diff --git a/L0002_lingjian.csv b/L0002_lingjian.csv
new file mode 100644
index 0000000..7eee51e
--- /dev/null
+++ b/L0002_lingjian.csv
@@ -0,0 +1,315 @@
+下料批次号,零件号,数量,外轮廓,允许旋转角度,面料号
+L0002,s000001,1,"[[2000.0, 1000.0], [2004.3, 1000.1], [2030.9, 1000.5], [2050.4, 1000.9], [2070.0, 1001.4], [2088.9, 1002.1], [2098.9, 1002.7], [2108.9, 1003.4], [2155.1, 1007.6], [2170.4, 1009.3], [2180.4, 1010.5], [2194.8, 1012.2], [2197.3, 1012.5], [2202.7, 1013.3], [2210.5, 1014.5], [2226.1, 1017.0], [2241.8, 1019.5], [2249.7, 1020.5], [2257.5, 1021.3], [2259.2, 1021.4], [2268.1, 1021.9], [2277.0, 1022.0], [2287.0, 1022.0], [2297.0, 1021.6], [2306.9, 1020.8], [2307.7, 1020.8], [2318.3, 1019.7], [2329.0, 1018.3], [2339.7, 1016.6], [2352.2, 1014.5], [2364.8, 1012.1], [2371.8, 1010.6], [2378.8, 1009.2], [2385.6, 1007.7], [2392.2, 1006.4], [2395.5, 1005.7], [2398.8, 1005.1], [2402.5, 1004.4], [2404.5, 1004.0], [2406.6, 1003.6], [2407.9, 1007.9], [2409.5, 1012.3], [2411.1, 1015.7], [2413.0, 1018.9], [2415.1, 1021.9], [2417.3, 1024.8], [2418.9, 1026.8], [2420.8, 1028.5], [2423.9, 1030.6], [2427.1, 1032.2], [2430.1, 1033.5], [2433.2, 1034.8], [2437.0, 1035.9], [2440.8, 1036.6], [2444.6, 1037.0], [2451.7, 1037.3], [2456.0, 1037.2], [2460.3, 1036.9], [2464.5, 1036.5], [2468.8, 1035.9], [2474.7, 1035.0], [2480.6, 1033.8], [2488.0, 1032.1], [2495.3, 1030.1], [2502.6, 1027.8], [2509.8, 1025.4], [2519.8, 1021.8], [2529.6, 1018.0], [2539.5, 1013.9], [2549.3, 1009.5], [2557.4, 1005.5], [2565.4, 1001.4], [2573.2, 997.3], [2581.1, 992.9], [2587.9, 989.0], [2594.8, 985.1], [2601.3, 981.2], [2604.4, 979.4], [2607.4, 977.7], [2611.4, 985.3], [2615.6, 993.2], [2619.8, 1001.4], [2624.1, 1009.7], [2624.5, 1010.4], [2632.5, 1026.7], [2636.7, 1035.3], [2640.6, 1043.9], [2646.1, 1056.3], [2651.5, 1068.7], [2656.8, 1081.0], [2662.2, 1093.2], [2666.4, 1101.9], [2670.6, 1110.7], [2671.6, 1112.6], [2674.2, 1117.9], [2677.7, 1125.1], [2681.1, 1132.1], [2682.8, 1135.5], [2684.3, 1138.6], [2678.3, 1139.3], [2672.1, 1140.1], [2666.6, 1141.0], [2661.2, 1142.0], [2657.4, 1142.9], [2653.7, 1144.0], [2646.3, 1146.5], [2641.1, 1148.6], [2636.0, 1151.0], [2630.8, 1153.8], [2625.7, 1156.8], [2621.5, 1159.5], [2617.3, 1162.5], [2613.4, 1165.7], [2609.6, 1169.1], [2605.0, 1173.9], [2602.2, 1177.2], [2600.7, 1179.0], [2597.8, 1183.2], [2595.2, 1187.5], [2592.9, 1192.0], [2590.8, 1196.5], [2588.6, 1202.5], [2586.6, 1208.6], [2584.7, 1215.4], [2583.0, 1222.1], [2582.0, 1226.3], [2581.2, 1230.5], [2580.5, 1234.5], [2579.9, 1238.6], [2579.3, 1242.5], [2578.8, 1246.0], [2576.0, 1246.9], [2573.4, 1247.8], [2568.4, 1249.4], [2563.7, 1250.7], [2558.9, 1251.9], [2549.0, 1254.1], [2535.7, 1256.7], [2522.4, 1259.0], [2505.1, 1261.6], [2487.6, 1263.8], [2470.2, 1265.7], [2452.7, 1267.2], [2435.3, 1268.4], [2417.8, 1269.4], [2402.8, 1269.9], [2386.6, 1270.3], [2354.6, 1270.6], [2294.9, 1270.6], [2267.1, 1270.4], [2253.0, 1270.1], [2238.9, 1269.6], [2221.4, 1268.8], [2203.8, 1267.7], [2186.2, 1266.5], [2168.6, 1265.1], [2149.7, 1263.4], [2135.4, 1261.9], [2121.1, 1260.2], [2103.8, 1257.7], [2086.5, 1255.0], [2068.1, 1251.8], [2054.0, 1249.2], [2039.8, 1246.3], [2025.1, 1243.0], [2010.5, 1239.5], [2001.5, 1237.2], [1992.5, 1234.8], [1985.9, 1232.8], [1979.4, 1230.6], [1973.3, 1228.3], [1967.4, 1225.7], [1963.7, 1223.8], [1960.1, 1221.6], [1955.2, 1218.4], [1950.5, 1214.8], [1948.4, 1212.9], [1946.9, 1211.3], [1945.6, 1209.5], [1943.2, 1206.2], [1941.0, 1202.8], [1938.4, 1198.0], [1936.1, 1192.9], [1934.8, 1189.5], [1933.7, 1186.2], [1933.1, 1183.8], [1932.5, 1181.4], [1932.1, 1178.7], [1931.6, 1175.8], [1931.3, 1173.7], [1930.8, 1169.4], [1930.6, 1167.4], [1930.4, 1165.6], [1930.3, 1164.2], [1930.1, 1162.8], [1902.1, 1162.7], [1902.4, 1159.4], [1902.7, 1156.4], [1903.0, 1153.5], [1903.2, 1150.8], [1903.4, 1148.2], [1903.7, 1145.9], [1904.1, 1141.5], [1904.4, 1137.5], [1904.8, 1133.8], [1905.1, 1130.2], [1905.5, 1126.6], [1906.2, 1119.9], [1907.0, 1112.6], [1907.8, 1105.0], [1908.7, 1097.1], [1909.6, 1088.9], [1910.5, 1080.5], [1912.5, 1063.3], [1914.5, 1046.0], [1915.4, 1037.5], [1916.4, 1029.1], [1917.4, 1021.0], [1918.3, 1013.2], [1919.2, 1005.7], [1920.0, 998.7], [1926.3, 998.8], [1932.3, 999.0], [1938.2, 999.1], [1943.9, 999.2], [1955.1, 999.5], [1966.3, 999.6], [1977.6, 999.8], [2000.0, 1000.0]]","0, 180",M0002
+L0002,s000002,1,"[[2000.0, 2000.0], [2000.8, 1994.4], [2002.0, 1988.9], [2003.5, 1983.3], [2005.4, 1977.9], [2007.6, 1972.5], [2010.1, 1967.4], [2013.1, 1962.5], [2016.5, 1958.0], [2020.2, 1954.0], [2024.1, 1950.2], [2028.4, 1946.8], [2033.0, 1943.6], [2039.2, 1940.0], [2045.7, 1936.7], [2052.4, 1933.8], [2059.2, 1931.3], [2066.1, 1929.0], [2078.1, 1925.6], [2090.0, 1922.6], [2102.0, 1920.0], [2133.3, 1913.5], [2150.2, 1910.2], [2167.1, 1907.2], [2181.7, 1904.8], [2196.3, 1902.6], [2210.2, 1900.8], [2224.1, 1899.1], [2237.5, 1897.7], [2250.9, 1896.5], [2261.6, 1895.7], [2272.4, 1895.0], [2293.9, 1893.9], [2329.2, 1892.6], [2359.3, 1891.8], [2373.7, 1891.5], [2398.1, 1891.2], [2422.4, 1891.1], [2446.7, 1891.2], [2471.1, 1891.5], [2487.4, 1891.8], [2502.3, 1892.4], [2519.8, 1893.4], [2537.2, 1894.7], [2554.7, 1896.2], [2572.2, 1898.1], [2589.6, 1900.4], [2607.0, 1903.1], [2620.2, 1905.4], [2633.6, 1908.1], [2643.5, 1910.4], [2648.4, 1911.6], [2652.9, 1912.9], [2655.3, 1913.6], [2657.8, 1914.4], [2660.4, 1915.3], [2663.4, 1916.3], [2664.4, 1923.3], [2665.5, 1930.5], [2666.7, 1936.8], [2668.1, 1943.0], [2670.6, 1952.5], [2672.1, 1957.1], [2673.7, 1961.8], [2676.2, 1967.7], [2679.1, 1973.5], [2682.4, 1978.8], [2685.0, 1982.5], [2686.9, 1984.9], [2687.8, 1986.1], [2690.7, 1989.5], [2693.9, 1992.8], [2697.7, 1996.2], [2701.7, 1999.5], [2705.9, 2002.6], [2710.2, 2005.5], [2715.0, 2008.4], [2720.0, 2011.0], [2725.2, 2013.5], [2730.5, 2015.6], [2737.1, 2017.8], [2743.7, 2019.5], [2750.2, 2020.9], [2756.6, 2022.1], [2761.0, 2022.8], [2765.4, 2023.4], [2769.8, 2023.7], [2774.3, 2023.9], [2771.8, 2029.2], [2769.5, 2034.3], [2765.0, 2044.4], [2762.3, 2051.0], [2759.5, 2057.6], [2756.9, 2064.2], [2754.4, 2070.6], [2742.4, 2067.5], [2730.2, 2064.3], [2705.8, 2058.2], [2682.5, 2052.8], [2659.3, 2047.7], [2637.5, 2043.1], [2632.7, 2042.1], [2605.2, 2036.6], [2589.6, 2033.6], [2570.5, 2030.0], [2546.8, 2025.8], [2523.0, 2021.7], [2499.3, 2018.0], [2487.4, 2016.2], [2475.5, 2014.6], [2463.3, 2013.2], [2451.1, 2011.7], [2441.1, 2010.6], [2425.2, 2009.0], [2409.3, 2007.8], [2394.3, 2007.0], [2379.3, 2006.3], [2364.4, 2005.8], [2349.4, 2005.4], [2336.1, 2005.1], [2306.3, 2004.7], [2289.9, 2004.9], [2275.9, 2005.3], [2262.0, 2005.9], [2234.1, 2007.4], [2215.1, 2008.3], [2171.8, 2010.7], [2150.2, 2012.0], [2128.3, 2013.4], [2108.9, 2014.6], [2089.5, 2016.0], [2070.3, 2017.4], [2060.9, 2018.1], [2051.6, 2018.9], [2039.2, 2019.9], [2026.7, 2021.0], [2020.3, 2021.6], [2013.7, 2022.3], [2006.8, 2022.9], [1999.6, 2023.6], [1999.4, 2017.7], [1999.2, 2011.7], [1999.5, 2005.9], [2000.0, 2000.0]]","0, 180",M0002
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diff --git a/nfp_function.py b/nfp_function.py
new file mode 100644
index 0000000..3bb87a5
--- /dev/null
+++ b/nfp_function.py
@@ -0,0 +1,753 @@
+# -*- coding: utf-8 -*-
+import placement_worker, nfp_utls
+import math
+import json
+import random
+import copy
+import matplotlib.pyplot as plt
+import matplotlib.patches as patches
+import pyclipper
+import time
+import qhull_2d
+from matplotlib.backends.backend_agg import FigureCanvasAgg as FigureCanvas
+from matplotlib.figure import Figure
+from settings import SPACING, CONTAINERSPACING, ROTATIONS, BIN_HEIGHT, POPULATION_SIZE, MUTA_RATE, CURVETOLERANCE, SCALING_FACTOR, CONVEX_WEIGHT, AREA_WEIGHT
+
+
+class Nester:
+    def __init__(self, container=None, shapes=None):
+        """Nester([container,shapes]): Creates a nester object with a container
+           shape and a list of other shapes to nest into it. Container and
+           shapes must be Part.Faces.
