cardioid



Hi

I want to draw special cardioid defined by equation:

e1:exp(t*%i)/2-exp(2*t*%i)/4;

Can I draw it in such form ?

I have done it by 2 methods:

/* draws cardioid in parametric form */
e1:exp(t*%i)/2-exp(2*t*%i)/4;
re:realpart(e1);
im:imagpart(e1);
/*demoivre(e1);*/
plot2d ([parametric,re,im,[t,0,2*%pi],[nticks,200]],[x,-2.5, 
0.5],[y,-1.5,1.5],[gnuplot_preamble, "set xzeroaxis; set grid"])$


I works good.

And second method :

/* draws cardioid in polar form */
e1:exp(t*%i)/2-exp(2*t*%i)/4;
r:abs(e1);
load(draw);
draw2d(nticks = 2000, xrange = [-2.5,0.5], yrange=[-1.5,1.5], color = 
blue, line_width
   = 3, polar(r,t,0,2*%pi),grid=true)$

It semms to me the same but graphical result is diffrent.

Can it be done better ?

regards

Adam