var('t u', domain='real');
def torus_knot(rates):
    cpx_expr = 2 + exp(2*pi*I*rates[1]*t);
    [u,v] = [cpx_expr.real(),cpx_expr.imag()];
    [x,y,z] = [cos(2*pi*rates[0]*t)*u,sin(2*pi*rates[0]*t)*u,v];
    return [x,y,z]

cm = colormaps.rainbow;
def c(t,u): return 1-(u-1)^2;

def curve_cone(gamma,t0,t1,P): #gamma a space curve parametrized by t for t0 ≤ t ≤ t1, P = point [x,y,z]
    [g1,g2,g3] = gamma;
    [x,y,z] = P;
    return parametric_plot3d([(1-u)*g1+u*x,(1-u)*g2+u*y,(1-u)*g3+u*z],(t,t0,t1),(u,0,1),plot_points=200,opacity=0.3,color=(c,cm));

curve_cone(torus_knot([3,5]),0,1,[0,0,-3])