+           Typical workflow:
+           n = Nester() # creates the nester
+           n.add_container(object) # adds a doc object as the container
+           n.add_objects(objects) # adds a list of doc objects as shapes
+           n.run() # runs the nesting
+           n.show() # creates a preview (compound) of the results
+           """
+        self.container = container  # 承载组件的容器
+        self.shapes = shapes        # 组件信息
+        self.shapes_max_length = 0   # 在一般无限长的布，设计一个布的尺寸
+        self.results = list()  # storage for the different results
+        self.nfp_cache = {}     # 缓存中间计算结果
+        # 遗传算法的参数
+        self.config = {
+            'curveTolerance': CURVETOLERANCE,  # 允许的最大误差转换贝济耶和圆弧线段。在SVG的单位。更小的公差将需要更长的时间来计算 More Info: http://www.angusj.com/delphi/clipper/documentation/Docs/Units/ClipperLib/Functions/CleanPolygon.htm
+            'spacing': SPACING,           # 组件间的间隔
+            'containerspacing':CONTAINERSPACING, #容器边缘间隔，负数表示向里预留量
+            'rotations': ROTATIONS,         # 旋转的颗粒度，360°的n份，如：4 = [0, 90 ,180, 270]
+            'populationSize': POPULATION_SIZE,    # 基因群数量
+            'mutationRate': MUTA_RATE,      # 变异概率
+            'useHoles': False,       # 是否有洞，暂时都是没有洞
+            'exploreConcave': False  # 寻找凹面，暂时是否
+        }
+
+        self.GA = None        # 遗传算法类
+        self.best = None      # 记录最佳结果
+        self.worker = None    # 根据NFP结果，计算每个图形的转移数据
+        self.container_bounds = None   # 容器的最小包络矩形作为输出图的坐标
+
+    def add_objects(self, objects):
+        """add_objects(objects): adds polygon objects to the nester"""
+        if not isinstance(objects, list):
+            objects = [objects]
+        if not self.shapes:
+            self.shapes = []
+            
+        p_id = 0
+        total_area = 0
+        for k,obj in enumerate(objects):
+            
+            shape = {
+                'area': 0,
+                'p_id': p_id,
+                'points': [{'x': p[0], 'y': p[1]} for p in obj],  
+            }
+
+            # Scaling shape
+            shape['points'] = self.scaling_polygon(shape['points'],SCALING_FACTOR)
+
+            #clean
+            len1 = len(shape['points'])
+            shape['points'] = self.clean_polygon(shape['points'])
+            print('清理第%d个块料轮廓点变化：%d --> %d' %(k,len1,len(shape['points'])))
+            
+            # 带上间隔的points
+            shape['points_offset'] = self.clean_polygon(self.polygon_offset(shape['points'], self.config['spacing']))
+            
+            # 确定多边形的线段方向
+            area = nfp_utls.polygon_area(shape['points'])
+            shape['area'] = abs(area)
+            if area > 0:
+                shape['points'].reverse()
+            
+            # 图形的凸包
+            convex_hull_points = qhull_2d.qhull2D([[point['x'],point['y']] for point in shape['points']])
+            shape['convex_hull'] = self.clean_polygon([{'x':p[0], 'y':p[1]} for p in convex_hull_points])
+            
+            # 图形是否为凸
+            shape['is_convex'] = nfp_utls.is_convex(shape['points'])
+            
+            # 与凸包的面积比
+            area_convex_hull = abs(nfp_utls.polygon_area(shape['convex_hull']))
+            shape['area_to_convex_hull'] = round(shape['area']/area_convex_hull,4)
+
+            
+            total_area += shape['area']
+            self.shapes.append(shape)
+
+        # 如果是一般布，需要这个尺寸
+        #self.shapes_max_length = total_area / BIN_HEIGHT * 3
+
+    def add_container(self, container):
+        """add_container(object): adds a polygon objects as the container"""
+        if not self.container:
+            self.container = {}
+
+        self.container['points'] = [{'x': p[0], 'y':p[1]} for p in container]
+        #clean
+        self.container['points'] = self.clean_polygon(self.container['points'])
+        #offset
+        self.container['points_offset'] = self.polygon_offset(self.container['points'], self.config['containerspacing'])
+            
+        self.container['p_id'] = '-1'
+        xbinmax = self.container['points'][0]['x']
+        xbinmin = self.container['points'][0]['x']
+        ybinmax = self.container['points'][0]['y']
+        ybinmin = self.container['points'][0]['y']
+
+        for point in self.container['points']:
+            if point['x'] > xbinmax:
+                xbinmax = point['x']
+            elif point['x'] < xbinmin:
+                xbinmin = point['x']
+            if point['y'] > ybinmax:
+                ybinmax = point['y']
+            elif point['y'] < ybinmin:
+                ybinmin = point['y']
+
+        self.container['width'] = xbinmax - xbinmin
+        self.container['height'] = ybinmax - ybinmin
+        # 最小包络多边形
+        self.container_bounds = nfp_utls.get_polygon_bounds(self.container['points'])
+
+    def clear(self):
+        """clear(): Removes all objects and shape from the nester"""
+        self.shapes = None
+
+    def run(self):
+        """
+        run(): Runs a nesting operation. Returns a list of lists of
+        shapes, each primary list being one filled container, or None
+        if the operation failed.
+        如果开多线程，可以在这里设计检查中断信号
+        """
+        if not self.container:
+            print("Empty container. Aborting")
+            return
+        if not self.shapes:
+            print("Empty shapes. Aborting")
+            return
+
+        # and still identify the original face, so we can calculate a transform afterwards
+        faces = list()
+        for i in range(0, len(self.shapes)):
+            shape = copy.deepcopy(self.shapes[i])
+            faces.append([i, shape])
+        # build a clean copy so we don't touch the original
+        
+        # order
+        max_area = max([shape['area'] for shape in self.shapes])
+        
+        faces = sorted(faces, reverse=True, key=lambda face: AREA_WEIGHT*face[1]['area']/max_area+face[1]['area_to_convex_hull']*CONVEX_WEIGHT)
+        
+        
+        
+        
+        
+        
+        
+        return self.launch_workers(faces)
+
+    def launch_workers(self, adam):
+        """
+        主过程，根据生成的基因组，求适应值，找最佳结果
+        :param adam:
+        :return:
+        """
+        if self.GA is None:
+            offset_bin = copy.deepcopy(self.container)
+            self.GA = genetic_algorithm(adam, offset_bin, self.config)
+        else:
+            self.GA.generation()
+
+        # 计算每一组基因的适应值
+        for i in range(0, self.GA.config['populationSize']):
+            res = self.find_fitness(self.GA.population[i]) #res 存储了在排列过程中得到的多个结果
+            self.GA.population[i]['fitness'] = max(res['fitness'])
+            self.results.append(res)
+
+        # 找最佳结果
+        if len(self.results) > 0:
+            best_result = self.results[0]
+
+            for p in self.results:
+                if max(p['fitness']) > max(best_result['fitness']):
+                    best_result = p
+
+            if self.best is None or max(best_result['fitness']) > self.best['fitness']:
+                best_result_index = best_result['fitness'].index(max(best_result['fitness']))
+                
+                best_result = {'placements':best_result['placements'][best_result_index],
+                               'fitness':best_result['fitness'][best_result_index]}
+                
+                self.best = best_result
+
+    def find_fitness(self, individual):
+        """
+        求解适应值
+        :param individual: 基因组数据
+        :return:
+        """
+        place_list = copy.deepcopy(individual['placement'])
+        rotations = copy.deepcopy(individual['rotation'])
+        ids = [p[0] for p in place_list]
+        for i in range(0, len(place_list)):
+            place_list[i].append(rotations[i])
+
+        nfp_pairs = list()
+        new_cache = dict()
+        for i in range(0, len(place_list)):
+            # 容器和图形的内切多边形计算
+            part = place_list[i]
+            key = {
+                'A': '-1',
+                'B': part[0],
+                'inside': True,
+                'A_rotation': 0,
+                'B_rotation': rotations[i]
+            }
+
+            tmp_json_key = json.dumps(key)
+            if not (tmp_json_key in self.nfp_cache):
+                nfp_pairs.append({
+                    'A': self.container,
+                    'B': part[1],
+                    'key': key
+                })
+            else:
+                # 是否已经计算过结果
+                new_cache[tmp_json_key] = self.nfp_cache[tmp_json_key]
+
+            # 图形与图形之间的外切多边形计算
+            for j in range(0, i):
+                placed = place_list[j]
+                key = {
+                    'A': placed[0],
+                    'B': part[0],
+                    'inside': False,
+                    'A_rotation': rotations[j],
+                    'B_rotation': rotations[i]
+                }
+                tmp_json_key = json.dumps(key)
+                if not (tmp_json_key in self.nfp_cache):
+                    nfp_pairs.append({
+                        'A': placed[1],
+                        'B': part[1],
+                        'key': key
+                    })
+                else:
+                    # 是否已经计算过结果
+                    new_cache[tmp_json_key] = self.nfp_cache[tmp_json_key]
+        
+        start = time.clock()
+        # 计算所有图形两两组合的相切多边形（NFP）
+        for pair in nfp_pairs:
+            
+            process_nfp_result = self.process_nfp(pair)
+            
+            key = json.dumps(process_nfp_result['key'])
+            new_cache[key] = process_nfp_result['value']         
+        print('计算NFP %d 个，耗时: %.1f'  %(len(nfp_pairs),time.clock()-start) )
+        # only keep cache for one cycle
+        #self.nfp_cache = new_cache 
+        
+        # keep all calculated cache during past cycles for the next cycle
+        self.nfp_cache.update(new_cache)
+
+        # 计算图形的转移量和适应值的类
+        self.worker = placement_worker.PlacementWorker(
+             self.container, place_list, ids, rotations, self.config, self.nfp_cache)
+
+        # 根据这些NFP，求解图形分布
+        place_res = self.worker.place_paths()
+        return place_res
+
+    def process_nfp(self, pair):
+        """
+        计算所有图形两两组合的相切多边形（NFP）
+        :param pair: 两个组合图形的参数
+        :return:
+        """
+        if pair is None or len(pair) == 0:
+            return None
+
+        # 考虑有没有洞和凹面
+        search_edges = self.config['exploreConcave']
+        use_holes = self.config['useHoles']
+
+        # 图形参数
+        A = copy.deepcopy(pair['A'])
+        A['points_offset'] = nfp_utls.rotate_polygon(A['points_offset'], pair['key']['A_rotation'])['points']
+        B = copy.deepcopy(pair['B'])
+        B['points'] = nfp_utls.rotate_polygon(B['points'], pair['key']['B_rotation'])['points']
+
+        if pair['key']['inside']:
+            # 内切或者外切
+            if nfp_utls.is_rectangle(A['points_offset'], 0.0001): #A是面料，用预留出边距后的实际面料去找NFP
+                nfp = nfp_utls.nfp_rectangle(A['points_offset'], B['points'])
+            else:
+                nfp = nfp_utls.nfp_polygon(A, B, True, search_edges)
+
+            # ensure all interior NFPs have the same winding direction
+            if nfp and len(nfp) > 0:
+                for i in range(0, len(nfp)):
+                    if nfp_utls.polygon_area(nfp[i]) > 0:
+                        nfp[i].reverse()
+            else:
+                pass
+                # print('NFP Warning:', pair['key'])
+
+        else:
+            if search_edges:
+                nfp = nfp_utls.nfp_polygon(A, B, False, search_edges) #去搜寻像 大“C”那样的内部凹点。在这个比赛中，不存在这个问题
+            else:
+                nfp = minkowski_difference(A, B)
+            
+            '''
+            # 检查NFP多边形是否合理
+            if nfp is None or len(nfp) == 0:
+                pass
+                # print('error in NFP 260')
+                # print('NFP Error:', pair['key'])
+                # print('A;', A)
+                # print('B:', B)
+                return None
+
+            for i in range(0, len(nfp)):
+                # if search edges is active, only the first NFP is guaranteed to pass sanity check
+                if not search_edges or i == 0:
+                    if abs(nfp_utls.polygon_area(nfp[i])) < abs(nfp_utls.polygon_area(A['points'])):
+                        pass
+                        # print('error in NFP area 269')
+                        # print('NFP Area Error: ', abs(nfp_utls.polygon_area(nfp[i])), pair['key'])
+                        # print('NFP:', json.dumps(nfp[i]))
+                        # print('A: ', A)
+                        # print('B: ', B)
+                        nfp.pop(i)
+                        return None
+            
+            if len(nfp) == 0:
+                return None
+            # for outer NFPs, the first is guaranteed to be the largest.
+            # Any subsequent NFPs that lie inside the first are hole
+            for i in range(0, len(nfp)):
+                if nfp_utls.polygon_area(nfp[i]) > 0:
+                    nfp[i].reverse()
+
+                if i > 0:
+                    if nfp_utls.point_in_polygon(nfp[i][0], nfp[0]):
+                        if nfp_utls.polygon_area(nfp[i]) < 0:
+                            nfp[i].reverse()
+
+            # generate nfps for children (holes of parts) if any exist
+            # 有洞的暂时不管 
+            if use_holes and len(A) > 0:  
+                pass # TODO
+            '''
+        return {'key': pair['key'], 'value': nfp}
+
+    '''
+    def generate_nfp(self):
+        """
+        计算图形的转移量和适应值
+        :param nfp: nfp多边形数据
+        :return:
+        """
+        if nfp:
+            for i in range(0, len(nfp)):
+
+                if nfp[i]:
+                    key = json.dumps(nfp[i]['key'])
+                    self.nfp_cache[key] = nfp[i]['value']
+        
+        # worker的nfp cache 只保留一次
+        self.worker.nfpCache = copy.deepcopy(self.nfp_cache)
+        # self.worker.nfpCache.update(self.nfpCache)
+        return self.worker.place_paths()
+    '''
+
+    def show_result(self):
+        draw_result(self.best['placements'], self.shapes, self.container, self.container_bounds)
+
+    def polygon_offset(self, polygon, offset):
+        is_list = True
+        if isinstance(polygon[0], dict):
+            polygon = [[p['x'], p['y']] for p in polygon]
+            is_list = False
+
+        miter_limit = 2
+        co = pyclipper.PyclipperOffset(miter_limit, self.config['curveTolerance'])
+        co.AddPath(polygon, pyclipper.JT_ROUND, pyclipper.ET_CLOSEDPOLYGON)
+        result = co.Execute(1*offset)
+        if not is_list:
+            result = [{'x': p[0], 'y':p[1]} for p in result[0]]
+        return result
+
+    def clean_polygon(self, polygon):
+        
+        polygon = [ [point['x'], point['y'] ] for point in polygon]
+        
+        simple = pyclipper.SimplifyPolygon(polygon,pyclipper.PFT_NONZERO)
+
+        if simple is None or len(simple) == 0:
+            return None
+
+        biggest = simple[0]
+        biggest_area = pyclipper.Area(biggest)
+        for i in range(1, len(simple)):
+            area = abs(pyclipper.Area(simple[i]))
+            if area > biggest_area:
+                biggest = simple[i]
+                biggest_area = area
+
+        clean = pyclipper.CleanPolygon(biggest, self.config['curveTolerance'])
+        if clean is None or len(clean) == 0:
+            return None
+        
+        clean = [{'x':point[0],'y':point[1]} for point in clean]
+        
+        return clean
+    
+    def scaling_polygon(self,polygon,scaling_factor):
+    
+        if polygon is None or len(polygon)<3:
+            return None
+
+        #Scaling
+        for point in polygon:
+            point['x'],point['y'] = point['x']*scaling_factor,point['y']*scaling_factor
+        
+        return polygon
+        
+def draw_result(placements, polygons, bin_polygon, bin_bounds):
+    """
+    从结果中得到平移旋转的数据，把原始图像移到到目标地方，然后保存结果
+    :param placements: 平移旋转数据
+    :param polygons: 原始图形数据
+    :param bin_polygon:
+    :param bin_bounds:
+    :return:
+    """
+    
+    class Polygon():
+        
+        def __init__(self, contour):
+            
+            self.contour = contour
+            self.contour_dict = [{'x':p[0],'y':p[1]} for p in contour]
+            self.area = nfp_utls.polygon_area(self.contour_dict)
+            
+        def rotate(self, radian, unknownI=0, unknownII=0):
+            self.contour_dict = nfp_utls.rotate_polygon(self.contour_dict, 
+                                                        radian * 180/math.pi)['points'] #rattate_polygon角度参数为 度数
+            self.contour = [[p['x'],p['y']] for p in self.contour_dict]
+            
+        def shift(self, dx, dy):
+            self.contour_dict = [{'x':p['x']+dx,'y':p['y']+dy } for p in self.contour_dict]
+            self.contour = [[p['x'],p['y']] for p in self.contour_dict] 
+    
+    
+    # 生产多边形类
+    shapes = list()
+    for polygon in polygons:
+        contour = [[p['x'], p['y']] for p in polygon['points']]
+        shapes.append(Polygon(contour))
+
+    bin_shape = Polygon([[p['x'], p['y']] for p in bin_polygon['points']])
+
+    solution = list()
+    rates = list()
+    
+    # 一个循环代表一个容器的排版
+    all_points = [{'x':0,'y':0}]
+    tmp_bin = list()
+    total_area = 0.0
+    for move_step in placements:
+        if move_step['rotation'] != 0:
+            # 坐标原点旋转
+            shapes[int(move_step['p_id'])].rotate(math.pi / 180 * move_step['rotation'], 0, 0)
+        # 平移
+        shapes[int(move_step['p_id'])].shift(move_step['x'], move_step['y'])
+        tmp_bin.append(shapes[int(move_step['p_id'])])
+        total_area += shapes[int(move_step['p_id'])].area
+        
+        #所有点
+        for point in shapes[int(move_step['p_id'])].contour_dict:
+            all_points.append({'x':point['x'],'y':point['y']})
+    # 当前排版的利用率
+    bin_area_used = nfp_utls.get_polygon_bounds(all_points)['width'] * BIN_HEIGHT
+    rates.append(total_area / bin_area_used)
+    solution.append(tmp_bin)
+    
+    # 显示结果
+    draw_polygon(solution, rates, bin_bounds, bin_shape)
+    
+    
+    
+class genetic_algorithm():
+    """
+    遗传算法类
+    """
+
+    def __init__(self, adam, bin_polygon, config):
+        """
+        初始化参数，根据参数生成基因群
+        :param adam: 图形
+        :param bin_polygon: 面布
+        :param config: 算法参数
+        """
+        self.bin_bounds = bin_polygon['points_offset']
+        self.bin_bounds = {
+            'width': bin_polygon['width'],
+            'height': bin_polygon['height'],
+        }
+        self.config = config
+        self.bin_polygon = bin_polygon
+        angles = list()
+        shapes = copy.deepcopy(adam)
+        for shape in shapes:
+            angles.append(self.random_angle(shape))
+
+        # 基因群，图形顺序和图形旋转的角度作为基因编码
+        self.population = [{'placement': shapes, 'rotation': angles}]
+
+        for i in range(1, self.config['populationSize']):
+            mutant = self.mutate(self.population[0])
+            self.population.append(mutant)
+
+    def random_angle(self, shape):
+        """
+        随机旋转角度的选取
+        :param shape:
+        :return:
+        """
+        angle_list = list()
+        for i in range(0, self.config['rotations']):
+            angle_list.append(i * (360/self.config['rotations']))
+
+        # 打乱顺序
+        def shuffle_array(data):
+            for i in range(len(data)-1, 0, -1):
+                j = random.randint(0, i)
+                data[i], data[j] = data[j], data[i]
+            return data
+
+        angle_list = shuffle_array(angle_list)
+
+        # 查看选择后图形是否能放置在里面
+        for angle in angle_list:
+            rotate_part = nfp_utls.rotate_polygon(shape[1]['points'], angle)
+            # 是否判断旋转出界,没有出界可以返回旋转角度,rotate 只是尝试去转，没有真正改变图形坐标
+            if rotate_part['width'] < self.bin_bounds['width'] and rotate_part['height'] < self.bin_bounds['height']:
+                return angle_list[i]
+
+        return 0
+
+    def mutate(self, individual):
+        clone = {
+            'placement': individual['placement'][:],
+            'rotation': individual['rotation'][:]
+        }
+        for i in range(0, len(clone['placement'])):
+            if random.random() < 0.01 * self.config['mutationRate']:
+                if i+1 < len(clone['placement']):
+                    clone['placement'][i],clone['placement'][i+1] = clone['placement'][i+1], clone['placement'][i]
+
+        if random.random() < 0.01 * self.config['mutationRate']:
+            clone['rotation'][i] = self.random_angle(clone['placement'][i])
+        return clone
+
+    def generation(self):
+        
+        # 适应度 从大到小排序
+        self.population = sorted(self.population, reverse=True, key=lambda a: a['fitness'])
+        new_population = [self.population[0]]
+        while len(new_population) < self.config['populationSize']:
+            male = self.random_weighted_individual()
+            female = self.random_weighted_individual(male)
+            # 交集下一代
+            children = self.mate(male, female)
+
+            # 轻微突变
+            new_population.append(self.mutate(children[0]))
+
+            if len(new_population) < self.config['populationSize']:
+                new_population.append(self.mutate(children[1]))
+
+        #print('new :', new_population)
+        self.population = new_population
+
+    def random_weighted_individual(self, exclude=None):
+        pop = self.population
+        if exclude and pop.index(exclude) >= 0:
+            pop.remove(exclude)
+
+        rand = random.random()
+        lower = 0
+        weight = 1.0 / len(pop)
+        upper = weight
+        pop_len = len(pop)
+        for i in range(0, pop_len):
+            if (rand > lower) and (rand < upper):
+                return pop[i]
+            lower = upper
+            upper += 2 * weight * float(pop_len-i)/pop_len
+        return pop[0]
+
+    def mate(self, male, female):
+        cutpoint = random.randint(0, len(male['placement'])-1)
+        gene1 = male['placement'][:cutpoint]
+        rot1 = male['rotation'][:cutpoint]
+
+        gene2 = female['placement'][:cutpoint]
+        rot2 = female['rotation'][:cutpoint]
+
+        def contains(gene, shape_id):
+            for i in range(0, len(gene)):
+                if gene[i][0] == shape_id:
+                    return True
+            return False
+
+        for i in range(len(female['placement'])-1, -1, -1):
+            if not contains(gene1, female['placement'][i][0]):
+                gene1.append(female['placement'][i])
+                rot1.append(female['rotation'][i])
+
+        for i in range(len(male['placement'])-1, -1, -1):
+            if not contains(gene2, male['placement'][i][0]):
+                gene2.append(male['placement'][i])
+                rot2.append(male['rotation'][i])
+
+        return [{'placement': gene1, 'rotation': rot1}, {'placement': gene2, 'rotation': rot2}]
+
+
+def minkowski_difference(A, B):
+    """
+    两个多边形的相切空间
+    http://www.angusj.com/delphi/clipper/documentation/Docs/Units/ClipperLib/Functions/MinkowskiDiff.htm
+    :param A:
+    :param B:
+    :return:
+    """
+
+    Ac = [[p['x'], p['y']] for p in A['points_offset']]
+    Bc = [[p['x'] * -1, p['y'] * -1] for p in B['points']]
+    solution = pyclipper.MinkowskiSum(Ac, Bc, True)
+    largest_area = None
+    clipper_nfp = None
+    for p in solution:
+        p = [{'x': i[0], 'y':i[1]} for i in p]
+        sarea = nfp_utls.polygon_area(p)
+        if largest_area is None or largest_area > sarea:
+            clipper_nfp = p
+            largest_area = sarea
+
+    clipper_nfp = [{
+                    'x': clipper_nfp[i]['x'] + Bc[0][0] * -1,
+                    'y':clipper_nfp[i]['y'] + Bc[0][1] * -1
+                   } for i in range(0, len(clipper_nfp))]
+
+    return [clipper_nfp]
+
+
+def draw_polygon_png(solution, bin_bounds, bin_shape, path=None):
+    base_width = 8
+    base_height = base_width * bin_bounds['height'] / bin_bounds['width']
+    num_bin = len(solution)
+    fig_height = num_bin * base_height
+    fig1 = Figure(figsize=(base_width, fig_height))
+    fig1.suptitle('Polygon packing', fontweight='bold')
+    FigureCanvas(fig1)
+
+    i_pic = 1   # 记录图片的索引
+    for shapes in solution:
+        # 坐标设置
+        ax = fig1.add_subplot(num_bin, 1, i_pic, aspect='equal')
+        ax.set_title('Num %d bin' % i_pic)
+        i_pic += 1
+        ax.set_xlim(bin_bounds['x']-10, bin_bounds['width']+50)
+        ax.set_ylim(bin_bounds['y']-10, bin_bounds['height']+50)
+
+        output_obj = list()
+        output_obj.append(patches.Polygon(bin_shape.contour, fc='green'))
+        for s in shapes[:-1]:
+            output_obj.append(patches.Polygon(s.contour, fc='yellow', lw=1, edgecolor='m'))
+        for p in output_obj:
+            ax.add_patch(p)
+
+    if path is None:
+        path = 'example'
+
+    fig1.savefig('%s.png' % path)
+
+
+def draw_polygon(solution, rates, bin_bounds, bin_shape):
+    base_width = 8 * 3
+    base_height = base_width * bin_bounds['height'] / bin_bounds['width']
+    num_bin = len(solution)
+    fig_height = num_bin * base_height
+    # fig1 = Figure(figsize=(base_width, fig_height))
+    # FigureCanvas(fig1)
+    fig1 = plt.figure(figsize=(base_width, fig_height))
+    fig1.suptitle('Polygon packing', fontweight='bold')
+
+    i_pic = 1  # 记录图片的索引
+    for shapes in solution:
+        # 坐标设置
+        ax = plt.subplot(num_bin, 1, i_pic, aspect='equal')
+        # ax = fig1.set_subplot(num_bin, 1, i_pic, aspect='equal')
+        ax.set_title('Num %d bin, rate is %0.4f' % (i_pic, rates[i_pic-1]))
+        i_pic += 1
+        ax.set_xlim(bin_bounds['x'] - 10, bin_bounds['width'] + 50)
+        ax.set_ylim(bin_bounds['y'] - 10, bin_bounds['height'] + 50)
+
+        output_obj = list()
+        output_obj.append(patches.Polygon(bin_shape.contour, fc='green'))
