# Implicit Region with Multiple Levels of Contraints

I'm trying to create an Implicit Region in the following way:

Let's say the 2D region is defined as

(* for -1 < e1, e2 < 1 *)
{x, y} = {1, 1} + e1 {1, -1} + e2 {2, 1};


I can draw this region with some difficulty by generating all the corners and computing the convex hull

{x, y} /. Thread /@ ({e1, e2} -> #1 &) /@ Tuples[{-1, 1}, 2] //
Show[ConvexHullMesh[#], ListPlot[Callout /@ #], Axes -> True] &


Although this method would break down if the region was a bit bit more complicated say

{x, y} = {1, 1} + Tanh[e1 {1, -1}] + e2 {2, 1};

My attempt was to try this

ImplicitRegion[
x == 1 + e1 + 2 e2 &&
y == 1 + e2 - e1 && -1 < e1 < 1 && -1 < e2 < 1, {x, y}]//RegionPlot


but unfortunately ImplicitRegion can only handle contraints that use it's variables.

Any ideas to help visualize more complicated regions of this form would be appreciated. Here's an example of one I'd like to see

{x, y} = {Ramp[-0.911 (1 + Subscript[\[Epsilon], 1]/10) +
1.72 (2 + Subscript[\[Epsilon], 2]/10)],
Ramp[-0.886 (1 + Subscript[\[Epsilon], 1]/10) +
0.242 (2 + Subscript[\[Epsilon], 2]/10)]}


where

-1 < Subscript[\[Epsilon], _] < 1

• You can use ParametricRegion[...] and Region[ParametricRegion[...]] to visualize. This works with Tanh example, but unfortunately gives empty plot for the last Ramp example.
– Alx
Commented Nov 1, 2019 at 14:07
• @Alx thanks ParametricRegion works even for the ramp after a bit of tweaking Commented Nov 4, 2019 at 0:15

ParametricRegion is the exact solution to this problem. The example I provided is rather uninteresting and comes out as a single line, but heres a slightly nicer example
ParametricRegion[{{Ramp[