检查点是否在圆S内

Question

我有一长串具有已知坐标的H-points。我还有TP-points的列表。我想知道H-points是否落在具有特定半径的任何（！）TP-point范围内（例如r=5）。

dfPoints = pd.DataFrame({'H-points' : ['a','b','c','d','e'],
               'Xh' :[10, 35, 52, 78, 9],
               'Yh' : [15,5,11,20,10]})

dfTrafaPostaje = pd.DataFrame({'TP-points' : ['a','b','c','d','e'],
               'Xt' :[15,25,35],
               'Yt' : [15,25,35],
               'M' : [5,2,3]})

def inside_circle(x, y, a, b, r):
    return (x - a)*(x - a) + (y - b)*(y - b) < r*r

我已经开始，但是..仅检查一个TP点会更容易。但是如果我有他们中的1500个和30.000个H点，那么我需要更通用的解决方案。谁能帮忙？

Answer 1

您可以使用scipy中的cdist计算成对距离，然后使用True创建一个距离小于半径的蒙版，最后进行过滤：

import pandas as pd
from scipy.spatial.distance import cdist

dfPoints = pd.DataFrame({'H-points': ['a', 'b', 'c', 'd', 'e'],
                         'Xh': [10, 35, 52, 78, 9],
                         'Yh': [15, 5, 11, 20, 10]})

dfTrafaPostaje = pd.DataFrame({'TP-points': ['a', 'b', 'c'],
                               'Xt': [15, 25, 35],
                               'Yt': [15, 25, 35]})

radius = 5
distances = cdist(dfPoints[['Xh', 'Yh']].values, dfTrafaPostaje[['Xt', 'Yt']].values, 'sqeuclidean')
mask = (distances <= radius*radius).sum(axis=1) > 0 # create mask

print(dfPoints[mask])

输出

  H-points  Xh  Yh
0        a  10  15

Answer 2

另一种选择是使用distance_matrix中的scipy.spatial：

dist_mat = distance_matrix(dfPoints [['Xh','Yh']], dfTrafaPostaje [['Xt','Yt']])
dfPoints [np.min(dist_mat,axis=1)<5]

1500 dfPoints和30000 dfTrafaPostje花费大约2s。

---

Update：获取得分最高的参考点的索引：

dist_mat = distance_matrix(dfPoints [['Xh','Yh']], dfTrafaPostaje [['Xt','Yt']])

# get the M scores of those within range
M_mat = pd.DataFrame(np.where(dist_mat <= 5, dfTrafaPosaje['M'].values[None, :], np.nan),
                     index=dfPoints['H-points'] ,
                     columns=dfTrafaPostaje['TP-points'])

# get the points with largest M values
# mask with np.nan for those outside range    
dfPoints['M'] = np.where(M_mat.notnull().any(1), M_mat.idxmax(1), np.nan)

对于随附的样本数据：

  H-points  Xh  Yh   TP
0        a  10  15    a
1        b  35   5  NaN
2        c  52  11  NaN
3        d  78  20  NaN
4        e   9  10  NaN