+        for s in shapes:
+            output_obj.append(patches.Polygon(s.contour, fc='yellow', lw=1, edgecolor='m'))
+        for p in output_obj:
+            ax.add_patch(p)
+    plt.show()
+    # fig1.save()
+
+
+def content_loop_rate(best, n, loop_time=20):
+    """
+    固定迭代次数
+    :param best:
+    :param n:
+    :param loop_time:
+    :return:
+    """
+    res = best
+    run_time = loop_time
+    while run_time:
+        n.run()
+        best = n.best
+        if best['fitness'] > res['fitness']:
+            res = best
+            print('the best fitness change fron %.4f to %.4f'%(best['fitness'],res['fitness']))
+        run_time -= 1
+    draw_result(res['placements'], n.shapes, n.container, n.container_bounds)
\ No newline at end of file
diff --git a/nfp_utls.py b/nfp_utls.py
new file mode 100644
index 0000000..4ea0a10
--- /dev/null
+++ b/nfp_utls.py
@@ -0,0 +1,1036 @@
+# -*- coding: utf-8 -*-
+import copy
+import math
+TOL = 0.0000001   # 计算过程中误差忽略值
+
+
+def almost_equal(a, b, tolerance=None):
+    """
+    A，B 两点是否约为相同
+    :param a: 坐标
+    :param b: 坐标
+    :param tolerance: 误差值
+    :return:
+    """
+    if tolerance is None:
+        tolerance = TOL
+    return abs(a - b) < tolerance
+
+def is_convex(poly):
+    zcrossproduct = []
+    j = len(poly) - 1
+    k = j - 1
+    for i in range(0,len(poly)):
+        dx1 = poly[j]['x'] - poly[k]['x']
+        dy1 = poly[j]['y'] - poly[k]['y']
+        dx2 = poly[i]['x'] - poly[j]['x']
+        dy2 = poly[i]['y'] - poly[j]['y']
+        zcrossproduct.append(dx1*dy2 - dy1*dx2)
+        
+        j,k = i,j
+    
+    return all([z >= 0 for z in zcrossproduct]) or all([z <= 0 for z in zcrossproduct])
+    
+
+
+def is_rectangle(poly, tolerance=None):
+    bb = get_polygon_bounds(poly)
+    tolerance = tolerance or TOL
+    for point in poly:
+        if not almost_equal(point['x'], bb['x'], tolerance) and not almost_equal(
+                point['x'], bb['x'] + bb['width'], tolerance):
+            return False
+        if not almost_equal(point['y'], bb['y'], tolerance) and not almost_equal(
+                point['y'], bb['y'] + bb['height'], tolerance):
+            return False
+
+    return True
+
+
+def normalize_vector(v):
+    """
+    normalize vector into a unit vector
+    :return:
+    """
+    if almost_equal(v['x'] * v['x'] + v['y'] * v['y'], 1):
+        # given vector was already a unit vector
+        return v
+    inverse = 1.0 / math.sqrt(v['x']**2 + v['y']**2)
+
+    return {'x': v['x']*inverse, 'y': v['y']*inverse}
+
+
+def on_segment(A, B, p):
+    """
+    returns true if p lies on the line segment defined by AB, but not at any endpoints
+    :param A:
+    :param B:
+    :param p:
+    :return:
+    """
+    # vertical line
+    if almost_equal(A['x'], B['x']) and almost_equal(p['x'], A['x']):
+        if not almost_equal(p['y'], B['y']) and not almost_equal(p['y'], A['y']) and \
+                        max(B['y'], A['y']) > p['y'] and p['y'] > min(B['y'], A['y']):
+            return True
+        else:
+            return False
+    # vertical line
+    if almost_equal(A['y'], B['y']) and almost_equal(p['y'], A['y']):
+        if not almost_equal(p['x'], B['x']) and not almost_equal(p['x'], A['x']) and \
+                        max(B['x'], A['x']) > p['x'] and p['x'] > min(B['x'], A['x']):
+            return True
+        else:
+            return False
+    # range check
+    if (p['x'] < A['x'] and p['x'] < B['x']) or (p['x'] > A['x'] and p['x'] > B['x']) or (
+                    p['y'] < A['y'] and p['y'] < B['y']) or (p['y'] > A['y'] and p['y'] > B['y']):
+        return False
+
+    # exclude end points
+    if (almost_equal(p['x'], A['x']) and almost_equal(p['y'], A['y'])) or (
+                almost_equal(p['x'], B['x']) and almost_equal(p['y'], B['y'])):
+        return False
+
+    cross = (p['y'] - A['y']) * (B['x'] - A['x']) - (p['x'] - A['x']) * (B['y'] - A['y'])
+    if abs(cross) > TOL:
+        return False
+    dot = (p['x'] - A['x']) * (B['x'] - A['x']) + (p['y'] - A['y']) * (B['y'] - A['y'])
+    if dot < 0 or almost_equal(dot, 0):
+        return False
+
+    len2 = (B['x'] - A['x']) * (B['x'] - A['x']) + (B['y'] - A['y']) * (B['y'] - A['y'])
+    if dot > len2 or almost_equal(dot, len2):
+        return False
+    return True
+
+
+def nfp_rectangle(A, B):
+    """
+    :param A: {x:12, y:10}
+    :param B: {x:12, y:10}
+    :return:
+    """
+    min_ax = A[0]['x']
+    min_ay = A[0]['y']
+    max_ax = A[0]['x']
+    max_ay = A[0]['y']
+
+    for point in A[1:]:
+        if point['x'] < min_ax:
+            min_ax = point['x']
+        if point['x'] > max_ax:
+            max_ax = point['x']
+        if point['y'] < min_ay:
+            min_ay = point['y']
+        if point['y'] > max_ay:
+            max_ay = point['y']
+
+    min_bx = B[0]['x']
+    min_by = B[0]['y']
+    max_bx = B[0]['x']
+    max_by = B[0]['y']
+
+    for point in B[1:]:
+        if point['x'] < min_bx:
+            min_bx = point['x']
+        if point['x'] > max_bx:
+            max_bx = point['x']
+        if point['y'] < min_by:
+            min_by = point['y']
+        if point['y'] > max_by:
+            max_by = point['y']
+
+    if max_bx - min_bx > max_ax - min_ax:
+        return None
+    if max_by - min_by > max_ay - min_ay:
+        return None
+
+    return [[
+        {'x': min_ax-min_bx+B[0]['x'], 'y': min_ay-min_by+B[0]['y']},
+        {'x': max_ax-max_bx+B[0]['x'], 'y': min_ay-min_by+B[0]['y']},
+        {'x': max_ax-max_bx+B[0]['x'], 'y': max_ay-max_by+B[0]['y']},
+        {'x': min_ax-min_bx+B[0]['x'], 'y': max_ay-max_by+B[0]['y']}
+    ]]
+
+
+def nfp_polygon(A, B, inside=True, search_edges=False):
+    """
+    given a static polygon A and a movable polygon B, compute a no fit polygon by orbiting B about A
+    if the inside flag is set, B is orbited inside of A rather than outside
+    if the searchEdges flag is set, all edges of A are explored for NFPs - multiple
+    """
+    if A is None or len(A['points']) < 3 or B is None or len(B['points']) < 3:
+        return None
+
+    # A last point = offsetx, offsety
+    A['offsetx'] = 0
+    A['offsety'] = 0
+
+    min_a = A['points'][0]['y']
+    min_a_index = 0
+    max_b = B['points'][0]['y']
+    max_b_index = 0
+
+    for i in range(1, len(A['points'])):
+        A['points'][i]['marked'] = False
+        if A['points'][i]['y'] < min_a:
+            min_a = A['points'][i]['y']
+            min_a_index = i
+
+    for i in range(1, len(B['points'])):
+        B['points'][i]['marked'] = False
+        if B['points'][i]['y'] > max_b:
+            max_b = B['points'][i]['y']
+            max_b_index = i
+
+    if not inside:
+        # shift B such that the bottom-most point of B is at the top-most point of A.
+        # This guarantees an initial placement with no intersections
+        start_point = {
+            'x': A['points'][min_a_index]['x'] - B['points'][max_b_index]['x'],
+            'y': A['points'][min_a_index]['y'] - B['points'][max_b_index]['y']
+        }
+    else:
+        #  no reliable heuristic for inside
+        start_point = search_start_point(A, B, inside)
+
+    NFP_list = list()
+
+    while start_point:
+        B['offsetx'] = start_point['x']
+        B['offsety'] = start_point['y']
+
+        # maintain a list of touching points/edges
+        prevvector = None
+        NFP = [{
+            'x': B['points'][0]['x'] + B['offsetx'],
+            'y': B['points'][0]['y'] + B['offsety'],
+        }]
+
+        referencex = B['points'][0]['x'] + B['offsetx']
+        referencey = B['points'][0]['y'] + B['offsety']
+        startx = referencex
+        starty = referencey
+        counter = 0
+        len_a = len(A['points'])
+        len_b = len(B['points'])
+        while counter < 10 * (len_a + len_b):
+            touching = list()
+            for i in range(0, len_a):
+                nexti = 0 if i == len_a - 1 else i + 1
+                for j in range(len_b):
+                    nextj = 0 if j == len_b - 1 else j + 1
+                    if almost_equal(A['points'][i]['x'], B['points'][j]['x'] + B['offsetx']) and almost_equal(
+                            A['points'][i]['y'], B['points'][j]['y'] + B['offsety']):
+                        touching.append({'type': 0, 'A': i, 'B': j})
+                    elif on_segment(A['points'][i], A['points'][nexti],
+                                    {'x': B['points'][j]['x']+B['offsetx'], 'y': B['points'][j]['y'] + B['offsety']}):
+                        touching.append({'type': 1, 'A': nexti, 'B': j})
+                    elif on_segment(
+                            {'x': B['points'][j]['x']+B['offsetx'], 'y': B['points'][j]['y'] + B['offsety']},
+                            {'x': B['points'][nextj]['x'] + B['offsetx'], 'y': B['points'][nextj]['y'] + B['offsety']},
+                            A['points'][i]):
+                        touching.append({'type': 2, 'A': i, 'B': nextj})
+
+            # generate translation vectors from touching vertices/edges
+            vectors = list()
+            for i in range(0, len(touching)):
+                vertex_a = {'A': A['points'][touching[i]['A']], 'marked': True}
+                prev_a_index = touching[i]['A'] - 1
+                next_a_index = touching[i]['A'] + 1
+                prev_a_index = len_a - 1 if prev_a_index < 0 else prev_a_index  # loop
+                next_a_index = 0 if next_a_index >= len_a else next_a_index  # loop
+
+                prev_a = A['points'][prev_a_index]
+                next_a = A['points'][next_a_index]
+
+                # adjacent B vertices
+                vertex_b = {'A': B['points'][touching[i]['B']]}
+                prev_b_index = touching[i]['B'] - 1
+                next_b_index = touching[i]['B'] + 1
+                prev_b_index = len_b - 1 if prev_b_index < 0 else prev_b_index  # loop
+                next_b_index = 0 if next_b_index >= len_b else next_b_index  # loop
+
+                prev_b = B['points'][prev_b_index]
+                next_b = B['points'][next_b_index]
+
+                if touching[i]['type'] == 0:
+                    v_a1 = {
+                        'x': prev_a['x'] - vertex_a['A']['x'],
+                        'y': prev_a['y'] - vertex_a['A']['y'],
+                        'start': vertex_a['A'],
+                        'end': prev_a
+                    }
+
+                    v_a2 = {
+                        'x': next_a['x'] - vertex_a['A']['x'],
+                        'y': next_a['y'] - vertex_a['A']['y'],
+                        'start': vertex_a['A'],
+                        'end': next_a
+                    }
+
+                    v_b1 = {
+                        'x': vertex_b['A']['x'] - prev_b['x'],
+                        'y': vertex_b['A']['y'] - prev_b['y'],
+                        'start': prev_b,
+                        'end': vertex_b['A']
+                    }
+
+                    v_b2 = {
+                        'x': vertex_b['A']['x'] - next_b['x'],
+                        'y': vertex_b['A']['y'] - next_b['y'],
+                        'start': next_b,
+                        'end': vertex_b['A']
+                    }
+
+                    vectors.append(v_a1)
+                    vectors.append(v_a2)
+                    vectors.append(v_b1)
+                    vectors.append(v_b2)
+                elif touching[i]['type'] == 1:
+                    vectors.append({
+                        'x': vertex_a['A']['x'] - (vertex_b['A']['x'] + B['offsetx']),
+                        'y': vertex_a['A']['y'] - (vertex_b['A']['y'] + B['offsety']),
+                        'start': prev_a,
+                        'end': vertex_a['A']
+                    })
+                    vectors.append({
+                        'x': prev_a['x'] - (vertex_b['A']['x'] + B['offsetx']),
+                        'y': prev_a['y'] - (vertex_b['A']['y'] + B['offsety']),
+                        'start': vertex_a['A'],
+                        'end': prev_a
+                    })
+                elif touching[i]['type'] == 2:
+                    vectors.append({
+                        'x': vertex_a['A']['x'] - (vertex_b['A']['x'] + B['offsetx']),
+                        'y': vertex_a['A']['y'] - (vertex_b['A']['y'] + B['offsety']),
+                        'start': prev_b,
+                        'end': vertex_b['A']
+                    })
+                    vectors.append({
+                        'x': vertex_a['A']['x'] - (prev_b['x'] + B['offsetx']),
+                        'y': vertex_a['A']['y'] - (prev_b['y'] + B['offsety']),
+                        'start': vertex_b['A'],
+                        'end': prev_b
+                    })
+
+            translate = None
+            max_d = 0
+            for i in range(0, len(vectors)):
+                if vectors[i]['x'] == 0 and vectors[i]['y'] == 0:
+                    continue
+                # if this vector points us back to where we came from, ignore it.
