var('t', 'y') animate([parametric_plot(((1 - c)*t + c*cos(t), c*sin(t)), (t, 0, pi), ymin=-2, ymax=4) for c in xsrange(0, 1, .05)]).show(gif = True)
animate([parametric_plot(((1 - c)*t + c*(cos(t) + 2*cos(4*t)), c*(sin(t) - 2*sin(4*t))), (t, -pi, pi), ymin=-pi, ymax=pi) for c in xsrange(0, 1, .05)]).show(gif = True, delay = 20)
var('u', 'v') animate([parametric_plot3d(((1-c)*u + c*(2 + cos(u))*cos(v), (1-c)*v + c*(2 + cos(u))*sin(v), c*sin(u)), (u, 0, 2*pi), (v, 0, 2*pi)) for c in xsrange(0, 1, 0.05)]).show()
var('u', 'v') parametric_plot3d(((2 + cos(u))*cos(v), (2 + cos(u))*sin(v), sin(u)), (u, 0, 2*pi), (v, 0, 1*pi), mesh = True)
(u, v)
3D rendering not yet implemented
#7 parametric_plot3d((u^2 + 1, v^3 + 1, u + v,), (u, -1, 1), (v, -1, 1))
3D rendering not yet implemented
#9 parametric_plot3d((u + v, u^2, v^2), (u, -1, 1), (v, -1, 1))
3D rendering not yet implemented
#11 parametric_plot3d((sin(v), cos(u)*sin(4*v), sin(2*u)*sin(4*v)), (u, 0, 2*pi), (v, -pi/2, pi/2), plot_points = [100, 100])
3D rendering not yet implemented
a = 1 b = 0.2 parametric_plot3d((a*cos(u)*sin(v), a*sin(u)*sin(v), a*(cos(v) + ln(tan(v/2))) + b*u), (u, 0, 8*pi), (v, 0, 2), plot_points = [100, 20])
3D rendering not yet implemented
a = 0.15 b = 2 f(u, v) = 1 + 0.05*sin(15.5*v)^4 # plot_points = [20, 1000] #f(u, v) = 1 + 0.03*sin(12*u)^8 # plot_points = [500, 50] #f(u, v) = 1 + 0.03*sin(15.5*v)^4 + 0.02*sin(12*u)^8 # plot_points = [200, 400] #f(u, v) = 2 / sqrt(16 + 4*cos(2*u)) # plot_points = [40, 100] parametric_plot3d((f(u, v)*cos(v)*(1 + cos(u))*exp(a*v), f(u, v)*sin(v)*(1 + cos(u))*exp(a*v), f(u, v)*(b + sin(u))*exp(a*v)), (u, 0, 2*pi), (v, 0, 4*pi), plot_points = [20, 1000])#.show(viewer = 'tachyon')
3D rendering not yet implemented
var('s', 't', 'u', 'v') (a, b) = (0.5, 0.5) #f(u, v) = (u, v, u^2 + v^2) f(u, v) = (u^2 - v^2, u*v, u + v) #f(u, v) = (u^2 + 1, v^3 + 1, u + v) S = parametric_plot3d(f(u, v), (u, -1, 1), (v, -1, 1), color = 'green', opacity = 0.7) Cu = parametric_plot3d(f(u, b), (u, -1, 1), color = 'blue') Cv = parametric_plot3d(f(a, v), (v, -1, 1), color = 'red') Vu = parametric_plot3d(f(a, b) + t*f(u, v).derivative(u).subs({u: a, v: b}), (t, 0, 0.4), color = 'black') Vv = parametric_plot3d(f(a, b) + t*f(u, v).derivative(v).subs({u: a, v: b}), (t, 0, 0.4), color = 'black') P = parametric_plot3d(f(a, b) + s*f(u, v).derivative(u).subs({u: a, v: b}) + t*f(u, v).derivative(v).subs({u: a, v: b}), (s, 0, 0.4), (t, 0, 0.4), color = 'yellow', opacity = 0.7) show(S + Cu + Cv + Vu + Vv + P)
(s, t, u, v)
3D rendering not yet implemented