# Parameters
R=5.0
r=1.2
s=0.7

# Torus 
f(u,v)=(R+r*cos(u))*cos(v)
g(u,v)=(R+r*cos(u))*sin(v)
h(u,v)=r*sin(u)

# d / du gives one tangent
f1(u,v)=-sin(u)*cos(v)
g1(u,v)=-sin(u)*sin(v)
h1(u,v)=cos(u)

# normal to torus
f2(u,v)=cos(u)*cos(v)
g2(u,v)=cos(u)*sin(v)
h2(u,v)=sin(u)

# Trefoil
f3(u,v)=f(3*u,2*u)+s*f1(3*u,2*u)*cos(v)+s*f2(3*u,2*u)*sin(v)
g3(u,v)=g(3*u,2*u)+s*g1(3*u,2*u)*cos(v)+s*g2(3*u,2*u)*sin(v)
h3(u,v)=h(3*u,2*u)+s*h1(3*u,2*u)*cos(v)+s*h2(3*u,2*u)*sin(v)

set parametric
set isosamples 50,20
set hidden
set nokey
set noborder
set noxtics
set noytics
set noztics
set view 0,210,1,1

set title "Parametric Trefoil"
set urange [-pi:pi]
set vrange [-pi:pi]
splot f3(u,v),g3(u,v),h3(u,v)