+                # ie cross product = 0, dot product < 0
+                if prevvector and (vectors[i]['y'] * prevvector['y'] + vectors[i]['x'] * prevvector['x']) < 0:
+                    # compare magnitude with unit vectors
+                    vectorlength = math.sqrt(vectors[i]['x']**2 + vectors[i]['y']**2)
+                    unitv = {'x': vectors[i]['x'] / vectorlength, 'y': vectors[i]['y'] / vectorlength}
+                    prevlength = math.sqrt(prevvector['x']**2+prevvector['y']**2)
+                    prevunit = {'x': prevvector['x'] / prevlength, 'y': prevvector['y'] / prevlength}
+
+                    # we need to scale down to unit vectors to normalize vector length. Could also just do a tan here
+                    if abs(unitv['y'] * prevunit['x'] - unitv['x'] * prevunit['y']) < 0.0001:
+                        continue
+
+                d = polygon_slide_distance(A, B, vectors[i], True)
+                vecd2 = vectors[i]['x']**2 + vectors[i]['y']**2
+
+                if d is None or d**2 > vecd2:
+                    vecd = math.sqrt(vectors[i]['x']**2 + vectors[i]['y']**2)
+                    d = vecd
+                if d and d > max_d:
+                    max_d = d
+                    translate = vectors[i]
+
+            if translate is None or almost_equal(max_d, 0):
+                NFP = None
+                break
+
+            translate['start']['marked'] = True
+            translate['end']['marked'] = True
+
+            prevvector = translate
+
+            # trim
+            vlength2 = translate['x']**2 + translate['y']**2
+            if max_d**2 < vlength2 and not almost_equal(max_d**2, vlength2):
+                scale = math.sqrt((max_d**2)/vlength2)
+                translate['x'] *= scale
+                translate['y'] *= scale
+
+            referencex += translate['x']
+            referencey += translate['y']
+
+            if almost_equal(referencex, startx) and almost_equal(referencey, starty):
+                # we have made a full loop
+                break
+
+            # if A and B start on a touching horizontal line, the end point may not be the start point
+            looped = False
+            if len(NFP) > 0:
+                for i in range(0, len(NFP)-1):
+                    if almost_equal(referencex, NFP[i]['x'] and almost_equal(referencey, NFP[i]['y'])):
+                        looped = True
+
+            if looped:
+                # we've made a full loop
+                break
+
+            NFP.append({
+                'x': referencex,
+                'y': referencey
+            })
+            B['offsetx'] += translate['x']
+            B['offsety'] += translate['y']
+
+            counter += 1
+
+            if NFP and len(NFP) > 0:
+                NFP_list.append(NFP)
+
+        if not search_edges: # TODO
+            # only get outer NFP or first inner NFP
+            break
+
+        start_point = search_start_point(A, B, inside, NFP_list)
+
+    return NFP_list
+
+
+def search_start_point(A, B, inside=True, NFP=None):
+    """
+    searches for an arrangement of A and B such that they do not overlap if an NFP is given,
+    only search for startpoints that have not already been traversed in the given NFP
+    :param A:
+    :param B:
+    :param inside:
+    :param NFP:
+    :return:
+    """
+    # clone arrays
+    A = copy.deepcopy(A)
+    B = copy.deepcopy(B)
+
+    for i in range(0, len(A['points'])-1):
+        if not A['points'][i].get('marked'):
+            A['points'][i]['marked'] = True
+            for j in range(0, len(B['points'])):
+                B['offsetx'] = A['points'][i]['x'] - B['points'][j]['x']
+                B['offsety'] = A['points'][i]['y'] - B['points'][j]['y']
+
+                # 判断 A，B 是否一样
+                # 点是否在多边形边上
+                bin_side = None
+                for k in range(0, len(B['points'])):
+                    inpoly = point_in_polygon(
+                        {'x': B['points'][k]['x']+B['offsetx'],
+                         'y': B['points'][k]['y']+B['offsety']}, A)
+                    if inpoly is not None:
+                        bin_side = inpoly
+                        break
+
+                if bin_side is None:
+                    return None
+
+                start_point = {
+                    'x': B['offsetx'],
+                    'y': B['offsety']
+                }
+                if ((bin_side and inside) or (not bin_side and not inside)) and (
+                            not intersect(A, B) and not inNfp(start_point, NFP)):
+                    return start_point
+
+                # slide B along vector
+                vx = A['points'][i+1]['x'] - A['points'][i]['x']
+                vy = A['points'][i+1]['y'] - A['points'][i]['y']
+
+                d1 = polygon_projection_distance(A, B, {'x': vx, 'y': vy})
+                d2 = polygon_projection_distance(B, A, {'x': -vx, 'y': -vy})
+
+                d = None
+
+                if d1 is not None and d2 is not None:
+                    d = min(d1, d2)
+                elif d1 is None and d2 is not None:
+                    d = d2
+                elif d1 is not None and d2 is None:
+                    d = d1
+
+                # only slide until no longer negative
+                if not (d is not None and not almost_equal(d, 0) and d > 0):
+                    continue
+
+                vd2 = vx * vx + vy * vy
+                if d * d < vd2 and not almost_equal(d*d, vd2):
+                    vd = math.sqrt(vx * vx + vy * vy)
+                    vx *= d /vd
+                    vy *= d /vd
+
+                B['offsetx'] += vx
+                B['offsety'] += vy
+
+                for k in range(0, len(B['points'])):
+                    inpoly = point_in_polygon(
+                        {'x': B['points'][k]['x']+B['offsetx'],
+                         'y': B['points'][k]['y']+B['offsety']}, A)
+                    if inpoly is not None:
+                        bin_side = inpoly
+                        break
+
+                start_point = {'x': B['offsetx'], 'y': B['offsety']}
+                if ((bin_side and inside) or (not bin_side and not inside)) and (
+                            not intersect(A, B) and not inNfp(start_point, NFP)):
+                    return start_point
+
+    return None
+
+
+def inNfp(p, nfp):
+    """
+    returns true if point already exists in the given nfp
+    :param p:
+    :param nfp:
+    :return:
+    """
+    if not nfp or len(nfp) == 0:
+        return False
+
+    for i in range(0, len(nfp)):
+        for j in range(0, len(nfp[i])):
+            if almost_equal(p['x'], nfp[i][j]['x']) and almost_equal(p['y'], nfp[i][j]['y']):
+                return True
+
+    return False
+
+
+def point_in_polygon(point, polygon):
+    if isinstance(polygon, list):
+        polygon = {'points': polygon}
+    if len(polygon.get('points')) < 3:
+        return None
+
+    inside = False
+    offsetx = polygon.get('offsetx') or 0
+    offsety = polygon.get('offsety') or 0
+
+    j = len(polygon['points']) - 1
+    for i in range(0, len(polygon['points'])):
+        xi = polygon['points'][i]['x'] + offsetx
+        yi = polygon['points'][i]['y'] + offsety
+        xj = polygon['points'][j]['x'] + offsetx
+        yj = polygon['points'][j]['y'] + offsety
+
+        if almost_equal(xi, point['x']) and almost_equal(yi, point['y']):
+            return None
+
+        if on_segment({'x': xi, 'y': yi}, {'x':xj, 'y':yj}, point):
+            return None  # exactly on the segment
+
+        if almost_equal(xi, xj) and almost_equal(yi, yj):
+            # ignore very small lines
+            continue
+
+        intersect = ((yi > point['y']) != (yj > point['y'])) and (point['x'] < (xj - xi) * (point['y'] - yi) / (yj - yi) + xi)
+        if intersect:
+            inside = not inside
+
+    return inside
+
+
+def intersect(A, B):
+
+    a_offsetx = A['offsetx'] or 0
+    a_offsety = A['offsety'] or 0
+
+    b_offsetx = B['offsetx'] or 0
+    b_offsety = B['offsety'] or 0
+
+    A = copy.deepcopy(A)
+    B = copy.deepcopy(B)
+    len_a = len(A['points'])
+    len_b = len(B['points'])
+    for i in range(0, len_a - 1):
+        for j in range(0, len_b - 1):
+            a1 = {'x': A['points'][i]['x']+a_offsetx, 'y': A['points'][i]['y']+a_offsety}
+            a2 = {'x': A['points'][i+1]['x']+a_offsetx, 'y': A['points'][i+1]['y']+a_offsety}
+            b1 = {'x': B['points'][j]['x']+b_offsetx, 'y': B['points'][j]['y']+b_offsety}
+            b2 = {'x': B['points'][j+1]['x']+b_offsetx, 'y': B['points'][j+1]['y']+b_offsety}
+
+            pre_vb_index = len_b - 1 if j == 0 else j - 1
+            pre_va_index = len_a - 1 if i == 0 else i - 1
+            next_b_index = 0 if j + 1 == len_b - 1 else j + 2
+            next_a_index = 0 if i + 1 == len_a - 1 else i + 2
+
+            # go even further back if we happen to hit on a loop end point
+            if B['points'][pre_vb_index] == B['points'][j] or almost_equal(
+                    B['points'][pre_vb_index]['x'], B['points'][j]['x']) and almost_equal(
+                B['points'][pre_vb_index]['y'], B['points'][j]['y']):
+                pre_vb_index = len_b - 1 if pre_vb_index == 0 else pre_vb_index - 1
+
+            if A['points'][pre_va_index] == A['points'][i] or almost_equal(
+                    A['points'][pre_va_index]['x'], A['points'][i]['x']) and almost_equal(
+                A['points'][pre_va_index]['y'], A['points'][i]['y']):
+                pre_va_index = len_a - 1 if pre_va_index == 0 else pre_va_index - 1
+
+            # go even further forward if we happen to hit on a loop end point
+            if B['points'][next_b_index] == B['points'][j+1] or almost_equal(
+                    B['points'][next_b_index]['x'], B['points'][j+1]['x']) and almost_equal(
+                B['points'][next_b_index]['y'], B['points'][j+1]['y']):
+                next_b_index = 0 if next_b_index == len_b - 1 else next_b_index + 1
+
+            if A['points'][next_a_index] == A['points'][i+1] or almost_equal(
+                    A['points'][next_a_index]['x'], A['points'][i+1]['x']) and almost_equal(
+                A['points'][next_a_index]['y'], A['points'][i+1]['y']):
+                next_a_index = 0 if next_a_index == len_a - 1 else next_a_index + 1
+
+            a0 = {'x': A['points'][pre_va_index]['x']+a_offsetx, 'y': A['points'][pre_va_index]['y']+a_offsety}
+            b0 = {'x': B['points'][pre_vb_index]['x']+b_offsetx, 'y': B['points'][pre_vb_index]['y']+b_offsety}
+            a3 = {'x': A['points'][next_a_index]['x']+a_offsetx, 'y': A['points'][next_a_index]['y']+a_offsety}
+            b3 = {'x': B['points'][next_b_index]['x']+b_offsetx, 'y': B['points'][next_b_index]['y']+b_offsety}
+
+            if on_segment(a1, a2, b1) or almost_equal(a1['x'], b1['x']) and almost_equal(a1['y'], b1['y']):
+                # if a point is on a segment, it could intersect or it could not. Check via the neighboring points
+                b0in = point_in_polygon(b0, A)
+                b2in = point_in_polygon(b2, A)
+                if (b0in and not b2in) or (not b0in and b2in):
+                    return True
+                else:
+                    continue
+
+            if on_segment(a1, a2, b2) or almost_equal(a2['x'], b2['x']) and almost_equal(a2['y'], b2['y']):
+                # if a point is on a segment, it could intersect or it could not.Check via the neighboring points
+                b1in = point_in_polygon(b1, A)
+                b3in = point_in_polygon(b3, A)
+                if (b1in and not b3in) or (not b1in and b3in):
+                    return True
+                else:
+                    continue
+
+            if on_segment(b1, b2, a1) or almost_equal(a1['x'], b2['x']) and almost_equal(a1['y'], b2['y']):
+                # if a point is on a segment, it could intersect or it could not.Check via the neighboring points
+                a0in = point_in_polygon(a0, B)
+                a2in = point_in_polygon(a2, B)
+                if (a0in and not a2in) or (not a0in and a2in):
+                    return True
+                else:
+                    continue
+
+            if on_segment(b1, b2, a2) or almost_equal(a2['x'], b1['x']) and almost_equal(a2['y'], b1['y']):
+                # if a point is on a segment, it could intersect or it could not.Check via the neighboring points
+                a1in = point_in_polygon(a1, B)
+                a3in = point_in_polygon(a3, B)
+                if (a1in and not a3in) or (not a1in and a3in):
+                    return True
+                else:
+                    continue
+
+            if line_intersect(b1, b2, a1, a2):
+                return True
+
+    return False
+
+
+def line_intersect(A, B, E, F, infinite=None):
+    """
+    returns the intersection of AB and EF, or null if there are no intersections or other numerical error
+    if the infinite flag is set, AE and EF describe infinite lines without endpoints,
+    they are finite line segments otherwise
+    :param A:
+    :param B:
+    :param E:
+    :param F:
+    :param infinite:
+    :return:
+    """
+    a1 = B['y'] - A['y']
+    b1 = A['x'] - B['x']
+    c1 = B['x'] * A['y'] - A['x'] * B['y']
+    a2 = F['y'] - E['y']
+    b2 = E['x'] - F['y']
+    c2 = F['x'] * E['y'] - E['x'] * F['y']
+    denom = a1 * b2 - a2 * b1
+    if denom == 0:
+        return None
+    x = (b1 * c2 - b2 * c1) / denom
+    y = (a2 * c1 - a1 * c2) / denom
+
+    if infinite is None:
+        if abs(A['x'] - B['x']) > TOL:
+            tmp = x < A['x'] or x > B['x'] if A['x'] < B['x'] else x > A['x'] or x < B['x']
+            if tmp:
+                return None
+            tmp = y < A['y'] or y > B['y'] if A['y'] < B['y'] else y > A['y'] or y < B['y']
+            if tmp:
+                return None
+        if abs(E['x'] - F['x']) > TOL:
