@Carl Love  Yes, .gif, 50 frames. My file is very small - about 10.5-11kb.

@abhilashun   If there is a desire to take a look here
http://www.mapleprimes.com/questions/144358-How-To-Extract-All-Points-From-An-Implicitplot3d#answer144371

@vv Totally agree with you. This information is likely, for experts in the field of materials processing. I at one time had  some job in this direction, and now just do what I had not done before, because to my hands came colossal Maple opportunities.
If you are interested in something specific, I'll try to answer you.

        Now distance 2.0 in the first example, and round parameterization. Main is a great distance, so the equidistant surface of this form.

@vv  

        If “something”, then take a look here  http://www.mapleprimes.com/questions/203875-Parametrising-A-Surfacevolume#answer214656
I do not have the opportunity to engage in scientific work, but I can show the texts of programs. Excuse me.

@Christopher2222  Excuse me, but you know what equidistant and how it differs from the displacement?
                             There will be more examples:
                             2. Equidistant radius of 0.3 to the surface  x1^4+x2^4+x3^4-1=0

@Carl Love   Firstly, thank you for the correct spelling of "Draghilev", and secondly, thank you for your understanding.
      Yes, it could be nice. Only I cannot do it for many reasons. But think fully I can to help enthusiasts to do it.

@Carl Love  It turns out that not only.

@roman_pearce 

Thank you too. I believe that the Gröbner bases is a great achievement in mathematics as a generalization of the Gauss method. I have a lot of examples of polynomial systems for finding a finite number of solutions to find then infinite solutions. However, the systems of equations occur transcendental, and then have to work without the Gröbner bases ..

@acer  Thank you.

@vv  It seems to me that so clear to understand.
Maple not always uses complex numbers by default.
For example, I do not know how to get all the solutions of a polynomial system by Maple, if not to make the proposed replacement (x+Iy). See RootFinding [Isolate]
Unless, of course, we do not use evalf (solve (...))

restart;
z := x+I*y;
f1 := evalc(Re(exp(z)+1));
f2 := evalc(Im(exp(z)+1));
fsolve({f1, f2});
solve({f1, f2});
solve({f1, f2}, allsolutions);

@Ronan If it is necessary a list
LS := convert(`union`(convert(L, set), convert(S, set)), list);
(or  L:=...)

У Вас есть ещё какие-нибудь открытия?

   @Bendesarts  Animation and text of the program

   Benjamin.mw