MATLAB: How to generate uniform random points with in a circle.

random number generationwireless communication

I used "rand" function to generate uniform random points within the circle, but points generated by this code are not uniformly distributed. The code used by me is given below.So, is there any way to do so?? If any body know the answer please help me. Any suggestions will be appreciated. Thanks in advance.

Code:

% Create a random set of coordinates in a circle.
% First define parameters that define the number of points and the circle.
n = 400;
R = 20;
x0 = 0; % Center of the circle in the x direction.
y0 = 0; % Center of the circle in the y direction.
% Now create the set of points.
t = 2*pi*rand(n,1);
r = R*sqrt(rand(n,1));
x = x0 + r.*cos(t);
y = y0 + r.*sin(t);
% Now display our random set of points in a figure.
plot(x,y, 'o', 'MarkerSize', 5)
axis square;
grid on;
% Enlarge figure to full screen.
%set(gcf, 'units','normalized','outerposition',[0 0 1 1]);
fontSize = 30;
xlabel('X', 'FontSize', fontSize);
ylabel('Y', 'FontSize', fontSize);
title('Random Locations Within a Circle', 'FontSize', fontSize);

Best Answer

http://mathworld.wolfram.com/DiskPointPicking.html

Best wishes

Torsten.

Related Solutions

MATLAB: Creating random points in a circle

Let the circle be of radius R and center at (x0,y0). Let n be the desired number of points within.

 t = 2*pi*rand(n,1);
 r = R*sqrt(rand(n,1));
 x = x0 + r.*cos(t);
 y = y0 + r.*sin(t);
 plot(x,y)

MATLAB: Uniform point interpolation along a line described by non-uniform distributed points

See this demo:

% Code to plot data, plus points interpolated in between the data.
clc;    % Clear the command window.
clearvars;
close all;  % Close all figures (except those of imtool.)
workspace;  % Make sure the workspace panel is showing.
format long g;
format compact;
fontSize = 22;
% Make up sample data.
numOriginalPoints = 20;
xOriginal = sort(100 * rand(1, numOriginalPoints), 'ascend');
yOriginal = 30 * rand(1, numOriginalPoints) - 10;
% Plot them
subplot(3, 1, 1);
plot(xOriginal, yOriginal, 'ro-', 'LineWidth', 2);
grid on;
xlabel('X', 'FontSize', fontSize);
ylabel('Y', 'FontSize', fontSize);
title('Training Points', 'FontSize', fontSize);
% Interpolate points in between, linearly from the min to the max.
numNewPoints = 100;
xInterpolated = linspace(min(xOriginal), max(xOriginal), numNewPoints);
yInterpolated = interp1(xOriginal, yOriginal, xInterpolated);
% Plot interpolated points.

subplot(3, 1, 2);
plot(xInterpolated, yInterpolated, 'bo-', 'LineWidth', 2);
% Plot training points over them so we can see where they are in relation to the new points.

hold on;
plot(xOriginal, yOriginal, 'ro', 'LineWidth', 2);
grid on;
title('Interpolated Points without Including Training Points', 'FontSize', fontSize);
xlabel('X', 'FontSize', fontSize);
ylabel('Y', 'FontSize', fontSize);
legend('Interpolated', 'Training');
% Enlarge figure to full screen.

set(gcf, 'Units', 'Normalized', 'OuterPosition', [0, 0.04, 1, 0.96]);
% Note, if you want the original points included in the set of new, interpolated points, 
% Add them to xInterpolated list.
subplot(3, 1, 3);
xInterpolated = sort([xInterpolated, xOriginal], 'ascend');
yInterpolated = interp1(xOriginal, yOriginal, xInterpolated);
% Plot interpolated points.
plot(xInterpolated, yInterpolated, 'bo-', 'LineWidth', 2);
% Plot training points over them so we can see where they are in relation to the new points.
hold on;
plot(xOriginal, yOriginal, 'ro', 'LineWidth', 2);
grid on;
xlabel('X', 'FontSize', fontSize);
ylabel('Y', 'FontSize', fontSize);
title('Interpolated Points Including Training Points', 'FontSize', fontSize);
legend('Interpolated', 'Training');
% Enlarge figure to full screen.
set(gcf, 'Units', 'Normalized', 'OuterPosition', [0, 0.04, 1, 0.96]);

Related Question