function hypotrochoid(r1,r2,len)
%animation of HYPOTROCHOID
%hypotrochoid(r1,r2,len);
%r1=radius of fixed circle on which smaller circle rolls
%r2=radius of rolling circle
%len=line connected to centre of rolling circle
%example: hypotrochoid(1,0.25,0.5);
% hypotrochoid(1,0.25,1);
%this code also trace hypocycloid
%when r2=len then it becomes hypocycloid
%example for hypocycloid: hypotrochoid(1,0.25,0.25);
%always keep r1>r2
if nargin==0
r1=1; %radius of fixed circle on which smaller circle rolls
r2=0.25; %radius of rolling circle
len=0.5; %line connected to centre of rolling circle
end
n=0;
dtheta=pi/20; %increase in angle per iteration
roughx=[]; %variable to trace trochoid
roughy=[]; %variable to trace trochoid
upto=2*r1*pi/r2+dtheta; %rotate upto
t=linspace(0,2*pi,75);
[x,y]=pol2cart(t,r2);
h1=patch(x,y,'r');%draw rolling circle
[phil,rl]=cart2pol([-len 0],[0 0]);
h2=line(0,0);%draw line connected to centre of rolling circle
[x_fix,y_fix]=pol2cart(t,r1);
line(x_fix,y_fix);%draw fixed circle,only once because it is fixed
axis equal
axis(r1*[-2 2 -2 2]) %fix axis
while n<upto && ishandle(h1)
[xl,yl]=pol2cart(phil-n,rl); %rotate line
[x2,y2]=transform2d(xl,yl,0,-(r1-r2),n*r2/r1,0,r1-r2);
set(h2,'xdata',x2,'ydata',y2);%draw line
[x,y]=pol2cart(t,r2); %rotate circle
[x3,y3]=transform2d(x,y,0,-(r1-r2),n*r2/r1,0,r1-r2);
set(h1,'xdata',x3,'ydata',y3);%draw rolling circle
line([roughx x2(1)],[roughy y2(1)]);%trace trochoid
roughx=x2(1);
roughy=y2(1);
pause(0.025)
n=n+dtheta;
end
%function end
