ResearchGate:
https:\/\/www.researchgate.net\/publication\/401344242_Condensing_Complexity_K-means_clustering_of_geometric_data_sets_as_a_design_tool<\/a>
CumInCAD:
https:\/\/papers.cumincad.org\/cgi-bin\/works\/paper\/ecaade2025_521<\/a><\/p>\n\n\n\n
![\"\"](\"https:\/\/inventorics.com\/wp-content\/uploads\/2025\/11\/grasshopper_component-1024x287.jpg\")
<\/figure>\n\n\n\nPython 3 code component for Rhino 8+Grasshopper:<\/strong><\/p>\n\n\n\n <\/p>\n\n\n\n Python 3 code for Rhino 8+Grasshopper code as a .py file:<\/strong><\/p>\n\n\n\n Python 3 for Rhino 8+Grasshopper code as plain text:<\/strong><\/p>\n\n\n\nimport math\nimport random as rnd\nimport ghpythonlib.treehelpers as th\n\n# Function to remap a value from one range to another\ndef translate(value, leftMin, leftMax, rightMin, rightMax):\n leftSpan = leftMax - leftMin\n rightSpan = rightMax - rightMin\n valueScaled = (value - leftMin) \/ leftSpan\n return rightMin + (valueScaled * rightSpan)\n\n# Function to normalize values to a target range [0, 1]\ndef normalize_values(lst, min_val, max_val):\n return [\n [translate(value, min_val, max_val, 0, 1) for value in sublist] \n for sublist in lst\n ]\n\n# Euclidean distance function for two vectors\ndef vector_dist(v1, v2):\n return math.sqrt(sum((v2[i] - v1[i])**2 for i in range(len(v1))))\n\n# KMeans++ initialization: Select initial cluster centers\ndef kMeansPlusPlusInitialization(vals, cls_num, first_center_index):\n if not ini:\n rnd.seed(42) # Set fixed seed for deterministic results\n \n cluster_centers = [] \n first_center = vals[first_center_index] # Choose first cluster center manually via component input\n cluster_centers.append(first_center)\n \n for _ in range(1, cls_num):\n distances = [\n min(vector_dist(val, center) for center in cluster_centers) \n for val in vals\n ]\n total_distance = sum(distances)\n probabilities = [dist \/ total_distance for dist in distances]\n\n cumulative_probabilities = []\n cumulative_sum = 0\n for p in probabilities:\n cumulative_sum += p\n cumulative_probabilities.append(cumulative_sum)\n \n r = rnd.random()\n for i, cumulative_prob in enumerate(cumulative_probabilities):\n if r < cumulative_prob:\n cluster_centers.append(vals[i])\n break\n \n return cluster_centers\n\n# Main K-Means clustering algorithm\ndef kMeanClustering(vals, pt_geometry, cls_num, iterations, first_center_index):\n # Normalize the input values\n norm_list = normalize_values(vals, min_val, max_val)\n \n # Initialize cluster centers using KMeans++\n cluster_centers = kMeansPlusPlusInitialization(norm_list, cls_num, first_center_index)\n \n for _ in range(iterations):\n clusters = [[] for _ in cluster_centers]\n clusters_ids = [[] for _ in cluster_centers]\n geom_clusters = [[] for _ in cluster_centers]\n \n for i, norm_val in enumerate(norm_list):\n # Find the closest cluster center for each value\n distances = [vector_dist(norm_val, center) for center in cluster_centers]\n best_center_id = distances.index(min(distances))\n \n clusters[best_center_id].append(norm_val)\n clusters_ids[best_center_id].append(i)\n geom_clusters[best_center_id].append(pt_geometry[i])\n \n # Update cluster centers as the mean of assigned points\n for i, cluster in enumerate(clusters):\n if cluster:\n new_center = [sum(dim) \/ len(cluster) for dim in zip(*cluster)]\n cluster_centers[i] = new_center\n else:\n cluster_centers[i] = rnd.choice(norm_list)\n \n # Compute geometric averages\n avg_geometry = []\n for cluster in geom_clusters:\n if cluster:\n avg_geom = [sum(dim) \/ len(cluster) for dim in zip(*cluster)]\n avg_geometry.append(avg_geom)\n else:\n avg_geometry.append([])\n \n # Map the cluster centers back to the original domain\n mapped_centers = [\n [translate(center[i], 0, 1, min_val, max_val) for i in range(len(center))]\n for center in cluster_centers\n ]\n \n # Return cluster IDs, mapped cluster centers, and geometric averages as Grasshopper DataTrees\n return th.list_to_tree(clusters_ids), th.list_to_tree(mapped_centers), th.list_to_tree(avg_geometry)\n\n# Main script execution\n# Flattened input: Extract values from Grasshopper tree structure\nvalues = [[item for item in branch] for branch in feature_vector.Branches]\npt_geom = [[item for item in branch] for branch in pt_geometry.Branches]\n\n# Compute min_val and max_val for the entire dataset\nall_values = [item for sublist in values for item in sublist]\nmin_val = min(all_values)\nmax_val = max(all_values)\n\n# Perform clustering\nids, avg_feature_vector, avg_geometry = kMeanClustering(values, pt_geom, clusters, iterations, first_center_index)<\/code><\/pre>\n\n\n\n