Question

我正在从事一个涉及将多边形转换为梯形的项目。我正在使用功能为here的seidel.py版本。该软件从本质上讲是获取多边形的坐标，并使用一种算法对它执行梯形分解，该算法可以找到垂直线的交点，这些垂直线从构成原始多边形的顶点开始。

您可以在这里找到我的版本：Poly2Trap 适用于Python 3.6.7。

我要实现的目标是：

输入多边形
使用seidel.py分解多边形
提取分解后的多边形的新添加的顶点
通过将三角剖分过程中创建的新顶点添加到原始顶点列表中来创建新顶点列表
使用新的顶点列表绘制多边形

发生了什么事

分解方法起作用并输出梯形列表。这些梯形分别具有三个或四个顶点，其中一些顶点已在原始多边形中定义。
获得所有梯形的列表后，我将所有顶点组合成一个顶点列表（所有梯形和原始多边形），并删除重复项。
这时，我剩下一组要重新描绘为多边形的不同顶点。
要实现这一点，我使用angular sort方法，该方法采用多边形的质心，并通过计算从顶点到质心的角度对顶点进行排序。
当我进行绘图和比较时，所得多边形不符合预期。

我需要您的帮助： 如果您知道任何其他方法可以对复杂多边形的顶点进行排序，因为我认为这是我所缺少的。

这是我的结果：

其他信息：

我想在将来使用顶点范围在几百个范围内的复杂多边形，这就是为什么我避免使用凸包的原因。

这里，点是具有x和y坐标的元组。并且多边形的所有顶点都存储在元组列表中。

poly_coords = [(x,y),]

最小，完整和可验证的示例： poly2trap.py

import numpy as np
import matplotlib.pyplot as plt

original_poly_coords = [(235.04275999999999, 739.07534999999996),
(218.13066000000001, 719.73902999999996),
(218.15215000000001, 709.96821),
(218.17362, 700.19740000000002),
(243.15215000000001, 685.27858000000003),
(268.13065, 670.35974999999996),
(268.13065, 660.81429000000003),
(268.13065, 651.26882999999998),
(314.55921999999998, 651.26882999999998),
(360.98779000000002, 651.26882999999998),
(360.98683999999997, 666.44740000000002),
(360.98046561000007, 669.27438118000009),
(360.96234088000011,672.68539864000013),
(360.93345946999995, 676.58895225999993),
(360.89481504000003, 680.89354191999996),
(360.84740125000002, 685.50766749999991),
(360.79221175999999, 690.33982888000003),
(360.73024022999999, 695.29852593999999),
(360.66248032000004, 700.29225856000005),
(360.58992569000003, 705.22952662000012),
(360.51357000000002, 710.01882999999998),
(360.04131999999998, 738.41168000000005),
(310.51454999999999, 738.41168000000005),
(260.98779999999999, 738.41168000000005),
(260.98779999999999, 748.41168000000005),
(260.98779999999999, 758.41168000000005),
(256.47133000000002, 758.41168000000005),
(251.95484999999999, 758.41168000000005),
(235.04275999999999, 739.07534999999996)
]

#After performing triangulation
coords_after_triangulation = [(257.22974168, 758.41168), (361.63905883, 651.2688300000154), 
(360.98046561000007, 669.2743811800001), (361.22358883000004, 651.26883), (361.29515521662, 651.26883),
(243.15215, 685.27858), (243.83742858, 685.27858), (361.36277257856005, 651.26883), 
(361.42553875594,651.26883), (361.48255158887997, 651.26883), (361.53290891750004, 651.26883),
(261.72621168, 738.41168), (251.95485, 758.41168), (261.72621168, 738.4116799999902),
(361.53290891750004, 685.5076675000018), (361.42553875594, 695.2985259399975),
(361.42553875594, 695.2985259400011), (315.21048883, 651.26883), (360.98684, 666.4474),
(360.84740125, 685.5076674999999), (361.57570858192, 680.8935419200061),
(360.9623408800001, 672.6853986400001), (361.57570858192, 680.8935419199988), 
(361.48255158887997, 690.3398288800017), (361.64973999118007, 662.6631410694681), 
(311.25296168, 738.41168), (268.80100975, 738.41168), (315.21048883, 738.41168), 
(218.13066, 719.73903), (218.86211821, 719.7524137325041), (218.8738174, 719.7657746356965),
(268.13065, 660.81429), (268.79146429, 660.8142900000094), (218.85039903, 719.73903), 
(218.85039903, 719.739029999997), (360.98779, 651.26883), (360.77973168, 651.26883), 
(218.17362, 700.1974), (218.8738174, 700.1974000000046), (218.8738174, 700.1974), 
(314.55922, 651.26883), (243.83742858, 739.07535), (361.63905883, 671.7505493924255), 
(360.93345946999995, 676.5889522599999), (360.04132, 738.41168), 
(360.73024023, 695.29852594), (360.77973168, 738.4116800000011), 
(360.77973168, 738.41168), (360.51357, 710.01883), (261.72621168, 674.5878176386889), 
(361.65328739999995, 666.4474000000046), (361.36277257856005, 700.292258559999), 
(218.15215, 709.96821), (218.86211821, 709.9682099999918), (218.86211821, 709.9682100000209), 
(268.13065, 670.35975), (268.80100975, 670.3597500000615), (268.80100975, 670.35975), 
(361.22358883000004, 710.0188300000009), (361.29515521662, 705.2295266200017), 
(361.57570858192, 651.26883), (361.6100484222599, 651.26883), 
(361.6350262786401, 651.26883), (360.89481504, 680.89354192), 
(260.9878, 748.41168), (361.63905883, 651.26883), (311.25296168, 651.26883), 
(252.71326168, 679.9741709800953), (361.6350262786401, 672.6853986399947), 
(310.51455, 738.41168), (235.04276, 739.07535), (235.78183535, 739.07535), 
(243.83742858, 748.2751425044893), (235.78183535, 690.0927851454428), (257.22974168, 677.2750150833695), 
(360.79221176, 690.33982888), (260.9878, 758.41168), (360.58992569000003, 705.2295266200001), 
(261.73621168, 748.4116799999902), (252.71326168, 758.41168), (268.13065, 651.26883), 
(360.66248032000004, 700.29225856), (261.74621168, 758.4116799999902), (261.74621168, 758.41168), 
(268.79146429, 651.26883), (268.80100975, 651.26883), (268.78191883, 651.2688300000154), 
(268.78191883, 651.26883), (361.6100484222599, 676.5889522599973), (261.73621168, 758.41168), 
(261.72621168, 758.41168), (256.47133, 758.41168), (361.64973999118007, 669.2743811799883), 
(361.64973999118007, 669.2743811800028), (260.9878, 738.41168),(257.22974168, 758.41168)]


def ccw_sort(p):
    """Sort given polygon points in CCW order"""
    p = np.array(p)
    mean = np.mean(p,axis=0)
    d = p-mean
    s = np.arctan2(d[:,0], d[:,1])
    return p[np.argsort(s),:]

#sort poly after triangulation
sorted_poly_coords = ccw_sort(coords_after_triangulation)

#plot
#How it should look like:
fig,ax = plt.subplots()    
xa = [i[0] for i in original_poly_coords[:]]
ya = [i[1] for i in original_poly_coords[:]]
ax.plot(xa,ya, color = 'b')

#How it looks like:
fig,bx = plt.subplots()
xb = [i[0] for i in sorted_poly_coords[:]]
yb = [i[1] for i in sorted_poly_coords[:]]
bx.plot(xb,yb, color='r')

plt.show()

感谢您的帮助。

顺时针排序多边形顶点

0 个答案: