13-1 Vector Functions and Space Curves.sagews

var('t')
parametric_plot3d((t, t^2, exp(t)), (t, -5, 5), aspect_ratio = [5, 5, 1])

t

3D rendering not yet implemented

#27
parametric_plot3d((sin(t), cos(t), t^2), (t, 0, 8*pi), aspect_ratio = [100, 100, 1])

#28
parametric_plot3d((t^4 - t^2 + 1, t, t^2), (t, -5, 5), aspect_ratio = [1, 20, 10])

#29
parametric_plot3d((t^2, sqrt(t - 1), sqrt(5 - t)), (t, 1, 5), aspect_ratio = [1, 5, 5])

3D rendering not yet implemented

#30
parametric_plot3d((sin(5*t), sin(2*t), sin(3*t)), (t, 0, 2*pi), plot_points = 500)

# intersection of surfaces
var('y', 'z')
C = parametric_plot3d((cos(t), sin(t), 3 - cos(t) - sin(t)), (t, 0, 2*pi), color = 'black')
S1 = plot3d(3 - x - y, (x, -2, 2), (y, -2, 2), color = 'green', opacity = 0.5)
S2 = parametric_plot3d((cos(t), sin(t), z), (t, 0, 2*pi), (z, 0, 6), color = 'blue', opacity = 0.5)
show(C + S1 + S2)

# intersection of surfaces
C = parametric_plot3d((2*cos(t), 2*sin(t), 4*(sin(t))^2), (t, 0, 2*pi), color = 'black')
S1 = plot3d(y^2, (x, -3, 3), (y, -3, 3), color = 'green', opacity = 0.5)
S2 = parametric_plot3d((2*cos(t), 2*sin(t), z), (t, 0, 2*pi), (z, -1, 7), color = 'blue', opacity = 0.5)
show(C + S1 + S2)

%var t x y z
A = parametric_plot3d( (sqrt(1-0.25*cos(10*t)^2)*cos(t), sqrt(1-0.25*cos(10*t)^2)*sin(t), 0.5*cos(10*t)), (t, 0, 2*pi), thickness=5, color='green', plot_points=500)
B = implicit_plot3d(x^2 + y^2 + z^2 - 1, (x, -1, 1), (y, -1, 1), (z, -1, 1), opacity=0.5)
show(A+B)

3D rendering not yet implemented