@Carl Love 

1. I'd like to know why did you use depends? Why not simply
B::And(list, satisfies(B-> nops(B)=nops(A)))

2. Is the newer satisfies more efficient than the classical if?
Bij:=proc(A::list,B::list)
if nops(A)<>nops(B) then error "The lists must have same dims" fi;
seq(zip(`[]`, A, convert(b,list)),  b=Iterator:-Permute(B))
end;

3. In the previous Bij procedure, the variable b was not declared local.
It should be local but type(b,`local`) gives false and type(b,`global`) also false. Why?
Edit. Ok, it should be type('b',`local`) , type('b',`global`)  and ==> false and true
but even if global,  a global variable b at top level seems to be not affected.
(I.e. b seems to be still local, but type sees the global variable, since it is not declared explicitely. Is it so?)

@robin1234 

It is an ad-hoc shooting method. Because the condition f(1/2)=1/2 is not viable (de ODE is not defined for f(b)=b), | f(1/2)-1/2 | was minimized.

If you have other parameters, just include them in the list parameters (see also my first answer).

PS. Maybe a more natural approach (with the same result) would be:

eqx:=diff(f(b),b,b) = -(1/2)*(6*(diff(f(b), b))*f(b)-8*b*(diff(f(b), b))-2*f(b)+diff(f(b),b)+2)*(diff(f(b),b))/((-b+f(b))*(-1+f(b))):
ic:=f(3/8)=0, D(f)(3/8)=d:
s:=dsolve({eqx,ic},numeric, output=listprocedure, parameters=[d]):
fb:=subs(s,f(b)): #Procedure to evaluate f(b)
bdr:=proc(u) s(parameters=[u]); (fb(1/2)-1/2)^2 end:  # minimize  | f(1/2)-1/2 |
Opt:=Optimization:-NLPSolve(bdr, 2..3);   P:=Opt[2][1];
s(parameters=[P]);

@Markiyan Hirnyk 

I simply don't undertand your position and the double moral stuff. The situation in your link is completely different.
As for the "western" part, I think that we live at almost the same longitude (I am in Romania).

@aamirkhan 

You probably forgot to replace L with K in T10.

(because L is a table; K is the scalar now).

P1x.mw

I would not say that using allvalues is necessarily better, unless the user knows exactly what happens in such situations. So, the equation exp(x) = x^2-2 has an infinity of (complex) solutions and solve gives all of them as a RootOf. But allvalues returns only 5 roots as explicit RootOfs.

@Markiyan Hirnyk 

@John Fredsted 

D is a procedure.
D(f):=g  or  D[1](f):=h  fills its remember table.

Maybe, but it's correct, isn't it? After all, it is only a workaround.

@John Fredsted 

I used the argument x only to be able to convert via convert(...,diff), as a workaround.
If you have no arguments, you can use the woekaround:
e := (D[1]@D[1])(f);
unapply(convert(e(x),diff),x);
    (D@@2)(f)

@John Fredsted 

We cannot have everything in this world.

@Markiyan Hirnyk 

@one man 

Unfortunately you use an undefined terminology:

- Equidistant surface (see previous discussions)
- Round parametrization.

So, all we can do is to look at the animations. Do you think that this is enough?

@Markiyan Hirnyk 

It was just a simple ad-hoc approach.

@Markiyan Hirnyk 

But I already did: each point on the surface is moved by fixed distance in the direction of the normal vector.
The code was posted.

chronologically (yours was the second, using the distance to the graph).
Please see that you have considered the graph of sin(x) in the whole real line, not in [0,2*Pi].

Anyway, my impression is that the OP used my version of the definition.

@Markiyan Hirnyk 

@Markiyan Hirnyk 

You took another definition for the equidistance.

If you think that it is better, consider in your example (and notice also that implicitplot did not find all the points):

plots:-implicitplot(['F(s, t)[1] = 2', t = sin(s)], s = -Pi .. 3*Pi, t = -4 .. 4, color = [red, blue], gridrefine = 2)

If you use the first definition:

dist = 1/10 ==>

dist = 1 ==>

Why not, according to the definition considered: each point on the surface is moved by 1/2 units in the direction of the normal vector. I did not check whether the computations made by Maple are correct, have you?

@Markiyan Hirnyk