What program can plot a parametric equation with 3 or more time parameters?

89 Views Asked by At

I'd like to make projections of this equation:

$$x(u,v) = (r\cos(u)+R_1)\cos(v)$$ $$y(u,v) = (r\cos(u)+R_1)\sin(v)$$ $$z(t,u) = (r\sin(u)+R_2)\cos(t)$$ $$w(t,u) = (r\sin(u)+R_2)\sin(t)$$

where,

$$0 < t < 2 \pi$$ $$0 < u < 2 \pi$$ $$0 < v < 2 \pi$$

and,

$$ R_1 >,<,= R_2 > r $$

Which is a really cool four dimensional torus, seen in slices, here:

Rotating slice at origin

Passing through a 3-plane at various angles

Unfortunately, the program I've been using only accepts 2 time parameters. Unless there's a way to 'consolidate' a 3-parameter equation into 2 (without loss of info about the shape), then I'm looking for another program. Any good suggestions?