# import requests # import urllib3 # import json # from utils import geoutil # import regex_spatial # from shapely.geometry import Polygon, MultiPoint, LineString, Point, mapping # import re # import geopandas as gpd # from geocoder import geo_level1 # from openai import OpenAI # import numpy as np # # client = OpenAI( # api_key='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' # ) # # # model = "gpt-4o" # # north = ["north", "N'", "North", "NORTH"] # south = ["south", "S'", "South", "SOUTH"] # east = ["east", "E'", "East", "EAST"] # west = ["west", "W'", "West", "WEST"] # northeast = ["north-east", "NE'", "north east", "NORTH-EAST", "North East", "NORTH EAST"] # southeast = ["south-east", "SE'", "south east", "SOUTH-EAST", "South East", "SOUTH EAST"] # northwest = ["north-west", "NW'", "north west", "NORTH-WEST", "North West", "NORTH WEST"] # southwest = ["south-west", "SW'", "south west", "SOUTH-WEST", "South West", "SOUTH WEST"] # center = ["center","central", "downtown","midtown"] # # # # # # def get_directional_coordinates(coordinates, direction, centroid, minimum, maximum, is_midmid): # # direction_coordinates = get_directional_coordinates_by_angle(coordinates, direction, minimum, maximum) # # midmid1, midmid2 = geoutil.get_midmid_point(centroid, direction_coordinates[0], direction_coordinates[-1], # # is_midmid) # # if direction in west: # # maxi = max(p[2] for p in direction_coordinates) # # mini = min(p[2] for p in direction_coordinates) # # index_mini = 0 # # index_maxi = 0 # # for idx, p in enumerate(direction_coordinates): # # if p[2] == mini: # # index_mini = idx # # if p[2] == maxi: # # index_maxi = idx # # # # direction_coordinates.insert(index_maxi + 1, midmid2) # # direction_coordinates.insert(index_mini + 1, midmid1) # # else: # # direction_coordinates.append(midmid2) # # direction_coordinates.append(midmid1) # # # # return direction_coordinates, midmid1, midmid2 # # # # # # def get_directional_coordinates_by_angle(coordinates, direction, minimum, maximum): # # direction_coordinates = [] # # for p in coordinates: # # if direction in east: # # if p[2] >= minimum or p[2] <= maximum: # # direction_coordinates.append(p) # # # # else: # # if p[2] >= minimum and p[2] <= maximum: # # direction_coordinates.append(p) # # return direction_coordinates # # # # # # def get_directional_coordinates_by_angle(coordinates, direction, minimum, maximum): # # direction_coordinates = [] # # for p in coordinates: # # if direction in east: # # if p[2] >= minimum or p[2] <= maximum: # # direction_coordinates.append(p) # # # # else: # # if p[2] >= minimum and p[2] <= maximum: # # direction_coordinates.append(p) # # return direction_coordinates # # # # # # def get_central(coordinates, centroid, direction, is_midmid): # # n_min_max = get_min_max("north") # # n_coordinates = get_directional_coordinates_by_angle(coordinates, "north", n_min_max[0], n_min_max[1]) # # n_mid1, n_mid2 = geoutil.get_midmid_point(centroid, n_coordinates[0], n_coordinates[-1], is_midmid) # # # # ne_min_max = get_min_max("north east") # # ne_coordinates = get_directional_coordinates_by_angle(coordinates, "north east", ne_min_max[0], ne_min_max[1]) # # ne_mid1, ne_mid2 = geoutil.get_midmid_point(centroid, ne_coordinates[0], ne_coordinates[-1], is_midmid) # # # # e_min_max = get_min_max("east") # # e_coordinates = get_directional_coordinates_by_angle(coordinates, "east", e_min_max[0], e_min_max[1]) # # e_mid1, e_mid2 = geoutil.get_midmid_point(centroid, e_coordinates[0], e_coordinates[-1], is_midmid) # # # # se_min_max = get_min_max("south