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Asked by James Simko
on 16 Nov 2012

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.

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Answer by Image Analyst
on 17 Nov 2012

Accepted answer

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

James Simko
on 25 Nov 2012

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

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