222 - Topic 5.5 - Playing with curves on surfaces

var('x,y,t') G = plot3d(9*x^2-y^2,(x,-2,2),(y,-2,3.5)) G += parametric_plot3d([1,t,9-t^2],(t,-2,3.5),color='red',thickness=10) G += parametric_plot3d([1,3+t,-6*t],(t,-2,2),color='yellow',thickness=10) G += point3d((1,3,0),color='green',size=15) G.show() 

var('x,y,t') G = plot3d(9*x^2-y^2,(x,-2,2),(y,-2,3.5)) G += parametric_plot3d([1+t,3-t,9*(1+t)^2-(3-t)^2],(t,-1,1),color='red',thickness=10) G += parametric_plot3d([1+t,3-t,24*t],(t,-1,1),color='yellow',thickness=10) G += point3d((1,3,0),color='green',size=15) G.show() 

var('x,y,t') f(x,y) = sqrt(x^2+y^2) G = plot3d(f,(x,-2,2),(y,-2,2)) G += parametric_plot3d([cos(t),e^t,f(x=cos(t),y=e^t)],(t,-6,0.5),color='red',thickness=10) #G += parametric_plot3d([1,3+t,-6*t],(t,-2,2),color='yellow',thickness=10) #G += point3d((1,3,0),color='green',size=15) G.show() 

cylindrical_plot3d?