east") # # se_coordinates = get_directional_coordinates_by_angle(coordinates, "south east", se_min_max[0], se_min_max[1]) # # se_mid1, se_mid2 = geoutil.get_midmid_point(centroid, se_coordinates[0], se_coordinates[-1], is_midmid) # # # # s_min_max = get_min_max("south") # # s_coordinates = get_directional_coordinates_by_angle(coordinates, "south", s_min_max[0], s_min_max[1]) # # s_mid1, s_mid2 = geoutil.get_midmid_point(centroid, s_coordinates[0], s_coordinates[-1], is_midmid) # # # # sw_min_max = get_min_max("south west") # # sw_coordinates = get_directional_coordinates_by_angle(coordinates, "south west", sw_min_max[0], sw_min_max[1]) # # sw_mid1, sw_mid2 = geoutil.get_midmid_point(centroid, sw_coordinates[0], sw_coordinates[-1], is_midmid) # # # # w_min_max = get_min_max("west") # # w_coordinates = get_directional_coordinates_by_angle(coordinates, "west", w_min_max[0], w_min_max[1]) # # w_mid1, w_mid2 = geoutil.get_midmid_point(centroid, w_coordinates[0], w_coordinates[-1], is_midmid) # # # # nw_min_max = get_min_max("north west") # # nw_coordinates = get_directional_coordinates_by_angle(coordinates, "north west", nw_min_max[0], nw_min_max[1]) # # nw_mid1, nw_mid2 = geoutil.get_midmid_point(centroid, nw_coordinates[0], nw_coordinates[-1], is_midmid) # # # # central_coordindates = [e_mid1, e_mid2, ne_mid1, ne_mid2, n_mid1, n_mid2, # # nw_mid1, nw_mid2, w_mid1, w_mid2, sw_mid1, sw_mid2, # # s_mid1, s_mid2, se_mid1, se_mid2] # # return central_coordindates # # # # # # def get_min_max(direction): # # regex = regex_spatial.get_directional_regex() # # direction_list = regex.split("|") # # if direction in direction_list: # # if direction in east: # # return (337, 22) # # if direction in northeast: # # return (22, 67) # # if direction in north: # # return (67, 112) # # if direction in northwest: # # return (112, 157) # # if direction in west: # # return (157, 202) # # if direction in southwest: # # return (202, 247) # # if direction in south: # # return (247, 292) # # if direction in southeast: # # return (292, 337) # # # # return None # # def get_level1_coordinates(coordinates, centroid, direction, is_midmid): # # min_max = get_min_max(direction) # # if min_max is not None: # # coordinates, mid1, mid2 = get_directional_coordinates(coordinates, direction, centroid, min_max[0], min_max[1], is_midmid) # # return coordinates, centroid, mid1, mid2 # # elif direction.lower() in center: # # return get_central(coordinates, centroid, direction, is_midmid), centroid, None, None # # else: # # return coordinates, centroid, None, None # def to_standard_2d_list(data): # arr = np.array(data) # # # 强制变成一维后 reshape,前提是元素总数是2的倍数 # flat = arr.flatten() # if flat.size % 2 != 0: # raise ValueError("元素个数不是2的倍数,不能 reshape 成 [N, 2] 格式") # # return flat.reshape(-1, 2).tolist() # # # def get_geojson(ent, arr, centroid): # poly_json = {} # poly_json['type'] = 'FeatureCollection' # poly_json['features'] = [] # coordinates= [] # coordinates.append(arr) # poly_json['features'].append({ # 'type':'Feature', # 'id': ent, # 'properties': { # 'centroid': centroid # }, # 'geometry': { # 'type':'Polygon', # 'coordinates': coordinates # } # }) # return poly_json # # # def get_coordinates(ent): # request_url = 'https://nominatim.openstreetmap.org/search.php?q= ' +ent +'&polygon_geojson=1&accept-language=en&format=jsonv2' # headers = { # "User-Agent": "Mozilla/5.0 (Macintosh; Intel Mac OS X 10_15_7) AppleWebKit/605.1.15 (KHTML, like Gecko) Version/18.3 Safari/605.1.15" # } # page = requests.get(request_url, headers=headers, verify=False) # json_content = json.loads(page.content) # all_coordinates = json_content[0]['geojson']['coordinates'][0] # centroid = (float(json_content[0]['lon']), float(json_content[0]['lat'])) # for p in all_coordinates: # p2 = (p[0], p[1]) # angle = geoutil.calculate_bearing(centroid, p2) # p.append(angle) # # geojson = get_geojson(ent, all_coordinates, centroid) # # return geojson['features'][0]['geometry']['coordinates'][0], geojson['features'][0]['properties']['centroid'] # # # def geojson(ent): # # request_url = 'https://nominatim.openstreetmap.org/search.php?q= ' +ent +'&polygon_geojson=1&accept-language=en&format=jsonv2' # # headers = { # # "User-Agent": "Mozilla/5.0 (Macintosh; Intel Mac OS X 10_15_7) AppleWebKit/605.1.15 (KHTML, like Gecko) Version/18.3 Safari/605.1.15" # # } # # page = requests.get(request_url, headers=headers, verify=False) # # json_content = json.loads(page.content) # # all_coordinates = json_content[0]['geojson']['coordinates'][0] # # centroid = (float(json_content[0]['lon']), float(json_content[0]['lat'])) # # for p in all_coordinates: # # p2 = (p[0], p[1]) # # angle = geoutil.calculate_bearing(centroid, p2) # # p.append(angle) # # # # geojson = get_geojson(ent, all_coordinates, centroid) # # # # return geojson # # # def get_coordinates(location): # request_url = f'https://nominatim.openstreetmap.org/search.php?q={location}&polygon_geojson=1&accept-language=en&format=jsonv2' # # print(request_url) # headers = {"User-Agent": "Mozilla/5.0"} # response = requests.get(request_url, headers=headers, verify=False) # json_content = json.loads(response.content) # # print(json_content) # if json_content[0]['geojson']['type'] == 'Polygon': # coordinates = json_content[0]['geojson']['coordinates'][0] # elif json_content[0]['geojson']['type'] == 'Point': # coordinates = json_content[0]['geojson']['coordinates'] # else: # print(json_content[0]['geojson']['type']) # centroid = (float(json_content[0]['lon']), float(json_content[0]['lat'])) # return (coordinates, centroid) # # # # level3 # def get_directional_coordinates_by_angle(coordinates, centroid, direction, minimum, maximum): # # minimum = 157 # # maximum = 202 # # direction_coordinates = [] # for p in coordinates: # angle = geoutil.calculate_bearing(centroid, p) # p2 = (p[0], p[1], angle) # if direction in geo_level1.east: # if angle >= minimum or angle <= maximum: # direction_coordinates.append(p2) # # else: # if angle >= minimum and angle <= maximum: # direction_coordinates.append(p2) # # print(type(direction_coordinates[0])) # # if(direction in geo_level1.west): # # direction_coordinates.sort(key=lambda k: k[2], reverse=True) # # return direction_coordinates # def get_level3(level3): # digits = re.findall('[0-9]+', level3)[0] # unit = re.findall('[A-Za-z]+', level3)[0] # return digits, unit # # def get_direction_coordinates(coordinates, centroid, level1): # min_max = geo_level1.get_min_max(level1) # if min_max is not None: # coord = get_directional_coordinates_by_angle(coordinates, centroid, level1, min_max[0], min_max[1]) # return coord # return coordinates # def sort_west(poly1, poly2, centroid): # coords1 = mapping(poly1)["features"][0]["geometry"]["coordinates"] # coords2 = mapping(poly2)["features"][0]["geometry"]["coordinates"] # coord1 = [] # coord2 = [] # coord = [] # for c in coords1: # pol = list(c[::-1]) # coord1.extend(pol) # for c in coords2: # pol = list(c[::-1]) # coord2.extend(pol) # coo1 = [] # coo2 = [] # for p in coord1: # angle = geoutil.calculate_bearing(centroid, p) # if angle >= 157 and angle <= 202: # coo1.append((p[0], p[1], angle)) # for