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In the case of 3d curve you can try something like:

var('t u')
p1=parametric_plot3d([cos(u),sin(u),u^2],(u,-1,1),thickness=10)
p2=sum([parametric_plot3d([cos(t),sin(t),z],(z,0,t^2)) for t in srange(-1,1,0.02)]) 
p1+p2

In the case of 3d curve you can try something like:

var('t u')
p1=parametric_plot3d([cos(u),sin(u),u^2],(u,-1,1),thickness=10)
p2=sum([parametric_plot3d([cos(t),sin(t),z],(z,0,t^2)) p2=sum([line([(cos(t),sin(t),0),(cos(t),sin(t),t^2)]) for t in srange(-1,1,0.02)]) 
p1+p2

In the case of 3d curve you can try something like:

var('t u')
p1=parametric_plot3d([cos(u),sin(u),u^2],(u,-1,1),thickness=10)
p2=sum([line([(cos(t),sin(t),0),(cos(t),sin(t),t^2)]) for t in srange(-1,1,0.02)]) 
p1+p2

var('x y')
f(x,y)=x^2*y+10
p0=plot3d(f(x,y),(x,1,3),(y,0,5),opacity=0.2)+plot3d(0,(x,1,3),(y,0,5),opacity=0.2)  
p1=sum([line([(t,0,0),(t,0,f(t,0))]) for t in srange(1,3,0.02)]) 
p2=sum([line([(3,u,0),(3,u,f(3,u))]) for u in srange(0,5,0.1)]) 
p0+p1+p2