+            tmp = x < E['x'] or x > F['x'] if E['x'] < F['x'] else x > E['x'] or x < F['x']
+            if tmp:
+                return None
+            tmp = y < E['y'] or y > F['y'] if E['y'] < F['y'] else y > E['y'] or y < F['y']
+            if tmp:
+                return None
+
+    return {'x': x, 'y': y}
+
+
+def polygon_projection_distance(A, B, direction):
+    """
+    project each point of B onto A in the given direction, and return the distance
+    :param A:
+    :param B:
+    :param direction:
+    :return:
+    """
+    b_offsetx = B.get('offsetx') or 0
+    b_offsety = B.get('offsety') or 0
+    a_offsetx = A.get('offsetx') or 0
+    a_offsety = A.get('offsety') or 0
+
+    A = copy.deepcopy(A)
+    B = copy.deepcopy(B)
+
+    edge_a = A['points']
+    edge_b = B['points']
+    distance = None
+    p = dict()
+    s1 = dict()
+    s2 = dict()
+    for i in range(0, len(edge_b)):
+        # the shortest/most negative projection of B onto A
+        min_projection = minp = None
+        for j in range(0, len(edge_a) - 1):
+            p['x'] = edge_b[i]['x'] + b_offsetx
+            p['y'] = edge_b[i]['y'] + b_offsety
+            s1['x'] = edge_a[j]['x'] + a_offsetx
+            s1['y'] = edge_a[j]['y'] + a_offsety
+            s2['x'] = edge_a[j+1]['x'] + a_offsetx
+            s2['y'] = edge_a[j+1]['y'] + a_offsety
+
+            if abs((s2['y'] - s1['y']) * direction['x'] - (s2['x'] - s2['x']) * direction['y']) < TOL:
+                continue
+
+            # project point, ignore edge boundaries
+            d = point_distance(p, s1, s2, direction)
+            if d and (min_projection is None or d < min_projection):
+                min_projection = d
+
+        if min_projection and (distance is None or min_projection > distance):
+            distance = min_projection
+
+    return distance
+
+
+def point_distance(p, s1, s2, normal, infinite=None):
+    normal = normalize_vector(normal)
+
+    dir_point = {
+        'x': normal['y'],
+        'y': -normal['x'],
+    }
+
+    pdot = p['x'] * dir_point['x'] + p['y'] * dir_point['y']
+    s1dot = s1['x'] * dir_point['x'] + s1['y'] * dir_point['y']
+    s2dot = s2['x'] * dir_point['x'] + s2['y'] * dir_point['y']
+
+    pdotnorm = p['x']*normal['x'] + p['y'] * normal['y']
+    s1dotnorm = s1['x']*normal['x'] + s1['y'] * normal['y']
+    s2dotnorm = s2['x'] * normal['x'] + s2['y'] * normal['y']
+
+    if infinite is None:
+        # dot doesn't collide with segment, or lies directly on the vertex
+        if ((pdot < s1dot or almost_equal(pdot, s1dot)) and (pdot < s2dot or almost_equal(pdot, s2dot))) or (
+                    (pdot > s1dot or almost_equal(pdot, s1dot)) and ((pdot > s2dot) or almost_equal(pdot, s2dot))):
+            return None
+        if (almost_equal(pdot, s1dot) and almost_equal(pdot, s2dot)) and (
+                        pdotnorm > s1dotnorm and pdotnorm > s2dotnorm):
+            return min(pdotnorm - s1dotnorm, pdotnorm - s2dotnorm)
+        if almost_equal(pdot, s1dot) and almost_equal(pdot, s2dot) and pdotnorm < s1dotnorm and pdotnorm < s2dotnorm:
+            return -min(s1dotnorm-pdotnorm, s2dotnorm-pdotnorm)
+
+    return -(pdotnorm - s1dotnorm + (s1dotnorm - s2dotnorm) * (s1dot - pdot)/(s1dot - s2dot))
+
+
+def polygon_slide_distance(A, B, direction, ignorenegative):
+
+    b_offsetx = B.get('offsetx') or 0
+    b_offsety = B.get('offsety') or 0
+    a_offsetx = A.get('offsetx') or 0
+    a_offsety = A.get('offsety') or 0
+
+    A = copy.deepcopy(A)
+    B = copy.deepcopy(B)
+
+    if not A['points'][-1] == A['points'][0]:
+        A['points'].append(A['points'][0])
+    if not B['points'][0] == B['points'][-1]:
+        B['points'].append(B['points'][0])
+
+    edge_a = A['points']
+    edge_b = B['points']
+    distance = None
+
+    dir_point = normalize_vector(direction)
+
+    for i in range(0, len(edge_b) - 1):
+
+        for j in range(0, len(edge_a) - 1):
+            A1 = {'x': edge_a[j]['x'] + a_offsetx, 'y': edge_a[j]['y'] + a_offsety}
+            A2 = {'x': edge_a[j+1]['x'] + a_offsetx, 'y': edge_a[j+1]['y'] + a_offsety}
+            B1 = {'x': edge_b[i]['x'] + b_offsetx, 'y': edge_b[i]['y'] + b_offsety}
+            B2 = {'x': edge_b[i + 1]['x'] + b_offsetx, 'y': edge_b[i + 1]['y'] + b_offsety}
+
+            if (almost_equal(A1['x'], A2['x']) and almost_equal(A1['y'], A2['y'])) or almost_equal(
+                    B1['x'], B2['x']) and almost_equal(B1['y'], B2['y']):
+                continue
+
+            d = segment_distance(A1, A2, B1, B2, dir_point)
+            if d and (distance is None or d < distance):
+                if not ignorenegative or d > 0 or almost_equal(d, 0):
+                    distance = d
+    return distance
+
+
+def segment_distance(A, B, E, F, direction):
+    normal = {
+        'x': direction['y'],
+        'y': -direction['x']
+    }
+    reverse = {
+        'x': -direction['x'],
+        'y': -direction['y']
+    }
+
+    dot_a = A['x'] * normal['x'] + A['y'] * normal['y']
+    dot_b = B['x'] * normal['x'] + B['y'] * normal['y']
+    dot_e = E['x'] * normal['x'] + E['y'] * normal['y']
+    dot_f = F['x'] * normal['x'] + F['y'] * normal['y']
+
+    cross_a = A['x'] * direction['x'] + A['y'] * direction['y']
+    cross_b = B['x'] * direction['x'] + B['y'] * direction['y']
+    cross_e = E['x'] * direction['x'] + E['y'] * direction['y']
+    cross_f = F['x'] * direction['x'] + F['y'] * direction['y']
+
+    ab_min = min(dot_a, dot_b)
+    ab_max = max(dot_a, dot_b)
+
+    ef_min = min(dot_e, dot_f)
+    ef_max = max(dot_e, dot_f)
+
+    # segments that will touch at one point
+    if almost_equal(ab_max, ef_min, TOL) or almost_equal(ab_min, ef_max, TOL):
+        return None
+
+    # segments miss each other completely
+    if ab_max < ef_min or ab_min > ef_max:
+        return None
+
+    if (ab_max > ef_max and ab_min < ef_min) or (ef_max > ab_max and ef_min < ab_min):
+        overlap = 1
+    else:
+        min_max = min(ab_max, ef_max)
+        max_min = max(ab_min, ef_min)
+        max_max = max(ab_max, ef_max)
+        min_min = min(ab_min, ef_min)
+
+        overlap = (min_max - max_min) / (max_max - min_min)
+
+    cross_abe = (E['y'] - A['y']) * (B['x'] - A['x']) - (E['x'] - A['x']) * (B['y'] - A['y'])
+    cross_abf = (F['y'] - A['y']) * (B['x'] - A['x']) - (F['x'] - A['x']) * (B['y'] - A['y'])
+
+    # lines are colinear
+    if almost_equal(cross_abe, 0) and almost_equal(cross_abf, 0):
+        ab_norm = {'x': B['y'] - A['y'], 'y': A['x'] - B['x']}
+        ef_norm = {'x': F['y'] - E['y'], 'y': E['x'] - F['x']}
+
+        ab_norm_length = math.sqrt(ab_norm['x']**2 + ab_norm['y']**2)
+        ab_norm['x'] /= ab_norm_length
+        ab_norm['y'] /= ab_norm_length
+
+        ef_norm_length = math.sqrt(ef_norm['x']**2 + ef_norm['y']**2)
+        ef_norm['x'] /= ef_norm_length
+        ef_norm['y'] /= ef_norm_length
+
+        # segment normals must point in opposite directions
+        if abs(ab_norm['y'] * ef_norm['x'] - ab_norm['x'] * ef_norm['y']) < TOL and (
+                            ab_norm['y'] * ef_norm['y'] + ab_norm['x'] * ef_norm['x'] < 0):
+            # normal of AB segment must point in same direction as given direction vector
+            norm_dot = ab_norm['y'] * direction['y'] + ab_norm['x'] * direction['x']
+            # the segments merely slide along eachother
+            if almost_equal(norm_dot, 0, TOL):
+                return None
+
+            if norm_dot < 0:
+                return 0
+
+        return None
+
+    distances = list()
+
+    # coincident points
+    if almost_equal(dot_a, dot_e):
+        distances.append(cross_a - cross_e)
+    elif almost_equal(dot_a, dot_f):
+        distances.append(cross_a - cross_f)
+    elif ef_min < dot_a and dot_a < ef_max:
+        d = point_distance(A, E, F, reverse)
+        # A currently touches EF, but AB is moving away from EF
+        if d and almost_equal(d, 0):
+            db = point_distance(B, E, F, reverse, True)
+            if db < 0 or almost_equal(db * overlap, 0):
+                d = None
+        if d:
+            distances.append(d)
+
+    if almost_equal(dot_b, dot_e):
+        distances.append(cross_b - cross_e)
+    elif almost_equal(dot_b, dot_f):
+        distances.append(cross_b - cross_f)
+    elif dot_b > ef_min and dot_b < ef_max:
+        d = point_distance(B, E, F, reverse)
+
+        if d and almost_equal(d, 0):
+            da = point_distance(A, E, F, reverse, True)
+            if da < 0 or almost_equal(da * overlap, 0):
+                d = None
+
+        if d:
+            distances.append(d)
+
+    if dot_e > ab_min and dot_e < ab_max:
+        d = point_distance(E, A, B, direction)
+        if d and almost_equal(d, 0):
+            df = point_distance(F, A, B, direction, True)
+            if df < 0 or almost_equal(df * overlap, 0):
+                d = None
+        if d:
+            distances.append(d)
+
+    if len(distances) == 0:
+        return None
+
+    if dot_f > ab_min and dot_f < ab_max:
+        d = point_distance(F, A, B, direction)
+        if d and almost_equal(d, 0):
+            de = point_distance(E, A, B, direction, True)
+            if de < 0 or almost_equal(de * overlap, 0):
+                d = None
+        if d:
+            distances.append(d)
+
+    if len(distances) == 0:
+        return None
+
+    return min(distances)
+
+
+def polygon_area(polygon):
+    area = 0
+    j = len(polygon) - 1
+    for i in range(0, len(polygon)):
+        area += (polygon[j]['x'] + polygon[i]['x']) * (polygon[j]['y'] - polygon[i]['y'])
+        j = i
+
+    return 0.5 * area
+
+
+def rotate_polygon(polygon, angle):
+    '''
+    rotated = {'points': list()}
+    angle = angle * math.pi / 180
+    for p in polygon:
+        x = p['x']
+        y = p['y']
+        rotated['points'].append({
+            'x': round(x * math.cos(angle) - y * math.sin(angle)),
+            'y': round(x * math.sin(angle) + y * math.cos(angle))
+        })
+
+    bounds = get_polygon_bounds(rotated['points'])
+    rotated['x'] = bounds['x']
+    rotated['y'] = bounds['y']
+    rotated['width'] = bounds['width']
+    rotated['height'] = bounds['height']
+    return rotated
+    '''
+    rotated = {'points': list()}
+    
+    if int(angle) == 0:
+        for p in polygon:
+            x = p['x']
+            y = p['y']
+            rotated['points'].append({
+                'x': x,
+                'y': y
+            })
+    if int(angle) == 90:
+        for p in polygon:
+            x = p['x']
+            y = p['y']
+            rotated['points'].append({
+                'x': -y,
+                'y': x
+            })
+    if int(angle) == 180:
+        for p in polygon:
+            x = p['x']
+            y = p['y']
+            rotated['points'].append({
+                'x': -x,
+                'y': -y
+            })
+    if int(angle) == 270:
+        for p in polygon:
+            x = p['x']
+            y = p['y']
+            rotated['points'].append({
+                'x': y,
+                'y': -x
+            })
+    
+    bounds = get_polygon_bounds(rotated['points'])
+    rotated['x'] = bounds['x']
+    rotated['y'] = bounds['y']
+    rotated['width'] = bounds['width']
+    rotated['height'] = bounds['height']
+    return rotated
+
+def get_polygon_bounds(polygon):
+    # 最小包络矩阵
+    if polygon is None or len(polygon) < 3:
+        return None
+
+    xmax = polygon[0]['x']
+    xmin = polygon[0]['x']
+    ymax = polygon[0]['y']
+    ymin = polygon[0]['y']
+
+    for point in polygon:
+        if point['x'] > xmax:
+            xmax = point['x']
+        elif point['x'] < xmin:
+            xmin = point['x']
+        if point['y'] > ymax:
+            ymax = point['y']
+        elif point['y'] < ymin:
+            ymin = point['y']
+
+    return {
+        'x': xmin,
+        'y': ymin,
+        'width': xmax - xmin,
+        'height': ymax - ymin
+    }
+    
+def D_function(a,b,p):
+            return (a['x']-b['x'])*(a['y']-p['y']) - (a['y']-b['y'])*(a['x']-p['x'])        
+        
+def edge_point_distance(edge,point):
+    if edge[0]['x'] == edge[1]['x']:
+        return abs(point['x'] - edge[0]['x'])
+    
+    else:
+        slope = (edge[1]['y']-edge[0]['y'])/(edge[1]['x']-edge[0]['x'])
+        
+        return abs( (point['y'] + slope*(edge[0]['x']-point['x']) - edge[0]['y'])/math.sqrt( 1 + slope**2 )  )
+ 
\ No newline at end of file
diff --git a/placement_worker.py b/placement_worker.py
new file mode 100644
index 0000000..87d1774
--- /dev/null
+++ b/placement_worker.py
@@ -0,0 +1,571 @@
+# -*- coding: utf-8 -*-
+import json
+from nfp_utls import almost_equal, rotate_polygon, get_polygon_bounds, polygon_area, is_convex, D_function, edge_point_distance
+from settings import BIN_HEIGHT, MAX_MOVE_X, MAX_MOVE_Y, SCALING_FACTOR
+import copy
+import pyclipper
+import time
+import cvxpy as cp
+TOL = 0.00001 * SCALING_FACTOR
+
+class PlacementWorker():
+    def __init__(self, bin_polygon, paths, ids, rotations, config, nfp_cache):
+        self.bin_polygon = bin_polygon
+        self.paths = copy.deepcopy(paths)
+        self.ids = ids       # 图形原来的ID顺序
+        self.rotations = rotations
+        self.config = config
+        self.nfpCache = copy.deepcopy(nfp_cache) or {}
+    
+    
+    def find_constraints(self,A,B,i,j,x,y,placements):
+        
+        # -*- coding: utf-8 -*-
+        """
+        Created on Thu Sep  5 11:22:11 2019
+        
+        @author: chend
+        """
+        
+        '''
+        param: A is a stationary polygon
+               B is the obitating polygon
+               i,j 当前寻找约束的两个polygon在当前排序中的位置，从0开始，-1表示bin
+               x,y LP的决策变量组，为points的第一个点的真实坐标，例如x[i]表示第i个块料的第一个点的横轴位置
+        output: [] constraints的列表
+        '''
+        
+        constraints = []
+        
+        key = {
+                'A': A['p_id'],
