SD14: Visualisation 2
system:sage

{{{id=0|
paraboloid = plot3d(lambda x, y: x^2 + y^2, (-2, 2), (-2, 2))
paraboloid.show()
///
}}}

{{{id=1|
# Clebsch cubic
x, y, z = var("x y z")
f = 81*(x^3+y^3+z^3)-189*(x^2*y+x^2*z+x*y^2+x*z^2+y^2*z+y*z^2)+54*x*y*z+126*(x*y+x*z+y*z)-9*(x^2+y^2+z^2)-9*(x+y+z)+1
clebsch = implicit_plot3d(f, (-1, 1), (-1, 1), (-1, 1), plot_points=100)
clebsch.show()
///
}}}

{{{id=2|
# cubic with D_4-singularity
f = x*(x^2-y^2) + z^2*(1+z) + 2/5*x*y + 2/5*y*z
cubic_d4 = implicit_plot3d(f, (-5, 5), (-5, 5), (-5, 5), plot_points=100)
cubic_d4.show()
///
}}}

{{{id=3|
# Barth sextic
c = RR((1+sqrt(5))/2)
f = (8*c+4)*x^2*y^2*z^2 - c^4*(x^4*y^2+y^4*z^2+x^2*z^4) + c^2*(x^2*y^4+y^2*z^4+x^4*z^2) - (2*c+1)/4*(x^2+y^2+z^2-1)^2
barth = implicit_plot3d(f, (-1, 1), (-1, 1), (-1, 1), plot_points=100)
barth.show()
///
}}}

{{{id=4|
# ordinary node
f = x^2 + y^2 - z^2
node = implicit_plot3d(f, (-2, 2), (-2, 2), (-2, 2), plot_points=100)
node.show()
///
}}}

{{{id=5|

///
}}}