根据点的密度对3D散点图的颜色点进行编码 [英] Color code points of 3D scatter plot according to density of points
问题描述
我在xyz球体中有一个点的3D散点图.我想知道是否有一种方法可以根据数据的密度对散点图进行颜色映射/色相绘制.基本上，散点图中具有最密集聚类数据点的部分将为暗红色，半密集聚类数据点将为中红色，而稀疏聚类数据点将为浅红色.
I have a 3D scatter plot of points in the xyz-sphere. I was wondering if there is a way to colormap/hue the scatter plot based on the density of the data. Basically, the parts of the scatter plot with the most densely clustered data points would be dark red, semi densely clustered data points would be medium red, and sparsely clustered data points would be light red.
这是我一直在想的方式，但是(希望)可能会有一个更简单的函数或命令来做到这一点.
This is the way that I was thinking of, but (hopefully) there might be a simpler function or command to do this.
设置散点中的数据点必须被包围的阈值:
Set a threshold that a data point in the scatter has to be surrounded by:
[> =半径1的球体内的10个其他点将被染成深红色，
[ >= 10 other points within a sphere of radius 1 to be colored dark red,
[半径1的球体内的5-9个其他点将变为红色，而
[ 5-9 other points within a sphere of radius 1 to be colored medium red, and
[半径为1的球体中的0-4将变为浅红色.
[ 0-4 within a sphere of radius 1 to be colored light red.
当然，我希望有一种更简单的方法可以在颜色图中涉及3种以上的颜色，因此，如果有人对如何编码有任何想法，我将非常感谢您的帮助！非常感谢.
Of course, I'm hoping there is a simpler way to do this that involves more than 3 colors in the color map, so if anyone has any ideas how to code this, I'd appreciate the help! Thank you so much.
这是我的数组的一个片段:
Here's a snippet of my array:
184 115 3915
185 115 3916
185 115 1205
186 115 4094
187 115 2237
192 115 1519
193 115 1327
201 115 1170
240 115 2946
241 115 1332
54 116 1244
58 116 3650
59 116 3984
60 116 1631
61 116 1198
61 116 1194
62 116 1189
65 116 1185
186 116 3669
188 116 3986
189 116 2027
197 116 1200
201 116 1254
226 116 3752
227 116 1457
242 116 1405
54 117 1191
54 117 1305
56 117 1177
58 117 1169
61 117 1367
62 117 1428
62 117 1434
62 117 1435
63 117 1422
198 117 1197
229 117 1312
230 117 1179
243 117 1272
55 118 1236
56 118 1166
61 118 1191
65 118 1755
57 119 1213
57 119 1176
58 119 1253
62 119 1365
62 119 1331
63 119 1457
63 119 1251
66 119 1842
66 119 1468
59 120 1489
59 120 1387
60 120 1218
60 120 1224
61 120 1214
61 120 1440
62 120 1198
64 120 1240
205 120 3601
205 120 1168
206 120 3727
207 120 4089
208 120 2128
208 120 1160
56 121 1293
57 121 1183
59 121 1371
59 121 1347
61 121 1314
64 121 1346
207 121 3562
208 121 3845
209 121 3534
210 121 1201
210 121 1405
83 122 1794
206 122 1259
207 122 1161
83 123 3550
推荐答案
在我的方法中，我使用阈值因子T来确定在计算每个单个点的距离时要考虑的其他点数. T = 1表示每个点到所有其他点的平均距离，T = 0.01表示每个点到其他点的最近1％的平均距离.
In my approach I'm using a threshold factor T to determine how many other points are considered in the calculation of distances for each individual point. T = 1 means for every point the average distance to all other points is calculated, T = 0.01 means for every point the average distance to the closest 1% of the the other points is calculated.
figure
%// example data
[X,Y,Z] = sphere(15);
x = [0.1*X(:); 0.4*X(:); 0.7*X(:)];
y = [0.2*Y(:); 0.5*Y(:); 0.8*Y(:)];
z = [0.3*Z(:); 0.6*Z(:); 0.9*Z(:)];
D = [x(:), y(:), z(:)];
N = numel(x);
%// calculation of color vector
[n,m] = ndgrid(1:N,1:N);
%// euclidian distance of each point to every other point
X = arrayfun(@(a,b) sum( (D(a,:) - D(b,:)).^2 ), n, m);
%% subplot 1
%// threshold factor
T = 0.01;
%// sort distances of points
Y = sort(X,2);
%// calculate average distance of the closest T% of all points
Z = mean(Y(:,2:ceil(N*T)),2);
%// plot
subplot(121)
scatter3(x,y,z,20,Z,'filled');
title('T = 0.01')
colormap
colorbar
%% subplot 2
%// threshold factor
T = 1;
Y = sort(X,2);
Z = mean(Y(:,2:ceil(N*T)),2);
%// plot
subplot(122)
scatter3(x,y,z,20,Z,'filled');
title('T = 1')
colormap
colorbar
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