Recently I needed an algorithm to generate equidistant points inside the unit disk with some of them placed on the boundary (circle). To my surprise, quick search didn’t reveal any simple method for this. Below is obvious solution & code, hopefully it will save some time for others.
MATLAB code:
function [x, y, Nb, Np] = eqdisk(Nr) %EQDISK Generates equidistant points inside the unit disk. % Nr [in] - number of radial circles % x,y [out] - coordinates of generated points % Np [out] - total number of generated points % Nb [out] - points on boundary (on r = 1 circle) dR = 1/Nr; x(1) = 0; y(1) = 0; k = 1; for r = dR:dR:1 n = round(pi/asin(1/(2*k))); theta = linspace(0, 2*pi, n+1)'; x = [x; r.*cos(theta(1:n))]; y = [y; r.*sin(theta(1:n))]; k = k+1; end; Nb = n; Np = size(x,1); end Algorithm is based on
Eigen