QPFit/star.m
3bfb25b5e70amaster

star.m
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			function [R,seg] = star(p, q, N, vel, doPlot)
			%
			% Generate a trajectory along the star polygon given by (p, q)
			%

			if nargin < 5
			doPlot = false;
			end

			th = linspace(0,2*pi,p+1);
			pts = [cos(th);sin(th)]; pts(:,end) = [];

			if doPlot
			clf;
			plot(pts(1,:), pts(2,:), 'o')
			axis square
			hold on
			end

			k = 1;
			clear seg
			for i = 1:100
			kp = mod(k+q, p) + 1;
			seg(i).line = [pts(:,k) pts(:,kp)];
			seg(i).indx = [k kp];

			if doPlot, plot([pts(1,k);pts(1,kp)],[pts(2,k);pts(2,kp)],'-'); end

			k = kp;
			if k == 1, break; end
			end

			numSegs = length(seg);
			for i = 1:numSegs
			seg(i).th = [(i-1) i];
			seg(i).dth = diff(seg(i).th);
			end

			R = zeros(2,N);

			th = 0;
			for i = 1:N
			th = mod(th + vel, numSegs);
			if th == 0
			pos = 1;
			else
			pos = mod(ceil(th)-1, p)+1;
			end

			percentage = (th - seg(pos).th(1)) / seg(pos).dth;
			x = seg(pos).line(:,1) + (seg(pos).line(:,2) - seg(pos).line(:,1)) * percentage;

			R(:,i) = x;
			end

			if doPlot, plot(R(1,:), R(2,:), 'r-o'); end