parametricSurfaceArea.sagews

var('u,v')
npi = RDF(pi)
@interact
def viewer(mesh = checkbox(default = False, label = 'Show u,v meshlines'), uc = slider(-2,2,1/10,0, label = '<span style="color:red">Constant u value</span>'), vc = slider(-2,2,1/10,0, label = '<span style="color:green">Constant v value</span>'), functions = input_box([u,v^2,u^2+v])):
    f1(u,v) = functions[0]
    f2(u,v) = functions[1]
    f3(u,v) = functions[2]
    surface_plot = parametric_plot3d([f1,f2,f3], (u,-2,2), (v,-2,2), mesh = mesh, opacity = .8)
    constant_u = line3d([[f1(uc,q), f2(uc,q), f3(uc,q)] for q in srange(-2,2,.01)], rgbcolor = (1,0,0), thickness = 3)
    constant_v = line3d([[f1(q,vc), f2(q,vc), f3(q,vc)] for q in srange(-2,2,.01)], rgbcolor = (0,1,0), thickness = 3)
    show(surface_plot + constant_u + constant_v, frame = False)

(u, v)

Interact: please open in CoCalc