p in coord2: # angle = geoutil.calculate_bearing(centroid, p) # if angle >= 157 and angle <= 202: # coo2.append((p[0], p[1], angle)) # coo1.extend(coo2) # return coo1 # # # def get_level3_coordinates(coordinates, level_3, level1): # distance, unit = get_level3(level_3) # kms = geoutil.get_kilometers(distance, unit) # coord = [] # # coords0, center = coordinates # # if not isinstance(coords0, list) or len(coords0) < 3: # # # 从原始点出发,根据方向移动距离 kms 得到新圆心 # lat_km = 111.32 # lon_km = 111.32 * np.cos(np.radians(center[1])) # # dx = dy = 0 # # if level1 is not None: # if level1 in geo_level1.east: # dx = kms / lon_km # elif level1 in geo_level1.west: # dx = -kms / lon_km # elif level1 in geo_level1.north: # dy = kms / lat_km # elif level1 in geo_level1.south: # dy = -kms / lat_km # # 你也可以支持 northeast、southwest 等复合方向 # # new_center = (center[0] + dx, center[1] + dy) # # # 用固定半径画个圆(例如半径2km) # r_km = 1 # 半径设为1km,你也可以设为其他值 # # circle_points = [] # for theta in np.linspace(0, 360, num=100): # theta_rad = np.radians(theta) # d_lat = (np.sin(theta_rad) * r_km) / lat_km # d_lon = (np.cos(theta_rad) * r_km) / lon_km # circle_points.append((new_center[0] + d_lon, new_center[1] + d_lat)) # # # 输出中心(使用新圆心) # if circle_points: # center_point = MultiPoint(circle_points).centroid # center = (center_point.x, center_point.y) # else: # center = new_center # # return circle_points, center # # # 正常 polygon 流程 # poly1 = Polygon(coords0) # polygon1 = gpd.GeoSeries(poly1) # # # 生成环形区域 # poly2 = polygon1.buffer(0.0095 * kms, join_style=2) # poly3 = polygon1.buffer(0.013 * kms, join_style=2) # poly = poly3.difference(poly2) # # # 获取坐标 # coords = mapping(poly)["features"][0]["geometry"]["coordinates"] # for c in coords: # pol = list(c[::-1]) # coord.extend(pol) # # # 方向裁剪 # if level1 is not None: # coord = get_direction_coordinates(coord, coordinates[1], level1) # if level1 in geo_level1.west: # coord = sort_west(poly3, poly2, coordinates[1]) # # # 计算质心 # if coord: # center_point = MultiPoint(coord).centroid # center = (center_point.x, center_point.y) # else: # center = coordinates[1] # # return coord, center # # level 3 end # # # between # def get_between_coordinates(coordinates1, coordinates2): # """ # 计算两个区域之间的中间点,并生成一个等面积的圆形区域。 # 如果某个输入仅为点(坐标长度 < 3),则其面积设为 0; # 如果两个输入都是点,则默认半径为 2km。 # :param coordinates1: 第一个区域的边界坐标和中心点 # :param coordinates2: 第二个区域的边界坐标和中心点 # :return: 圆形区域的坐标集和圆心 # """ # # def is_valid_polygon(coords): # return isinstance(coords, list) and len(coords) >= 3 # # coords1, center1 = coordinates1 # coords2, center2 = coordinates2 # # # 判断输入是否为合法多边形(>=3个点) # if is_valid_polygon(coords1): # poly1 = Polygon(coords1) # area1 = poly1.area # else: # area1 = 0 # # if is_valid_polygon(coords2): # poly2 = Polygon(coords2) # area2 = poly2.area # else: # area2 = 0 # # # 计算中心点(两个中心的中点) # midpoint = ( # (center1[0] + center2[0]) / 2, # (center1[1] + center2[1]) / 2 # ) # # # 如果两个区域都是点,则使用默认半径 2km # if area1 == 0 and area2 == 0: # r_km = 2 # else: # avg_area = (area1 + area2) / 2 # r_km = np.sqrt(avg_area / np.pi) * 111.32 # 近似 km 半径 # # # 经纬度距离换算因子 # lat_km = 111.32 # lon_km = 111.32 * np.cos(np.radians(midpoint[1])) # # # 生成圆形区域坐标(100个点) # circle_points = [] # for theta in np.linspace(0, 360, num=100): # theta_rad = np.radians(theta) # d_lat = (np.sin(theta_rad) * r_km) / lat_km # d_lon = (np.cos(theta_rad) * r_km) / lon_km # circle_points.append((midpoint[0] + d_lon, midpoint[1] + d_lat)) # # return circle_points, midpoint # # between end # # # def llmapi(text): # system_prompt = ( # "你是一个资深的地理学家,你的任务是通过给定的一段自然语言,来选择正确的定位函数顺序以及他们的输入。