I have the expression of a vector e, with 3 parameters tt1 tt2 and tt3:

e1 = -(Sin[tt1]*Sin[tt2])/2 - (Sin[tt2]*Sin[tt3])/2 e2 = (Cos[tt1]*Sin[tt2])/2 - (Cos[tt3]*Sin[tt2])/2 e3 = (Cos[tt1]*Cos[tt2]*Sin[tt3])/2 - (Cos[tt3]*Sin[tt1])/ 2 - (Cos[tt1]*Sin[tt3])/2 + (Cos[tt2]*Cos[tt3]*Sin[tt1])/2 e = {e1, e2, e3};

and the range of tt1 to tt3 are all from 0 to 2Pi. In this case, since we have 3 parameters, the endpoints of e should form a region rather than a surface, and I'd like to plot this region, or its boundary (preferably both).

The only relevant command I found is the RegionPlot3D command, but seems that one handles the Cartesian coordinates with inequalities as constraints, which is not true in my case.

Could someone give me a hand? Thanks a lot!

Update

Thanks a lot for your reply! But when I try this code:

GroebnerBasis[{e1 == -(Sin[tt1]*Sin[tt2])/2 - (Sin[tt2]*Sin[tt3])/2, 

e2 == (Cos[tt1]*Sin[tt2])/2 - (Cos[tt3]*Sin[tt2])/2, e3 == (Cos[tt1]*Cos[tt2]*Sin[tt3])/2 - (Cos[tt3]*Sin[tt1])/ 2 - (Cos[tt1]*Sin[tt3])/2 + (Cos[tt2]*Cos[tt3]*Sin[tt1])/2, Cos[tt1]^2 + Sin[tt1]^2 == 1, Cos[tt3]^2 + Sin[tt3]^2 == 1}, {e1, e2, e3}, {Cos[tt1], Sin[tt1], Cos[tt3], Sin[tt3]}]'

it gives me an error: General::ivar: "-(1/2)\ Cos[tt3]\ Sin[tt1]+1/2\ Cos[tt2]\ Cos[tt3]\ Sin[tt1]-1/2\ Cos[tt1]\ Sin[tt3]+1/2\ Cos[tt1]\ Cos[tt2]\ Sin[tt3] is not a valid variable.

I thought that the GroebnerBasis is used for solving equations, but in my case, I'm not trying to solve e1=e2=e3=0, instead, I'm trying to plot the region that can be traced by the endpoints of e, besides, t1 t2 t3 are independent variables, so I doubt if we could eliminate some of them, when I'm trying to plot the boundary of the region?

Thanks again!

best