-voronoi_utility.py:

	-currently: trying to improve code performance based on practical profiling results
	-voronoi_region_vertices_spherical_surface() function has been reverted to the pre-vectorization state (after all that work!) because it surprisingly performs better with all the Python for loops (in practical testing) -- it was worth a shot...

Author: tylerjereddy

voronoi_utility.py

@@ -124,6 +124,7 @@ def poly_area(poly):
 
 def calculate_surface_area_of_a_spherical_Voronoi_polygon(array_ordered_Voronoi_polygon_vertices,sphere_radius):
     '''Calculate the surface area of a polygon on the surface of a sphere. Based on equation provided here: http://mathworld.wolfram.com/SphericalPolygon.html'''
+    spherical_array_Voronoi_polygon_vertices_before_filtering = convert_cartesian_array_to_spherical_array(array_ordered_Voronoi_polygon_vertices)
     array_ordered_Voronoi_polygon_vertices = filter_polygon_vertex_coordinates_for_extreme_proximity(array_ordered_Voronoi_polygon_vertices,sphere_radius) #filter vertices for extreme proximity
     #theta = calculate_and_sum_up_inner_sphere_surface_angles_Voronoi_polygon(array_ordered_Voronoi_polygon_vertices,sphere_radius) #suppressing this calculation while I test the pure-planar SA calculation approach
     n = array_ordered_Voronoi_polygon_vertices.shape[0]
@@ -387,45 +388,53 @@ def delaunay_triangulation_spherical_surface(self):
         array_points_vertices_Delaunay_triangulation = produce_triangle_vertex_coordinate_array_Delaunay_sphere(self.hull_instance)
         return array_points_vertices_Delaunay_triangulation
 
-    #@profile
     def voronoi_region_vertices_spherical_surface(self):
-        '''Returns a dictionary with the sorted (non-intersecting) polygon vertices for the Voronoi regions associated with each generator (original data point) index. A dictionary entry would be structured as follows: `{generator_index : array_polygon_vertices, ...}`. Now modifying the function to return a numpy array of indices instead -- to improve performance, reduce memory usage, etc.'''
+        '''Returns a dictionary with the sorted (non-intersecting) polygon vertices for the Voronoi regions associated with each generator (original data point) index. A dictionary entry would be structured as follows: `{generator_index : array_polygon_vertices, ...}`.'''
+        #print '---------------------'
+        #print 'Producing Voronoi Diagram'
         #generate the array of Voronoi vertices:
         facet_coordinate_array_Delaunay_triangulation = produce_triangle_vertex_coordinate_array_Delaunay_sphere(self.hull_instance)
         array_Voronoi_vertices = produce_array_Voronoi_vertices_on_sphere_surface(facet_coordinate_array_Delaunay_triangulation,self.estimated_sphere_radius,self.sphere_centroid)
+        #print 'array_Voronoi_vertices:', array_Voronoi_vertices
+        #print 'array_Voronoi_vertices.shape:', array_Voronoi_vertices.shape
         assert facet_coordinate_array_Delaunay_triangulation.shape[0] == array_Voronoi_vertices.shape[0], "The number of Delaunay triangles should match the number of Voronoi vertices."
         #now, the tricky part--building up a useful Voronoi polygon data structure
-        #testing new code idea -- directly grab the Voronoi indices closest to each generator
-        distance_matrix_generators_to_Voronoi_vertices = scipy.spatial.distance.cdist(self.original_point_array,array_Voronoi_vertices) #too many decimals causes problems in practical test cases 
-        #distance_matrix_generators_to_Voronoi_vertices = numpy.around(distance_matrix_generators_to_Voronoi_vertices,decimals=3) #too many decimals causes problems in practical test cases 
-        #each Voronoi vertex (column in above distance matrix) should have >= 3 minimum distance values relative to the generators (rows) for which it is a Voronoi cell vertex
-        #so, I want access to the row and column index information for the columnwise minima (then all flagged values for a given row form the set of Voronoi vertices for that generator)
-        minimum_distances_generators_to_Voronoi_vertices = numpy.amin(distance_matrix_generators_to_Voronoi_vertices,axis=0)[:,numpy.newaxis]
-        #distance_matrix_indices_for_columnar_minima = numpy.where(distance_matrix_generators_to_Voronoi_vertices.T == minimum_distances_generators_to_Voronoi_vertices)[::-1] #a bit tricky to get columnar indices and then use back on original distance matrix
-        distance_matrix_indices_for_columnar_minima = numpy.where(abs(distance_matrix_generators_to_Voronoi_vertices.T - minimum_distances_generators_to_Voronoi_vertices) < 0.001)[::-1] #a bit tricky to get columnar indices and then use back on original distance matrix
-        indices_Voronoi_vertices_forming_polygon_around_each_generator = distance_matrix_indices_for_columnar_minima
-        
-        #need to use the indices of the generator_indices to group the corresponding_Voronoi_vertex_indices_forming_Voronoi_cell
-        #I think pandas GroupBy may be useful here (i.e., to group voronoi vertices by common generator index)
-        d = {'generator_indices':indices_Voronoi_vertices_forming_polygon_around_each_generator[0]}
-        df = pandas.DataFrame(d,index=indices_Voronoi_vertices_forming_polygon_around_each_generator[1])
-        grouped = df.groupby('generator_indices')
-        dictionary_unsorted_Voronoi_point_indices_for_each_generator = grouped.groups
-
-        
-
-
 