+                'B': B['p_id'],
+                'inside': False,
+                'A_rotation': A['rotation'],
+                'B_rotation': B['rotation']
+                } #nfp是按 B的第一个点绕出来的
+        json_key = json.dumps(key)
+        
+        nfp = self.nfpCache[json_key][0]
+        nfp_current_location = [{'x':point['x']+placements[i]['x']  , 'y':point['y']+placements[i]['y']} for point in nfp]
+        ref_point_B = B['current_location'][0]
+        
+        # nfp逆时针，当ref_point_B在nfp上edge的右边时，便是valid_edge,找出所有valid_edge
+        valid_edge = []
+        valid_distance = []
+        valid_point_index = []
+        for k in range(0,len(nfp_current_location)):
+            
+            point_1 = nfp_current_location[k-1]
+            point_2 = nfp_current_location[k]
+            
+            D_func_value = D_function(point_1,point_2,ref_point_B)
+            dis          = edge_point_distance([point_1,point_2],ref_point_B)
+            
+            #D_func为负数说明在右边,0表示在向量上;由于精度问题，这里距离足够小的话，我们也认为是在外面
+            if  (D_func_value <= 0 + TOL): #or  (dis <= 0 + TOL): 
+                valid_edge.append([{'x':point_1['x'],'y':point_1['y']}, {'x':point_2['x'],'y':point_2['y']}])
+                valid_distance.append( edge_point_distance(valid_edge[-1],ref_point_B) )
+                valid_point_index.append([k-1,k])
+        
+        
+        
+        
+        #有一点点由于精度引起的重叠，加一个constraint要求距离不能继续变大
+        if len(valid_edge) == 0:
+            min_dis,point_index = min( (edge_point_distance([nfp_current_location[k-1],nfp_current_location[k]] , ref_point_B),k) 
+                                      for k in range(len(nfp_current_location))  )
+            print(u'(%s,%s) ref_point在nfp内部了'%(A['p_id'],B['p_id']),
+                  u'离最近边的距离为:', min_dis )
+            print()
+
+            constraints.append( D_function(nfp_current_location[point_index-1],nfp_current_location[point_index],
+                                                  {'x':x[j],'y':y[j]}) <= 
+                                D_function(nfp_current_location[point_index-1],nfp_current_location[point_index],
+                                                  ref_point_B))
+            return constraints
+        
+        elif len(valid_edge) > 0:
+            if is_convex(nfp_current_location):
+                
+                max_distance = max(valid_distance)
+                
+                #目前不在nfp上
+                if max_distance > 0:            
+                    max_distance_index = valid_distance.index(max_distance)
+                    point_1 = valid_edge[max_distance_index][0]
+                    point_2 = valid_edge[max_distance_index][1]
+                    constraints.append( D_function(point_1,point_2,{'x':x[j],'y':y[j]}) <= 0 )
+                    
+                    
+                #目前在 nfp上，在nfp上的话，只可能在vertex上，或在edge上
+                elif max_distance == 0:
+                
+                    #在vertex上
+                    if len(valid_edge) == 1:
+                        edge = valid_edge[0]
+                        constraints.append(  D_function(edge[0],edge[1],{'x':x[j],'y':y[j]}) <= 0 )
+                    
+                    #在edge上
+                    if len(valid_edge) == 2:
+                        edge_1 = valid_edge[0]
+                        if edge_1[0]['x'] == edge_1[1]['x']:
+                            slope_1 = 1000000
+                        else:
+                            slope_1 = (edge_1[1]['y'] - edge_1[0]['y'])/(edge_1[1]['x']-edge_1[0]['x'])                    
+                        #slope_2
+                        edge_2 = valid_edge[1]
+                        if edge_2[0]['x'] == edge_2[1]['x']:
+                            slope_2 = 1000000
+                        else:
+                            slope_2 = (edge_2[1]['y'] - edge_2[0]['y'])/(edge_2[1]['x']-edge_2[0]['x'])                    
+                        
+                        if abs(slope_1) <= abs(slope_2):
+                            constraints.append( D_function(edge_1[0],edge_1[1],{'x':x[j],'y':y[j]}) <= 0 )
+                        else:
+                            constraints.append( D_function(edge_2[0],edge_2[1],{'x':x[j],'y':y[j]}) <= 0 )
+                
+            if not is_convex(nfp_current_location):
+                
+                max_distance = max(valid_distance)
+                edge = valid_edge[ valid_distance.index(max_distance) ]
+                point_1_index,point_2_index = valid_point_index[valid_distance.index(max_distance)][0],valid_point_index[valid_distance.index(max_distance)][1]
+                
+                #加入edge构成的约束
+                constraints.append( D_function(edge[0],edge[1],{'x':x[j],'y':y[j]}) <= 0 )
+                
+                if len(edge) is not 0:
+                    ON_RIGHT = True
+                else:
+                    ON_RIGHT = False
+                
+                #逆时针寻找，下一条边的终点在edge右侧的，则加入下一条边构成的约束
+                while ON_RIGHT:
+                    if point_2_index < len(nfp_current_location)-1:
+                        point_3_index = point_2_index + 1
+                    if point_2_index == len(nfp_current_location)-1:
+                        point_3_index = 0
+                    
+                    point_1 = nfp_current_location[point_1_index]
+                    point_2 = nfp_current_location[point_2_index]
+                    point_3 = nfp_current_location[point_3_index]
+                        
+                    ON_RIGHT =  D_function( point_1,point_2,point_3) <= 0 
+                    
+                    point_1_index = point_2_index
+                    point_1 = nfp_current_location[point_1_index]
+                    
+                    point_2_index = point_3_index
+                    point_2 = nfp_current_location[point_2_index]
+                    
+                    if point_3_index == len(nfp_current_location)-1:
+                        point_3_index = 0
+                        point_3 = nfp_current_location[point_3_index]
+                    
+                    if ON_RIGHT:
+                        constraints.append( D_function(point_1,point_2,{'x':x[j],'y':y[j]}) <= 0 )
+                
+                
+                #顺时针寻找，下一条边的终点在上一条右侧的，则加入这条边构成的约束
+                point_1_index = valid_point_index[valid_distance.index(max_distance)][0]
+                point_2_index = valid_point_index[valid_distance.index(max_distance)][1]
+                point_0_index = point_1_index - 1
+                
+                point_0 = nfp_current_location[point_0_index]
+                point_1 = nfp_current_location[point_1_index]
+                point_2 = nfp_current_location[point_2_index]
+                
+                if len(edge) is not 0:
+                    ON_RIGHT = True
+                while ON_RIGHT:
+                    
+                    ON_RIGHT = D_function( point_0,point_1,point_2) <= 0 
+                         
+                    point_0_index = point_0_index - 1
+                    point_1_index = point_1_index - 1
+                    point_2_index = point_2_index - 1
+                    
+                    point_0 = nfp_current_location[point_0_index]
+                    point_1 = nfp_current_location[point_1_index]
+                    point_2 = nfp_current_location[point_2_index]
+                    
+                    if ON_RIGHT:
+                        constraints.append( D_function(point_1,point_2,{'x':x[j],'y':y[j]}) <= 0 )
+                        
+            return constraints
+
+    def compact_layout(self,current_layout):
+        # -*- coding: utf-8 -*-
+        """
+        Created on Thu Sep  5 11:22:11 2019
+        
+        @author: chend
+        """
+        
+        '''
+        Param: current_layout = {'placed':[], 'placements':[]}   其中placed是经旋转的块料
+        output: placement: [{'x': ,'y':},{},....]    
+        '''
+        placed = copy.deepcopy(current_layout['placed'])
+        placements = copy.deepcopy(current_layout['placements'])
+        
+        if len(placed)<2 and len(placements)<2:
+            return placements
+        
+        
+        for i in range(0,len(placed)):
+            
+            placed[i]['current_location'] = [{'x':point['x']+placements[i]['x'],
+                                              'y':point['y']+placements[i]['y']} for point in placed[i]['points']]
+        
+            # Linear Programming 
+        
+        #variable
+        x = cp.Variable(shape=len(placed))#integer=True
+        y = cp.Variable(shape=len(placed))
+        z = cp.Variable(shape=1)
+        #obj
+        obj = cp.Minimize(z)
+        #constraints
+        constraints = []
+        constraints += [x[i]>=0 for i in range(len(placed))]
+        constraints += [y[i]>=0 for i in range(len(placed))]
+        constraints += [z>=0]
+        
+        # i是固定的块， j是待移动方块
+        for j in range(0,len(placed)):
+            
+            B = placed[j]
+            
+            # 每个块的移动不能超过一定距离
+            ref_point = B['points'][0]
+            distance_from_ref_point_to_part_right = B['x'] + B['width'] - ref_point['x']
+            distance_from_ref_point_to_part_left  = ref_point['x'] - B['x']
+            distance_from_ref_point_to_part_top   = B['y'] + B['width'] - ref_point['y']
+            distance_from_ref_point_to_part_bottom= ref_point['y'] - B['y']
+            # x-axis
+            current_x = ref_point['x'] + placements[j]['x']
+            constraints.append( x[j] - current_x <= MAX_MOVE_X )
+            constraints.append( x[j] - current_x >= -MAX_MOVE_X )
+            # y-axis 
+            current_y = ref_point['y'] + placements[j]['y']
+            constraints.append( y[j] - current_y <= MAX_MOVE_Y )   
+            constraints.append( y[j] - current_y >= -MAX_MOVE_Y )
+            
+            # 目标函数 z >= x_i + W_i, W_i是当前ref点到该块料最右侧距离
+            constraints.append( z >= x[j] + distance_from_ref_point_to_part_right )
+            
+            # 每个块料都需要在 bin_offset里面
+            bin_offset = get_polygon_bounds(self.bin_polygon['points_offset'])
+            constraints.append( x[j] - distance_from_ref_point_to_part_left >= bin_offset['x'] )
+            constraints.append( y[j] + distance_from_ref_point_to_part_top <= bin_offset['y'] + bin_offset['width'] )
+            constraints.append( y[j] - distance_from_ref_point_to_part_bottom >= bin_offset['y'] )
+            
+
+            for i in range(0,j):
+                
+                A = placed[i]
+                
+                constraints += self.find_constraints(A,B,i,j,x,y,placements)
+        
+        # compaction problem
+        prob = cp.Problem(obj,constraints)
+        prob.solve(solver = cp.CVXOPT)#,**{'cplex_filename':'a.lp'}
+        print('x:',x.value)
+        print('y:',y.value)
+        
+        if prob.status == 'optimal':
+            best_location = [{'x':x_loc,'y':y_loc}  for x_loc,y_loc in zip(x.value,y.value)]
+            shift_vector  = [{'x': best_location[k]['x'] - placed[k]['current_location'][0]['x'],
+                             'y': best_location[k]['y'] - placed[k]['current_location'][0]['y']}
+                              for k in range(0,len(placed))]
+            
+            placements = [{'x':placements[k]['x'] + shift_vector[k]['x'],
+                           'y':placements[k]['y'] + shift_vector[k]['y'],
+                           'p_id':placements[k]['p_id'],
+                           'rotation':placements[k]['rotation']} 
+                           for k in range(0,len(placements))]
+            print(u'找到最优解，已压缩一次\n')
+            
+        elif prob.status == 'infeasible':
+            print(u'压缩模型无解,无法压缩\n')
+        
+        else:
+            print(u'压缩模型出错\n')
+        
+        return placements
+
+    def place_paths(self):
+        start = time.clock()
+        # 排列图形
+        if self.bin_polygon is None:
+            return None
+
+        # rotate paths by given rotation
+        rotated = list()
+        for i in range(0, len(self.paths)):
+            
+            r = copy.deepcopy(self.paths[i][1])
+            
+            #旋转本体
+            rot_return = rotate_polygon(self.paths[i][1]['points'], self.paths[i][2])
+            r['points'] = rot_return['points']
+            r['x'] = rot_return['x']
+            r['y'] = rot_return['y']
+            r['width'] = rot_return['width']
+            r['height'] = rot_return['height']
+            
+            #旋转 offset 和 convex_hull
+            r['points_offset'] = rotate_polygon(self.paths[i][1]['points_offset'], self.paths[i][2])['points']
+            r['convex_hull'] = rotate_polygon(self.paths[i][1]['convex_hull'], self.paths[i][2])['points']
+            
+            #其他信息
+            r['rotation'] = self.paths[i][2]
+            r['source'] = self.paths[i][1]['p_id']
+            r['p_id'] = self.paths[i][0]
+            rotated.append(r)
+
+        paths = rotated
+        # 保存所有转移数据
+        all_placements = list()
+        orders = list()
+        rotations = list()
+        # 基因组的适应值
+        fitness = []
+        bin_area = abs(polygon_area(self.bin_polygon['points']))
+        min_width = None
+        while len(paths) > 0:
+            placed = list()
+            placements = list()
+            # add 1 for each new bin opened (lower fitness is better)
+            #fitness += 1
+            for i in range(0, len(paths)):
+                path = paths[i]
+                # 图形的坐标
+                key = json.dumps({
+                    'A': '-1',
+                    'B': path['p_id'],
+                    'inside': True,
+                    'A_rotation': 0,
+                    'B_rotation': path['rotation']
+                })
+
+                binNfp = self.nfpCache.get(key)
+                if binNfp is None or len(binNfp) == 0:
