
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LOGN( "\t\tHull of",len(hull_edges),"edges" )
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LOGN( "\tRemove triangles that have at least one edge in common with the convex hull" )
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def adjoin_hull(triangle):
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"""Return True if the given triangle has at least one edge that is in the set hull_edges."""
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for (p,q) in utils.tour(list(triangle)):
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if (p,q) in hull_edges or (q,p) in hull_edges:
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return True
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return False
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LOGN( "\tRemove triangles that are not sub-parts of the Penrose tiling" )
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# def adjoin_hull(triangle):
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# """Return True if the given triangle has at least one edge that is in the set hull_edges."""
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# for (p,q) in utils.tour(list(triangle)):
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# if (p,q) in hull_edges or (q,p) in hull_edges:
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# return True
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# return False
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def acute_triangle(triangle):
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"""Return True if the center of the circumcircle of the given triangle lies inside the triangle.
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That is if the triangle is acute."""
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return triangulation.in_triangle( triangulation.circumcircle(triangle)[0], triangle )
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# FIXME at depth 3, some triangles have an edge in the convex hull...
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# Filter out edges that are in hull_edges
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tri_nohull = list(filter_if_not( adjoin_hull, triangles ))
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# tri_nohull = list(filter_if_not( adjoin_hull, triangles ))
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# Filter out triangles that are obtuse
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triangulated = list(filter_if_not( acute_triangle, tri_nohull ))
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# triangulated = list(filter_if_not( acute_triangle, tri_nohull ))
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triangulated = list(filter_if_not( acute_triangle, triangles ))
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LOGN( "\t\tRemoved", len(triangles)-len(triangulated), "triangles" )
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triangulation_edges = triangulation.edges_of( triangulated )
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@ -189,15 +192,18 @@ else:
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########################################################################
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if args.voronoi:
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voronoi_centers = utils.load_points(args.voronoi)
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# voronoi_centers = utils.load_points(args.voronoi)
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pass
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else:
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LOGN( "Compute the nodes of the Voronoï diagram" )
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voronoi_centers = voronoi.centers(triangulated)
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# LOGN( "Compute the nodes of the Voronoï diagram" )
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voronoi_graph = voronoi.dual( triangulated )
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voronoi_edges = voronoi.edges_of( voronoi_graph )
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voronoi_centers = voronoi_graph.keys()
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with open("d%i_voronoi_centers.points" % depth, "w") as fd:
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for p in voronoi_centers:
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fd.write( "%f %f\n" % (p[0],p[1]) )
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# with open("d%i_voronoi_centers.points" % depth, "w") as fd:
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# for p in voronoi_centers:
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# fd.write( "%f %f\n" % (p[0],p[1]) )
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########################################################################
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@ -238,8 +244,9 @@ uberplot.scatter_segments( ax, penrose_segments, edgecolor=tcol, alpha=0.9, line
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# triangulation
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uberplot.plot_segments( ax, triangulation_edges, edgecolor="green", alpha=0.2, linewidth=1 )
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# Voronoï centers
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uberplot.scatter_points( ax, voronoi_centers, edgecolor="none", facecolor="green", linewidth=0 )
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# Voronoï
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uberplot.scatter_points( ax, voronoi_centers, edgecolor="magenta", facecolor="white", s=200, alpha=0.5 )
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uberplot.plot_segments( ax, voronoi_edges, edgecolor="magenta", alpha=0.2, linewidth=1 )
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ax.set_aspect('equal')
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@ -39,7 +39,8 @@ def scatter_segments( ax, segments, **kwargs ):
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def scatter_points( ax, points, **kwargs ):
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x = [i[0] for i in points]
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y = [i[1] for i in points]
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ax.scatter( x,y, s=20, marker='o', **kwargs)
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# ax.scatter( x,y, s=20, marker='o', **kwargs)
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ax.scatter( x,y, marker='o', **kwargs)
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if __name__=="__main__":
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118
voronoi.py
Normal file
118
voronoi.py
Normal file
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@ -0,0 +1,118 @@
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#/usr/bin/env python
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from utils import tour,LOG,LOGN,x,y
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import triangulation
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def nodes( triangles ):
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"""Compute the locations of the centers of all the circumscribed circles of the given triangles"""
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for triangle in triangles:
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(cx,cy),r = triangulation.circumcircle(triangle)
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yield (cx,cy)
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def edge_in( edge, edges ):
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"""Return True if the given edge (or its symetric) is in the given polygon."""
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n,m = edge
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assert( len(n) == 2 )
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assert( len(m) == 2 )
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return (n,m) in edges or (m,n) in edges
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def neighbours( triangle, polygons ):
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"""Returns the set of triangles in candidates that have an edge in common with the given triangle."""
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for polygon in polygons:
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if polygon == triangle:
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continue
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# Convert list of points to list of edges, because we want to find EDGE neighbours.
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edges_poly = list(tour(list(polygon )))
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assert( len(list(edges_poly)) > 0 )
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edges_tri = list(tour(list(triangle)))
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assert( len(list(edges_tri)) > 0 )
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# If at least one of the edge that are in availables polygons are also in the given triangle.
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# Beware the symetric edges.
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# if any( edge_in( edge, edges_tri ) for edge in edges_poly ):
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# yield polygon
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for edge in edges_poly:
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if edge_in( edge, edges_tri ):
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yield polygon
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break
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def dual( triangles ):
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graph = {}
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def add_edge( current, neighbor ):
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if current in graph:
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if neighbor not in graph[current]:
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graph[current].append( neighbor )
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else:
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graph[current] = [ neighbor ]
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for triangle in triangles:
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assert( len(triangle) == 3 )
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current_node = triangulation.circumcircle(triangle)[0]
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assert( len(current_node) == 2 )
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for neighbor_triangle in neighbours( triangle, triangles ):
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neighbor_node = triangulation.circumcircle(neighbor_triangle)[0]
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assert( len(neighbor_node) == 2 )
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add_edge( current_node, neighbor_node )
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add_edge( neighbor_node, current_node )
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return graph
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def edges_of( graph ):
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# edges = set()
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edges = []
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for k in graph:
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for n in graph[k]:
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if k != n and (k,n) not in edges and (n,k) not in edges:
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# edges.add( (k,n) )
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edges.append( (k,n) )
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return edges
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if __name__ == "__main__":
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import sys
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import random
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import utils
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import uberplot
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import triangulation
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import matplotlib.pyplot as plot
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if len(sys.argv) > 1:
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scale = 100
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nb = int(sys.argv[1])
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points = [ (scale*random.random(),scale*random.random()) for i in range(nb)]
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else:
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points = [
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(0,40),
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(100,60),
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(40,0),
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(50,100),
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(90,10),
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# (50,50),
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]
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fig = plot.figure()
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triangles = triangulation.delaunay_bowyer_watson( points )
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delaunay_edges = triangulation.edges_of( triangles )
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voronoi_graph = dual( triangles )
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voronoi_edges = edges_of( voronoi_graph )
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print voronoi_edges
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ax = fig.add_subplot(111)
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ax.set_aspect('equal')
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uberplot.scatter_segments( ax, delaunay_edges, facecolor = "blue" )
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uberplot.plot_segments( ax, delaunay_edges, edgecolor = "blue" )
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uberplot.scatter_segments( ax, voronoi_edges, facecolor = "red" )
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uberplot.plot_segments( ax, voronoi_edges, edgecolor = "red" )
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plot.show()
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