MATLAB: Generate random polar angles

MATLABpolar anglepolar angle distributionuniform distributionunit sphere

I want to generate random polar angles given a uniform distribution on the unit sphere. In other words, I want to generate random numbers from the probability density function p(theta) = sin(theta)/2 in the interval [0,pi]. How do I do this?

Best Answer

The requested distribution of theta is generated below. Consequently the following code will places yellow dots on the unit sphere surface in a statistically uniform manner.

n = 8192;
theta = acos(1-2*rand(n,1)); % <-- The requested distribution
phi = 2*pi*rand(n,1);
x = sin(theta).*cos(phi);
y = sin(theta).*sin(phi);
z = cos(theta);
plot(x,y,z,'y.')

(Corrected)

Related Solutions

MATLAB: How to define a function that evaluates in input

function y=T(theta_Degree)
theta=theta_Degree*pi/180;
y=[cos(theta)^2 sin(theta)^2 2*cos(theta)*sin(theta);sin(theta)^2 cos(theta)^2 -2*cos(theta)*sin(theta);-cos(theta)*sin(theta) cos(theta)*sin(theta) cos(theta)^2-sin(theta)^2];
end

Then type in command line

T(40)

and see the results.

MATLAB: Solving non linear equation using fsolve

You are not passing theta_n and other parameters to root2d(). One fix is to make root2d a Nested Function. Also, you must choose a different initial point. phi0 = [10,10] worked for me.

function solve_it()
    beta_a = 10;
    alpha_n = 10 ;
    eta= 18;
    i = 18;
    theta_i = 10;
    theta_n = 10 ;
    
    fun = @root2d;
    phi0 = [10,10];
    phi = fsolve(fun,phi0);
    phi_n = phi(1),
    phi_i = phi(2),
    function F = root2d(phi)
    F = zeros(2,1);
    F(1) = (pi*sin((pi*(phi(1) + theta_n))/180)*cos((pi*phi(2))/180)*(cos((pi*theta_n)/180) + tan((pi*i)/180)*tan((pi*theta_i)/180)))/(180*sin((pi*phi(1))/180)*(cos((pi*(phi(1) + theta_n))/180)*cos((phi(2)*pi)/180) + sin((phi(2)*pi)/180)*tan((theta_i*pi)/180))^2) - (pi*cos((pi*phi(1))/180)*(cos((pi*theta_n)/180) + tan((pi*i)/180)*tan((pi*theta_i)/180)))/(180*sin((phi(1)*pi)/180)^2*(cos((pi*(phi(1) + theta_n))/180)*cos((pi*phi(2))/180) + sin((pi*phi(2))/180)*tan((pi*theta_i)/180)));
    F(2) = ((cos((pi*theta_n)/180) + tan((pi*i)/180)*tan((pi*theta_i)/180))*((pi*cos((pi*(phi(1) + theta_n))/180)*sin((pi*phi(2))/180))/180 - (pi*cos((pi*phi(2))/180)*tan((pi*theta_i)/180))/180))/(sin((pi*phi(1))/180)*(cos((pi*(phi(1) + theta_n))/180)*cos((phi(2)*pi)/180) + sin((phi(2)*pi)/180)*tan((theta_i*pi)/180))^2);
    end
end

Best Answer

Related Solutions

MATLAB: How to define a function that evaluates in input

MATLAB: Solving non linear equation using fsolve

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