+        #new strategy--I already have the Voronoi vertices and the generators, so work based off a distance matrix between them
+        distance_matrix_Voronoi_vertices_to_generators = scipy.spatial.distance.cdist(array_Voronoi_vertices,self.original_point_array)
+        #now, each row of the above distance array corresponds to a single Voronoi vertex, which each column of that row representing the distance to the respective generator point
+        #if we iterate through each of the rows and determine the indices of the minimum distances, we obtain the indices of the generators for which that voronoi vertex is a polygon vertex 
+        generator_Voronoi_region_dictionary = {} #store the indices of the generators for which a given Voronoi vertex is also a polygon vertex
+        for Voronoi_point_index, Voronoi_point_distance_array in enumerate(distance_matrix_Voronoi_vertices_to_generators):
+            Voronoi_point_distance_array = numpy.around(Voronoi_point_distance_array,decimals=3)
+            indices_of_generators_for_which_this_Voronoi_point_is_a_polygon_vertex = numpy.where(Voronoi_point_distance_array == Voronoi_point_distance_array.min())[0]
+            #print 'Voronoi_point_index:', Voronoi_point_index
+            #print '5 closest distances:', numpy.sort(Voronoi_point_distance_array)[0:5]
+            assert indices_of_generators_for_which_this_Voronoi_point_is_a_polygon_vertex.size >= 3, "By definition, a Voronoi vertex must be equidistant to at least 3 generators, but in this case only got {num_gens} generators for Voronoi vertex at {coords}, which has 5 closest distances: {distances}.".format(num_gens=indices_of_generators_for_which_this_Voronoi_point_is_a_polygon_vertex.size,coords=array_Voronoi_vertices[Voronoi_point_index],distances=numpy.sort(Voronoi_point_distance_array)[0:5])
+            generator_Voronoi_region_dictionary[Voronoi_point_index] = indices_of_generators_for_which_this_Voronoi_point_is_a_polygon_vertex #so dictionary looks like 0: array(12,17,27), ...
+
+        #now, go through the above dictionary and collect the Voronoi point indices forming the polygon for each generator index
+        dictionary_Voronoi_point_indices_for_each_generator = {}
+        for Voronoi_point_index, indices_of_generators_for_which_this_Voronoi_point_is_a_polygon_vertex in generator_Voronoi_region_dictionary.iteritems():
+            for generator_index in indices_of_generators_for_which_this_Voronoi_point_is_a_polygon_vertex:
+                if generator_index in dictionary_Voronoi_point_indices_for_each_generator:
+                    list_Voronoi_indices = dictionary_Voronoi_point_indices_for_each_generator[generator_index] 
+                    list_Voronoi_indices.append(Voronoi_point_index)
+                    dictionary_Voronoi_point_indices_for_each_generator[generator_index] = list_Voronoi_indices
+                else: #initialize the list of Voronoi indices for that generator key
+                    dictionary_Voronoi_point_indices_for_each_generator[generator_index] = [Voronoi_point_index]
+        #so this dictionary should have format: {generator_index: [list_of_Voronoi_indices_forming_polygon_vertices]}
+
+        #now, I want to sort the polygon vertices in a consistent, non-intersecting fashion
         dictionary_sorted_Voronoi_point_coordinates_for_each_generator = {}
-        for generator_index,unsorted_Voronoi_polygon_indices in dictionary_unsorted_Voronoi_point_indices_for_each_generator.iteritems():
-            unsorted_Voronoi_cell_vertex_coord_array = array_Voronoi_vertices[unsorted_Voronoi_polygon_indices]
-            #average_2D_projection_coordinate = numpy.average(unsorted_Voronoi_cell_vertex_coord_array[...,:2],axis=0)
-            average_2D_projection_coordinate = self.original_point_array[generator_index,:2]
-            translated_2D_projection_coordinates = unsorted_Voronoi_cell_vertex_coord_array[...,:2] - average_2D_projection_coordinate
-            polar_coord_array_unsorted_vertices = numpy.arctan2(translated_2D_projection_coordinates[...,1],translated_2D_projection_coordinates[...,0])
-            array_sort_indices_by_increasing_polar_angle = numpy.argsort(polar_coord_array_unsorted_vertices)
-            assert array_sort_indices_by_increasing_polar_angle.size >= 3, "All generators should be within Voronoi regions (polygons with at least 3 vertices)."
-            dictionary_sorted_Voronoi_point_coordinates_for_each_generator[generator_index] = unsorted_Voronoi_cell_vertex_coord_array[array_sort_indices_by_increasing_polar_angle]
+        for generator_index, list_unsorted_Voronoi_region_vertices in dictionary_Voronoi_point_indices_for_each_generator.iteritems():
+            current_array_Voronoi_vertices = array_Voronoi_vertices[list_unsorted_Voronoi_region_vertices]
+            if current_array_Voronoi_vertices.shape[0] > 3:
+                polygon_hull_object = scipy.spatial.ConvexHull(current_array_Voronoi_vertices[...,:2]) #trying to project to 2D for edge ordering, and then restore to 3D after
+                point_indices_ordered_vertex_array = polygon_hull_object.vertices
+                current_array_Voronoi_vertices = current_array_Voronoi_vertices[point_indices_ordered_vertex_array]
+            assert current_array_Voronoi_vertices.shape[0] >= 3, "All generators should be within Voronoi regions (polygons with at least 3 vertices)."
+            dictionary_sorted_Voronoi_point_coordinates_for_each_generator[generator_index] = current_array_Voronoi_vertices
 
