# The Heart of Euler

I could not resist to do a bit more with the heart function. Here is the plane heart again.

>plot2d("(x^2+y^2-1)^3-x^2*y^3",r=1.3, ...
style="#",color=red,<outline, ...
level=[-2;0],n=100):

Starting form this expression, we define a numerical expression, which computes the radius given the argument of (x,y).

>expr &= (x^2+y^2-1)^3-x^2*y^3
2    2     3    2  3
(y  + x  - 1)  - x  y
>function fr(r,a) &= expr with [x=r*cos(a),y=r*sin(a)] | trigreduce
5
2     3   (sin(5 a) - sin(3 a) - 2 sin(a)) r
(r  - 1)  + -----------------------------------
16
>function map f(a) := bisect("fr",0,2;a)

Once, we have this, we can plot the heart turned around the y-axis.

>t=linspace(-pi/2,pi/2,100); r=f(t);
>s=linspace(0,2pi,100)';
>plot3d(r*cos(t)*sin(s),r*cos(t)*cos(s),r*sin(t), ...
> >hue,<frame,color=red,zoom=4.5,amb=0,max=0.7,grid=12):

Or, if we change the definition of s a little bit,

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