Delaunay地形图

Question

我有一组(x，y)坐标，我想使用这些(x，y)坐标创建一个图形(igraph)。首先，我从这里创建Delaunay三角形，然后使用"delaunay.simplices“查找边缘，以便在in中使用它。问题是，我的数据点几乎是在一个完整的圆圈上(这是视网膜细胞的位置)。问题是，当我绘制Delaunay图时，它会将彼此相距较远的点连接起来(请参阅附图)。我如何创建一个Delaunay三角形的方式，只是点是相互联系的？换句话说，我需要去除整个圆圈(视网膜)的边缘。数据点样本：

[[ -337.97697446,  7540.58307945],
       [-1815.6445473 ,  7056.03016277],
       [ -443.129876  ,   742.95651638],
       [  560.91116647,  8221.13103087],
       [-2043.59680333,  6927.41838391],
       [-3176.31452551,  3346.89857915],
       [ -784.1490326 ,   760.8154378 ],
       [ 5170.40467349,  8136.41340492],
       [ -742.23061811,   799.05871867],
       [ 1462.82113245,   978.95894247],
       [-1874.57436117,  6983.1503229 ],
       [-2310.81830323,  1530.35866448],
       [-2910.71747603,  5246.51145717],
       [ -888.21996994,   798.45066095],
       [ 4498.63094122,  8260.69637833],
       [-2899.33052683,  2130.60899211],
       [-1700.36710286,  7173.3962959 ],
       [-1610.2063535 ,  7214.58267473],
       [ 1378.99115594,  8329.96965215],
       [-3089.39467232,  2513.75733145],
       [-3194.07782921,  3820.99309382],
       [-3209.92285253,  2896.37506385],
       [ 7197.81822286,  5896.18071003],
       [ -450.75080896,  7525.26743227],
       [ -113.62034104,   627.17361551],
       [-3263.17851197,  3425.66085986],
       [ 3692.02214764,  8503.70959198],
       [ 2074.11632568,  8349.8755875 ],
       [ 6015.49872449,  3635.69969512],
       [ 7003.71354705,  6648.72238021],
       [ 6912.25041128,  4732.48378599],
       [ 3171.75729506,  8364.60820082],
       [-2218.36898372,  1409.32375715],
       [ 6695.93283727,  7010.2533557 ],
       [ 2189.84584047,  8368.56645389],
       [ 3406.81534596,  8432.77932065],
       [-2569.97377757,  6210.20316803],
       [ 4238.33917379,  8285.06998187],
       [ 2260.16101844,  8429.82132311],
       [ 3519.53740115,  8291.11207523],
       [ 2682.00418224,  8356.9073382 ],
       [ 3583.38759555,  8341.96511715],
       [-2480.84539734,  6324.03943137],
       [-1608.29692142,  7137.9205374 ],
       [ 4772.58940226,  8312.16759039],
       [  912.35520444,  8313.72411438],
       [ 6951.82432889,  6805.60977411],
       [ 4631.51637666,  8359.21654299],
       [-2960.74382434,  5388.2309139 ],
       [-1554.58457283,  1103.3527351 ]]

​

Answer 1

计算距离矩阵，然后过滤出彼此间距离最短的点；对于大型数据集(数百个点)可能需要一段时间。

Answer 2

我是格拉维斯的作者，这是一个开放源代码的包，用于在Python中进行交互式图形可视化。它可以从网络分析库中识别图形对象，如NetworkX、igraph、图形工具等.

这里有一个解决方案，它使用scipy计算一个Delaunay三角剖分，NetworkX创建一个图形，并将其可视化。它使用三角剖分的凸包连接最外面的点(红色边)，然后简单地连接内部点(黑色边)，但只有那些在选定的阈值范围内，你可以根据需要变化。我已经使用了你在问题中提供的观点。

import math

import gravis as gv
import networkx as nx
import scipy.spatial


triangulation = scipy.spatial.Delaunay(points)

g = nx.Graph()

for i, (x, y) in enumerate(points):
    g.add_node(i, x=x/10, y=y/10)

for i, j in triangulation.convex_hull:
    g.add_edge(i, j, color='red', size=2)

threshold = 2000
for i, j, k in triangulation.simplices:
    for a, b in [(i, j), (j, k), (k, i)]:
        p1 = points[a]
        p2 = points[b]
        distance = math.dist(p1, p2)
        if distance < threshold:
            g.add_edge(a, b)
    
gv.d3(g)

结果是木星笔记本电脑：图形可视化