如何生成随机的两个同心球合成数据？

Question

如何在MATLAB中用radius1=40和radius2 =100生成随机的两个同心球体合成数据，并将该数据保存为*.mat格式，只有一个变量。(1000*3 double)？另外，如何用 2 种颜色（红色和蓝色）以 3D 形式绘制此数据？

我的代码：

rng(0,'twister');
rvals = 2*rand(1000,1)-1;
elevation = asin(rvals);

azimuth = 2*pi*rand(1000,1);

radii = 3*(rand(1000,1).^(1/3));

[x,y,z] = sph2cart(azimuth,elevation,radii);
data=[x,y,z];
figure
plot3(x,y,z,'.');
axis equal

预期输出：

Answer 1

简单，在球坐标中采样

phi = 2 * Pi * U(0,1)
cos(theta) = 2 * U(0,1) - 1
r          = r_min * U(0,1)^(1/3) (r_max - r_min)

sin(theta) = sqrt(1-cos^2(theta))
x = r * sin(theta) * cos(phi)
y = r * sin(theta) * sin(phi)
z = r * cos(theta)

Answer 2

如果你想要一个固定的半径，那么给它们分配一个常量值（而不是随机值）并为方向角保留随机数（azimuth/elevation或theta/phi 取决于符号）。

此代码：

rng(0,'twister');
nptSet = 500 ; r1 = 40 ; r2 = 100 ;                 %// your constraints

%// first data set (r1=40)
r1    = zeros(nptSet,1)+r1  ;           %// assign radius (fixed)
azi1  = rand( size(r1) ) * 2*pi ;       %// random azimuth   [  0     2pi]
elev1 = (rand(size(r1)) .* pi)-pi/2 ;   %// random elevation [-pi/2  pi/2]

%// second data set (r2=100)
r2    = zeros(nptSet,1)+r2  ;           %// assign radius (fixed)
azi2  = rand( size(r2) ) * 2*pi ;       %// random azimuth   [  0     2pi]
elev2 = (rand(size(r2)) .* pi)-pi/2 ;   %// random elevation [-pi/2  pi/2]

%// convert to cartesian
[x1,y1,z1] = sph2cart(azi1,elev1,r1);
[x2,y2,z2] = sph2cart(azi2,elev2,r2);

%// display and refine
figure ; hold on
plot3(x1,y1,z1,'or','MarkerSize',2);
plot3(x2,y2,z2,'+b');
xlabel('x') ; ylabel('y') ; zlabel('z')
axis equal ; grid off ; view(50,30)

会给你那个数字：

如何生成随机的两个同心球合成数据？

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