         return dictionary_sorted_Voronoi_point_coordinates_for_each_generator
 
@@ -435,7 +444,7 @@ def voronoi_region_surface_areas_spherical_surface(self):
         dictionary_Voronoi_region_surface_areas_for_each_generator = {}
         for generator_index, Voronoi_polygon_sorted_vertex_array in dictionary_sorted_Voronoi_point_coordinates_for_each_generator.iteritems():
             current_Voronoi_polygon_surface_area_on_sphere = calculate_surface_area_of_a_spherical_Voronoi_polygon(Voronoi_polygon_sorted_vertex_array,self.estimated_sphere_radius)
-            assert current_Voronoi_polygon_surface_area_on_sphere > 0, "Obtained a surface area of zero for a Voronoi region [Actual value = {actual_value}; polygon_vertices = {polygon_vertices}].".format(actual_value = current_Voronoi_polygon_surface_area_on_sphere,polygon_vertices=Voronoi_polygon_sorted_vertex_array)
+            assert current_Voronoi_polygon_surface_area_on_sphere > 0, "Obtained a surface area of zero for a Voronoi region."
             dictionary_Voronoi_region_surface_areas_for_each_generator[generator_index] = current_Voronoi_polygon_surface_area_on_sphere
         return dictionary_Voronoi_region_surface_areas_for_each_generator