\n" # "你能选择的定位函数有:\n" # "1. 相对定位(Relative Positioning):输入为地点坐标,方位,距离。输出为距离‘距离’输入的地点坐标的‘方位’的坐标。\n" # "2. 中间定位(Between Positioning):输入为两个地点的坐标,输出为两个地点坐标的中点。\n" # "请先进行思维链(CoT)推理,并最终用 JSON 格式输出你的答案,用 `<<>>` 和 `<<>>` 包裹起来。\n" # "请确保所有输入仅包含:地点名称(字符串)、索引(整数)、方位(字符串,必须是英文)或距离(字符串,带单位),不允许返回诸如 'Chatswood 南4 km的坐标' 这样的内容。\n" # "每个步骤编号都有 id 记录,然后如果某个输入是之前步骤的输出,那么输入对应步骤的 id。\n" # "所有方向必须使用英文(如 south, west, northeast, etc.)。\n" # "示例输出:\n" # "<<>>\n" # "[{\"id\": 1, \"function\": \"Relative\", \"inputs\": [\"Chatswood\", \"south\", \"4 km\"]}," # "{\"id\": 2, \"function\": \"Relative\", \"inputs\": [\"North Sydney\", \"west\", \"2 km\"]}," # "{\"id\": 3, \"function\": \"Between\", \"inputs\": [1, 2]}," # "{\"id\": 4, \"function\": \"Relative\", \"inputs\": [3, \"southwest\", \"5 km\"]}]\n" # "<<>>") # # messages = [ # {"role": "system", "content": system_prompt}, # {"role": "user", "content": text}, # ] # # chat_completion = client.chat.completions.create( # messages=messages, # model=model, # ) # # result = chat_completion.choices[0].message.content # json_match = re.search(r'<<>>\n(.*?)\n<<>>', result, re.DOTALL) # # if json_match: # # print(json.loads(json_match.group(1))) # return json.loads(json_match.group(1)) # else: # raise ValueError("LLM 输出未包含预期的 JSON 格式数据。") # def llmapi(text): # system_prompt = ( # "You are an experienced geographer. Your task is to determine the correct sequence of positioning functions and their inputs based on a given piece of natural language.\n" # "The positioning functions you can choose from are:\n" # "1. Relative Positioning: Inputs is (location coordinate or location name, direction, and distance). Outputs the coordinates that are in the given 'direction' and 'distance' from the input location.\n" # "2. Between Positioning: Inputs is (location 1 coordinates or location 1 name, location 2 coordinates or location 2 name). Outputs the midpoint coordinate between the two locations.\n" # "You can only use the given functions, and the inputs to the functions must obey the above properties. The given functions can be combined to solve complex situations." # "First, perform chain-of-thought (CoT) reasoning, and finally output your answer in JSON format, wrapped between `<<>>` and `<<>>`.\n" # "Make sure all inputs only include: location names (strings), step indices (integers), directions (strings, must be in English), or distances (strings with units). Do not return expressions like 'the coordinate 4 km south of Chatswood'.\n" # "Each step must have an 'id'. If the input of a step is the output of a previous step, use that step’s 'id' as the input.\n" # "All directions must be in English (e.g., south, west, northeast, etc.).\n" # "Example output:\n" # "<<>>\n" # "[{\"id\": 1, \"function\": \"Relative\", \"inputs\": [\"Chatswood\", \"south\", \"4 km\"]}," # "{\"id\": 2, \"function\": \"Relative\", \"inputs\": [\"North Sydney\", \"west\", \"2 km\"]}," # "{\"id\": 3, \"function\": \"Between\", \"inputs\": [1, 2]}," # "{\"id\": 4, \"function\": \"Relative\", \"inputs\": [3, \"southwest\", \"5 km\"]}]\n" # "<<>>") # # messages = [ # {"role": "system", "content": system_prompt}, # {"role": "user", "content": text}, # ] # # chat_completion = client.chat.completions.create( # messages=messages, # model=model, # ) # # result = chat_completion.choices[0].message.content # print(result) # json_match = re.search(r'<<>>\n(.*?)