Question

数学实验mathematica应用构造单位球面上依曲面面积服从均匀分布的随机点

Answer 1

=.;

dot =.;

dot[r_] := Module[{rand,rz,u,rxy},

rand = 2 r*Random[] - r;

rz = rand;

rand = 2 Pi*Random[];

u = rand;

rxy = Sqrt[r^2 - rz^2];

{rxy*Cos[u],rxy*Sin[u],rz}

]

Graphics3D[Point[Table[dot[1],{r,1,5000}]],Boxed -> False]

(*复制即可 *)