3005.sagews

var('u,v,r,R,p,q')

rho(r,R) = (R-r)/2.0
phi(u,r,R) = (r + rho(r,R)) + rho(r,R)*cos(u)
psi(u,r,R) = rho(r,R)*sin(u)

T(u,v,r,R) = [phi(u,r,R)*cos(v), phi(u,r,R)*sin(v), psi(u,r,R)]

generalKnot(r,R,p,q,t) = [phi(2*pi*q*t,r,R)*cos(2*pi*p*t), phi(2*pi*q*t,r,R)*sin(2*pi*p*t), psi(2*pi*q*t,r,R)]

@interact
def plotKnot(s1=slider(1,29,step_size=1,default=2, label="p"), s2=slider(1,29,step_size=1, default=3, label="q"),opac=slider(0.1,1,step_size=0.05,default=0.85,label="Torus Opacity"),chkBox=("Show Torus",False),frame=("Show Frame",False)):
    	p1 = parametric_plot3d(T(r=1,R=2), (u,0,2*pi), (v,0,2*pi),opacity=opac, color='yellow',aspect_ratio=1,frame=False)
	p2 = parametric_plot3d(generalKnot(r=1,R=2, p=s1,q=s2), (t,0,1), thickness=6, color='purple',frame=frame,aspect_ratio=1)
	if chkBox == True:
            (p1+p2).show()
        else:
                p2.show()

p  q  Torus Opacity  Show Torus  Show Frame  [removed] [removed] [removed] [removed]