+                    continue
+
+                # part unplaceable, skip
+                error = False
+
+                
+                # ensure all necessary NFPs exist
+                for p in placed:
+                    key = json.dumps({
+                        'A': p['p_id'],
+                        'B': path['p_id'],
+                        'inside': False,
+                        'A_rotation': p['rotation'],
+                        'B_rotation': path['rotation']
+                    })
+                    nfp = self.nfpCache.get(key)
+                    if nfp is None:
+                        error = True
+                        break
+
+                # part unplaceable, skip
+                if error:
+                    continue
+                
+                #把第一个图形放到布料左下角
+                position = None
+                if len(placed) == 0:
+                    for j in range(0, len(binNfp)):
+                        for k in range(0, len(binNfp[j])):
+                            if position is None or (binNfp[j][k]['x']-path['points'][0]['x'] < position['x']):
+                                position = {
+                                    'x': binNfp[j][k]['x'] - path['points'][0]['x'],
+                                    'y': binNfp[j][k]['y'] - path['points'][0]['y'],
+                                    'p_id': path['p_id'],
+                                    'rotation': path['rotation']
+                                }
+
+                    placements.append(position)
+                    placed.append(path)
+                    continue
+
+                clipper_bin_nfp = list()
+                for j in range(0, len(binNfp)):
+                    clipper_bin_nfp.append([[p['x'], p['y']] for p in binNfp[j]])
+
+                # 找出 待放置方块 和 已放置方块 的 combined_NFP
+                clipper = pyclipper.Pyclipper()
+                for j in range(0, len(placed)):
+                    p = placed[j]
+                    key = json.dumps({
+                        'A': p['p_id'],
+                        'B': path['p_id'],
+                        'inside': False,
+                        'A_rotation': p['rotation'],
+                        'B_rotation': path['rotation']
+                    })
+                    nfp = self.nfpCache.get(key)
+
+                    if nfp is None:
+                        continue
+                    for k in range(0, len(nfp)):
+                        clone = [[np['x'] + placements[j]['x'], np['y'] + placements[j]['y']] for np in nfp[k]]
+                        clone = pyclipper.CleanPolygon(clone)
+                        if len(clone) > 2:
+                            clipper.AddPath(clone, pyclipper.PT_SUBJECT, True)
+                combine_nfp = clipper.Execute(pyclipper.CT_UNION, pyclipper.PFT_NONZERO, pyclipper.PFT_NONZERO)
+                if len(combine_nfp) == 0:
+                    continue
+                
+                # 以 combined_NFP 为 夹子(clip) 夹掉 待放方块和画布的内部NFP
+                clipper = pyclipper.Pyclipper()
+                clipper.AddPaths(combine_nfp, pyclipper.PT_CLIP, True)
+                try:
+                    clipper.AddPaths(clipper_bin_nfp, pyclipper.PT_SUBJECT, True)
+                except:
+                    print(u'图形坐标出错', clipper_bin_nfp)
+                # choose placement that results in the smallest bounding box
+                finalNfp = clipper.Execute(pyclipper.CT_DIFFERENCE, pyclipper.PFT_NONZERO, pyclipper.PFT_NONZERO)
+                if len(finalNfp) == 0:
+                    continue
+                
+                #这里clean nfp后会有很多重叠的地方，不能clean
+                #finalNfp = pyclipper.CleanPolygons(finalNfp)
+
+                for j in range(len(finalNfp)-1, -1, -1):
+                    if len(finalNfp[j]) < 3:
+                        finalNfp.pop(j)
+                if len(finalNfp) == 0:
+                    continue
+
+                finalNfp = [[{'x': p[0], 'y': p[1]}for p in polygon] for polygon in finalNfp]
+
+                min_width = None
+                min_area = None
+                min_x = None
+                
+                #all_points 是已摆好的方块的转移后摆好的坐标点集合
+                all_points = list() 
+                for m in range(0, len(placed)):
+                    for p in placed[m]['points']:
+                        all_points.append({
+                            'x': p['x']+placements[m]['x'],
+                            'y': p['y']+placements[m]['y']
+                        })
+                
+                # 生成nfp多边形
+                for nf in finalNfp:
+
+                    if abs(polygon_area(nf)) < 2:
+                        continue
+
+                    for p_nf in nf:
+                        
+                        all_points_deepcopy = copy.deepcopy(all_points)
+                        
+                        # path 坐标
+                        shift_vector = {
+                            'x': p_nf['x'] - path['points'][0]['x'],
+                            'y': p_nf['y'] - path['points'][0]['y'],
+                            'p_id': path['p_id'],
+                            'rotation': path['rotation'],
+                        }
+
+                        # 找新坐标后的最小矩形
+                        for m in range(0, len(path['points'])):
+                            all_points_deepcopy.append({
+                                'x': path['points'][m]['x'] + shift_vector['x'],
+                                'y': path['points'][m]['y'] + shift_vector['y']
+                            })
+                        
+                        all_points_deepcopy.append({'x':0,'y':0})
+                        rect_bounds = get_polygon_bounds(all_points_deepcopy)
+                        # weigh width more, to help compress in direction of gravity 
+                        # ???  width*2 不就是对width做更多的惩罚吗？这样图形会尽量往左下边放
+                        area = rect_bounds['height'] + rect_bounds['width']
+                        
+                        if (min_area is None or area < min_area or almost_equal(min_area, area)) and (
+                                        min_x is None or shift_vector['x'] <= min_x):
+                            min_area = area
+                            min_width = rect_bounds['width']
+                            position = shift_vector
+                            min_x = shift_vector['x']
+
+                if position:
+                    placed.append(path)
+                    placements.append(position)
+
+            for p in placed:
+                p_id = paths.index(p)
+                if p_id >= 0:
+                    paths.pop(p_id)
+            
+            if placements and len(placements) > 0:
+                all_placements.append(placements)
+
+            else:
+                # something went wrong
+                break
+            
+
+        placed_area = 0
+        all_points = []
+        for k,path in enumerate(placed):
+            placed_area += abs(polygon_area(path['points']))
+            for point in path['points']:
+                all_points.append({
+                        'x': point['x'] + placements[k]['x'],
+                        'y': point['y'] + placements[k]['y']
+                            })
+        all_points.append({'x':0,'y':0})
+        min_rect_area = get_polygon_bounds(all_points)['width']*BIN_HEIGHT
+        
+        #保存第一次heuristic排列得到的结果
+        all_placements.append(placements)
+        orders.append([ self.paths[i][0] for i in range(len(self.paths))])
+        rotations.append([self.rotations ] )
+        fitness.append(placed_area/min_rect_area)
+        
+        print('由Heuristic得到的最小包络矩阵利用率: %.4f'%fitness[0])
+        print('排列一次耗时:%.1f'%(time.clock()-start),'\n-----------\n' )
+        print('排列得到：',all_placements)
+        
+        #压缩
+        IMPROVED = True
+        while IMPROVED:
+            start = time.clock()
+            
+            placements = self.compact_layout({'placed':placed,'placements':placements}) 
+            
+            #new_fitness 
+            placed_area = 0
+            all_points = []
+            for k,path in enumerate(placed):
+                placed_area += abs(polygon_area(path['points']))
+                for point in path['points']:
+                    all_points.append({
+                            'x': point['x'] + placements[k]['x'],
+                            'y': point['y'] + placements[k]['y']
+                                })
+            all_points.append({'x':0,'y':0})
+            min_rect_area = get_polygon_bounds(all_points)['width']*BIN_HEIGHT
+            new_fitness = placed_area/min_rect_area
+        
+            if new_fitness > fitness[-1]:
+                print(u'已压缩现有排列方式,新排列方式的利用率为: %.4f' %new_fitness)
+                print('压缩一次用时: %.2f' %(time.clock()-start),'\n-------------\n')
+                fitness.append(new_fitness)
+                all_placements.append(placements)
+            else:
+                IMPROVED = False
+                print('压缩完成，已无法继续压缩')
+            
+        print('压缩总用时:%.2f' %(time.clock()-start))
+        print('全部placements:',all_placements)
+        
+        
+        return {'placements': all_placements, 'fitness': fitness, 'paths': paths, 'area': bin_area}
diff --git a/qhull_2d.py b/qhull_2d.py
new file mode 100644
index 0000000..8912760
--- /dev/null
+++ b/qhull_2d.py
@@ -0,0 +1,55 @@
+#!/usr/bin/python
+
+# Compute the convex hull of a set of 2D points
+# A Python implementation of the qhull algorithm
+# 
+# Tested with Python 2.6.5 on Ubuntu 10.04.4
+
+# Copyright (c) 2008 Dave (www.literateprograms.org)
+#
+# Permission is hereby granted, free of charge, to any person obtaining a copy 
+# of this software and associated documentation files (the "Software"), to deal 
+# in the Software without restriction, including without limitation the rights 
+# to use, copy, modify, merge, publish, distribute, sublicense, and/or sell 
+# copies of the Software, and to permit persons to whom the Software is 
+# furnished to do so, subject to the following conditions:
+#
+# The above copyright notice and this permission notice shall be included in 
+# all copies or substantial portions of the Software.
+#
+# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR 
+# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 
+# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE 
+# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER 
+# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING 
+# FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS 
+# IN THE SOFTWARE.
+
+from __future__ import division
+from numpy import *
+
+link = lambda a, b: concatenate((a, b[1:]))
+edge = lambda a, b: concatenate(([a], [b]))
+
+
+def qhull2D(sample):
+    def dome(sample, base):
+        h, t = base
+        dists = dot(sample - h, dot(((0, -1), (1, 0)), (t - h)))
+        outer = repeat(sample, dists > 0, 0)
+        if len(outer):
+            pivot = sample[argmax(dists)]
+            return link(dome(outer, edge(h, pivot)),
+                        dome(outer, edge(pivot, t)))
+        else:
+            return base
+
+    if type(sample) == type([]):
+        sample = array(sample)
+    if len(sample) > 2:
+        axis = sample[:, 0]
+        base = take(sample, [argmin(axis), argmax(axis)], 0)
+        return link(dome(sample, base), dome(sample, base[::-1])).tolist()
+    else:
+
+        return sample.tolist()
diff --git a/settings.py b/settings.py
new file mode 100644
index 0000000..3bb940a
--- /dev/null
+++ b/settings.py
@@ -0,0 +1,23 @@
+# -*- coding: utf-8 -*-
+
+SCALING_FACTOR = 10 #缩放画布和块料 到整数
+
+LOOP_TIME = 1
+POPULATION_SIZE = 1  # 基因组数
+MUTA_RATE = 20        # 变异概率
+ROTATIONS = 1   # 旋转选择， 1： 不能旋转
+# 单位都是MM(毫米)
+SPACING = 5*SCALING_FACTOR     # 图形间隔空间
+CONTAINERSPACING = -0*SCALING_FACTOR #容器预留边距,负数表示向内
+CURVETOLERANCE = 0.15*SCALING_FACTOR # polygon点之间判定为两个点的最小距离
+CONVEX_WEIGHT  = 0.2   # 在寻找初始序列时，convexity的权重
+AREA_WEIGHT    = 0.8   # 在寻找初始序列时，area的权重
+
+MAX_MOVE_X = 2 * SCALING_FACTOR #压缩时，X方向最大位移
+MAX_MOVE_Y = 2 * SCALING_FACTOR #压缩时，Y方向最大位移
+# 不同面料尺寸
+BIN_HEIGHT = 1600 * SCALING_FACTOR
+BIN_WIDTH = 20000 * SCALING_FACTOR
+BIN_NORMAL = [[0, 0], [0, BIN_HEIGHT], [BIN_WIDTH, BIN_HEIGHT], [BIN_WIDTH, 0]]        # 一般布是无限长
+BIN_CUT_BIG = [[0, 0], [0, 1570], [2500, 1570], [2500, 0]]       # 切割机尺寸 1
+BIN_CUT_SMALL = [[0, 0], [0, 1200], [1500, 1200], [1500, 0]]     # # 切割机尺寸 2
\ No newline at end of file
diff --git a/test_nfp.py b/test_nfp.py
new file mode 100644
index 0000000..b18822d
--- /dev/null
+++ b/test_nfp.py
@@ -0,0 +1,46 @@
+# -*- coding: utf-8 -*-
+from nfp_function import Nester, content_loop_rate
+from settings import BIN_WIDTH, BIN_NORMAL, BIN_CUT_BIG, LOOP_TIME
+
+import ast
+import pandas as pd
+lingjian = pd.read_csv('.\L0002_lingjian.csv')
+
+if __name__ == '__main__':
+    n = Nester()
+    s = [ast.literal_eval(contour) for contour in lingjian['外轮廓']]
+
+    n.add_objects(
+               #[ [ [0,0],[0,20],[20,0]    ],
+               #  [ [20,0],[20,10],[30,10],[30,0] ],
+               #  [[10,0],[20,0],[20,10],[10,10]]
+               #        ]
+               
+               
+                #[
+                #[[10,0],[20,0],[20,10],[10,10]],
+                #[[10,20],[20,20],[15,30]],
+                #[[30,10],[50,10],[35,15],[40,30],[30,30]]
+                 #]
+        s[:50]#,lingjian['零件号'].values
+            )
+
+    if n.shapes_max_length > BIN_WIDTH:
+        BIN_NORMAL[2][0] = n.shapes_max_length
+        BIN_NORMAL[3][0] = n.shapes_max_length
+
+    # 选择面布
+    n.add_container(BIN_NORMAL)
+    # 运行计算 
+    n.run() #进行一次未生成子代的计算
+
+    # 设计退出条件
+    res_list = list()
+    best = n.best
+    # 放置在一个容器里面
+    # set_target_loop(best, n)    # T6
+
+    # 循环特定次数
+    content_loop_rate(best, n, loop_time=LOOP_TIME-1)   # T7 , T4
+
+