Determining if a curve is a closed loop

This is for a lab assignment for an intro to matlab course

assuming a parametric curve composed of

    x=3*cos(t);
    y=3*sin((3+ee)*t);
where ee is an epsilon between -.5 and .5

I must find where what value of ee makes the curve a closed curve

my initial code is

t=[0:.1:10]; ee=-0.5; hold on for i=1:100

    x=3*cos(t);
    y=3*sin((3+ee)*t);
    if y(1) ~= y(length(t))
              ee=ee+.01;

    else
    plot(x,y)
    ee
    y(i)
    x(i)
    end
    end

however this does not return an answer, I am wondering if there is something I am not addressing correctly.

Answer 1

Your curve never closes. Run this code to see why:

clc;    % Clear the command window.
clearvars;  % Erase all existing variables.
workspace;  % Make sure the workspace panel is showing.
format longg;
format compact;
fontSize = 20;

t=[0:.1:10];
ee=-0.5;
tolerance = 0.05;
for i=1:100
	
	x=3*cos(t);
	y=3*sin((3+ee)*t);
	if abs(y(1) - y(end)) < tolerance
		break;
	end
	ee = ee + .01;
		
	cla;
	plot(x,y, 'bo-');
	hold on;
	% Plot end points
	plot(x(1), y(1), 'rs', 'MarkerSize', 20, 'LineWidth', 3);
	plot(x(end), y(end), 'rs', 'MarkerSize', 20, 'LineWidth', 3);
	grid on;
	if i == 1
		% Enlarge figure to full screen.
		set(gcf, 'units','normalized','outerposition',[0 0 1 1]);
	end
	promptMessage = sprintf('Do you want to Continue processing,\nor Cancel to abort processing?');
	titleBarCaption = 'Continue?';
	button = questdlg(promptMessage, titleBarCaption, 'Continue', 'Cancel', 'Continue');
	if strcmp(button, 'Cancel')
		close all;
		break;
	end
end

Oh man, that is a really good idea, using a tolerance to break the loop.