Curves on a Surface

The Surface: Enter r(u,v) as a function of u and v:     
 
r(u,v) =  
 ,   ,  
Enter ranges for u and v.  The r settings can be either numbers or functions of q:
u min:       v min(# or g(q) ):      Grid (u) :    Axes:
u max:    v max(# or g(q) ): Grid (v) :
 

The curves are of the form ρ(t) = r( u(t), v(t) ): Enter the number of points for the curves: )

The Blue Curve:  Enter u(t) and v(t) for the curve ρ(t) = r( u(t), v(t) ) to be drawn in blue:
u
(t) 
=   
 ,     
v
(t) 
=  
  ,    t in      ,  
  The Green Curve:  Enter u(t) and v(t) for the curve ρ(t) = r( u(t), v(t) ) to be drawn in green:
u
(t) 
=   
 ,     
v
(t) 
=  
  ,    t in      ,  
  The Red Curve:  Enter u(t) and v(t) for the curve ρ(t) = r( u(t), v(t) ) to be drawn in red:
u
(t) 
=   
 ,     
v
(t) 
=  
  ,    t in      ,  
 

The Plot button below will create a new window with the surface as a wireframe, the curve in blue, and an estimate of the length of the curve.