118 lines
3.5 KiB
Python
118 lines
3.5 KiB
Python
#/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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