\n<<>>', result, re.DOTALL) # # if json_match: # return json.loads(json_match.group(1)) # else: # raise ValueError("LLM 输出未包含预期的 JSON 格式数据。") # # # # # # def execute_steps(steps): # data = {} # # for step in steps: # step_id = step['id'] # function = step['function'] # inputs = step['inputs'] # # print('-' * 50) # # print(function) # # print(inputs) # # # resolved_inputs = [] # for inp in inputs: # if isinstance(inp, int): # resolved_inputs.append(data[inp]) # else: # resolved_inputs.append(inp) # if function == "Relative": # location, direction, distance = resolved_inputs # if isinstance(location, str): # location = get_coordinates(location) # # location = [to_standard_2d_list(location[0])] + list(location[1:]) # location = [[[151.214901,-33.859175]], (151.214901,-33.859175)] # result = get_level3_coordinates(location, distance, direction) # data[step_id] = result # # elif function == "Between": # # # location1, location2 = resolved_inputs # # print(location1) # # print(111) # # print(location2) # if isinstance(location1, str): # location1 = get_coordinates(location1) # # location1 = [to_standard_2d_list(location1[0])] + list(location1[1:]) # if isinstance(location2, str): # # location2 = get_coordinates(location2) # location2 = [to_standard_2d_list(location2[0])] + list(location2[1:]) # result = get_between_coordinates(location1, location2) # # data[step_id] = result # # return data # # # # if __name__ == '__main__': # # a = get_coordinates('Burwood') # # a2 = get_coordinates('Glebe') # # b = get_level3_coordinates(a, '5 km', 'east') # # c = get_between_coordinates(a, a2) # # # 完整通道 # # 默认输入 # # default_input_text = "在Chatswood南边4公里与North Sydney 东边2公里的中间的西南5公里。" # # default_input_text = "你是一位规划师,正在为华盛顿州的一项新森林监测站选址。两个潜在的参考位置分别是雷尼尔山国家公园(Mount Rainier National Park)和北喀斯喀特国家公园(North Cascades National Park)。首先,你想在这两个国家公园之间找到一个中间点。接着,你希望在这个中间点与北喀斯喀特国家公园之间,再取一个中间位置,以便确定最终的建设候选地。" # # default_input_text = "在Chatswood和North Sydney的中间靠近North Sydney的四分之一位置" # # default_input_text = "Plan a trip that involves determining the midpoint between Paris and London, and then finding another midpoint between this location and Paris to identify potential stopovers during travel." # # default_input_text = "5km southwest of Chatswood, 4km south of Chatswood and 2km north of North Sydney." # # # # # 解析 LLM 结果 # # parsed_steps = llmapi(default_input_text) # # parsed_steps = [{'id': 1, 'function': 'Relative', 'inputs': ['Chatswood', 'south', '4 km']}, {'id': 2, 'function': 'Relative', 'inputs': ['North Sydney', 'east', '2 km']}, {'id': 3, 'function': 'Between', 'inputs': [1, 2]}, {'id': 4, 'function': 'Relative', 'inputs': [3, 'south west', '5 km']}] # # parsed_steps = [{"id": 1, "function": "Between", "inputs": ["Chatswood", "North Sydney"]},{"id": 2, "function": "Between", "inputs": [1, "North Sydney"]}] # # parsed_steps = [{"id": 1, "function": "Relative", "inputs": ["Katoomba", "southeast", "3 km"]}, {"id": 2, "function": "Between", "inputs": [1, "Echo Point"]}] # # parsed_steps = [{'id': 1, 'function': 'Relative', 'inputs': ['Scafell Pike', 'east', '9 km']}] # # parsed_steps = [{'id': 1, 'function': 'Relative', 'inputs': ['Colosseum', 'northeast', '8 km']}, {'id': 2, 'function': 'Relative', 'inputs': [1, 'northeast', '2 km']}] # parsed_steps = [ # {"id": 1, "function": "Between", "inputs": ["Statue of Liberty", "Eiffel Tower"]}, # {"id": 2, "function": "Relative", "inputs": [1, "west", "8 km"]} # ] # # # 执行步骤 # result = execute_steps(parsed_steps) # # 输出最终计算结果 # print(result) # print('-' * 100) # print(result[(max(result.keys()))][0]) # # 通道结束 # # # location = get_coordinates('Chatswood') # # result = get_level3_coordinates(location, '4 km', 'north west') # # print(result) # #