How to fill area between several paths

I have the folling tikz code, where several paths intersect each other. I struggle to find a way to fill the six different regions of the resulting picture, each with a different pattern (not necessarily a plain color).

documentclass{article}

usepackage{tikz} %used for theorem style
usetikzlibrary{positioning}
usetikzlibrary{hobby}
usetikzlibrary{intersections}

begin{document}

begin{tikzpicture}
coordinate (upleft) at (0,0);
coordinate[right = 12cm of upleft] (upright);
coordinate[below = 14cm of upright] (downright);
coordinate[below = 14cm of upleft] (downleft);

draw[name path=UP] (upleft) -- (upright);
draw[name path=RIGHT] (upright) -- (downright);
draw[name path=DOWN] (downright) -- (downleft);
draw[name path=LEFT] (downleft) -- (upleft);

coordinate[above right = 8cm and 6cm of downleft] (halt);
coordinate[right = 2.5cm of upleft] (coneupleft);
coordinate[left = 2.5cm of upright] (coneupright);
coordinate[right = 4cm of downleft] (conedownleft);
coordinate[left = 4cm of downright] (conedownright);

%left to right Curve
coordinate[below = 2cm of upleft] (curve1left);
coordinate[below = 2cm of upright] (curve1right);
coordinate[below = 4cm of halt] (curve1middle);
coordinate[left = 3cm of halt] (curve1middle1);
coordinate[right = 3cm of halt] (curve1middle2);
draw[name path=HIGH] (curve1left) to [curve through = {(curve1middle1) (curve1middle) (curve1middle2)}] (curve1right);

%up to bottom curves
coordinate[right = 1cm of upleft] (vcurve1upl);
coordinate[left = 1cm of upright] (vcurve1upr);
coordinate[left = 3cm of conedownleft] (vcurve1bottoml);
coordinate[right = 3cm of conedownright] (vcurve1bottomr);
coordinate[left = 3.5cm of halt] (vcurve1ml);
coordinate[right = 3.5cm of halt] (vcurve1mr);
draw[name path=DNCLEFT] (vcurve1upl) to [curve through = {(vcurve1ml)}] (vcurve1bottoml);
draw[name path=DNCRIGHT] (vcurve1upr) to [curve through = {(vcurve1mr)}] (vcurve1bottomr);

end{tikzpicture}

end{document}

The result looks like this:

The goal is to fill the six regions with different patterns, if possible without touching the existing code, but only by adding new lines of code.

From what I could see looking at various similar questions, there may be a possibility with a combination of pieces of code like:

fill[orange, intersection segments={
                of=HIGH and DNCLEFT,
                sequence={L2--R2}
              }];

However the above code is made to fill a pattern between two paths and not more. Also I do not understand the meaning of L2 and R2 (which apparently could also range from R0 to R2 or L0 to L2, and used with some reverse keyword), so I have trouble mixing them together to achieve what I want.

Note that the full picture I’m working with has much more regions than the one I’m giving here, which is sort of a minimal exemple.

Ideally a combination of some clipping command of the form "clip everything to the left/right/top/bottom of a given path*" would be great, but I could not find how to do it.

documentclass{article}

usepackage{tikz} %used for theorem style
usetikzlibrary{positioning}
usetikzlibrary{hobby}
usetikzlibrary{intersections}
usetikzlibrary{backgrounds}
begin{document}

begin{tikzpicture}
coordinate (upleft) at (0,0);
coordinate[right = 12cm of upleft] (upright);
coordinate[below = 14cm of upright] (downright);
coordinate[below = 14cm of upleft] (downleft);

draw[name path=UP] (upleft) -- (upright);
draw[name path=RIGHT] (upright) -- (downright);
draw[name path=DOWN] (downright) -- (downleft);
draw[name path=LEFT] (downleft) -- (upleft);

coordinate[above right = 8cm and 6cm of downleft] (halt);
coordinate[right = 2.5cm of upleft] (coneupleft);
coordinate[left = 2.5cm of upright] (coneupright);
coordinate[right = 4cm of downleft] (conedownleft);
coordinate[left = 4cm of downright] (conedownright);

%left to right Curve
coordinate[below = 2cm of upleft] (curve1left);
coordinate[below = 2cm of upright] (curve1right);
coordinate[below = 4cm of halt] (curve1middle);
coordinate[left = 3cm of halt] (curve1middle1);
coordinate[right = 3cm of halt] (curve1middle2);
tikzset{HIGH/.style={insert path={(curve1left) to [curve through = {(curve1middle1) (curve1middle) (curve1middle2)}] (curve1right)}}}
draw[name path=HIGH,HIGH] ;

%up to bottom curves
coordinate[right = 1cm of upleft] (vcurve1upl);
coordinate[left = 1cm of upright] (vcurve1upr);
coordinate[left = 3cm of conedownleft] (vcurve1bottoml);
coordinate[right = 3cm of conedownright] (vcurve1bottomr);
coordinate[left = 3.5cm of halt] (vcurve1ml);
coordinate[right = 3.5cm of halt] (vcurve1mr);
tikzset{DNCLEFT/.style={insert path={(vcurve1upl) to [curve through = {(vcurve1ml)}] (vcurve1bottoml)}},
DNCRIGHT/.style={insert path={(vcurve1upr) to [curve through = {(vcurve1mr)}] (vcurve1bottomr)}}}
draw[name path=DNCLEFT,DNCLEFT] ;
draw[name path=DNCRIGHT,DNCRIGHT];
begin{scope}[on background layer]
 begin{scope}
  fill[orange,HIGH] -- (upright) -- (upleft) -| cycle;
 end{scope}
 %
 begin{scope}
  fill[cyan,HIGH] -- (downright) -- (downleft) -| cycle;
 end{scope}
 %
 begin{scope}
  clip[DNCLEFT] -- (downleft)  |- (upleft) -| cycle;
  fill[red,HIGH] --  (upright) -- (upleft) -- cycle;
 end{scope}
 %
 begin{scope}
  clip[DNCRIGHT] -- (downright)  -- (upright) -| cycle;
  fill[blue,HIGH] -- (upright) -| cycle;
 end{scope}
 %
 begin{scope}
  clip[DNCLEFT] -- (downleft)  |- (upleft) -| cycle;
  fill[magenta,HIGH] -- (downright) -- (downleft) -| cycle;
 end{scope}
 %
 begin{scope}
  clip[DNCRIGHT] -- (downright)  -- (upright) -| cycle;
  fill[purple,HIGH] -- (downright) -- (downleft) -| cycle;
 end{scope}
end{scope}
end{tikzpicture}
end{document}