# Shading between two regions of two separate parametric curves/function

I have two long functions g12 and g14 in terms of g2:

g12 = √(-(30374999/480000) - g2^2 + 44401/(150000000 2^(2/3) (7026667556070696253202/244140625 - (1637971061985345024 g2^2)/78125 - (190911920799744 g2^4)/625 + √(4 (-(231106915244401/390625) - (107745652224 g2^2)/625)^3 + (7026667556070696253202/244140625 - (1637971061985345024 g2^2)/78125 - (190911920799744 g2^4)/625)^2))^(1/3)) + (96294548 2^(1/3))/(125 (7026667556070696253202/244140625 - (1637971061985345024 g2^2)/78125 - (190911920799744 g2^4)/625 + √(4 (-(231106915244401/390625) - (107745652224 g2^2)/625)^3 + (7026667556070696253202/244140625 - (1637971061985345024 g2^2)/78125 - (190911920799744 g2^4)/625)^2))^(1/3)) + (140293818 2^(1/3) g2^2)/(625 (7026667556070696253202/244140625 - (1637971061985345024 g2^2)/78125 - (190911920799744 g2^4)/625 + √(4 (-(231106915244401/390625) - (107745652224 g2^2)/625)^3 + (7026667556070696253202/244140625 - (1637971061985345024 g2^2)/78125 - (190911920799744 g2^4)/625)^2))^(1/3)) + (1/(768 2^(1/3)))((7026667556070696253202/244140625 - (1637971061985345024 g2^2)/78125 - (190911920799744 g2^4)/625 + √(4 (-(231106915244401/390625) - (107745652224 g2^2)/625)^3 + (7026667556070696253202/244140625 - (1637971061985345024 g2^2)/78125 - (190911920799744 g2^4)/625)^2))^(1/3)))
g14 = √(-(30374999/480000) - g2^2 - 34681467/(100000000 2^(2/3) (7026667556070696253202/244140625 - (1637971061985345024 g2^2)/78125 - (190911920799744 g2^4)/625 + √(4 (-(231106915244401/390625) - (107745652224 g2^2)/625)^3 + (7026667556070696253202/244140625 - (1637971061985345024 g2^2)/78125 - (190911920799744 g2^4)/625)^2))^(1/3)) - (144441757 2^(1/3))/(375 (7026667556070696253202/244140625 - (1637971061985345024 g2^2)/78125 - (190911920799744 g2^4)/625 + √(4 (-(231106915244401/390625) - (107745652224 g2^2)/625)^3 + (7026667556070696253202/244140625 - (1637971061985345024 g2^2)/78125 - (190911920799744 g2^4)/625)^2))^(1/3)) + (1150640 I 2^(1/3))/(Sqrt[3] (7026667556070696253202/244140625 - (1637971061985345024 g2^2)/78125 - (190911920799744 g2^4)/625 + √(4 (-(231106915244401/390625) - (107745652224 g2^2)/625)^3 + (7026667556070696253202/244140625 - (1637971061985345024 g2^2)/78125 - (190911920799744 g2^4)/625)^2))^(1/3)) + (34681467 I Sqrt[3])/(100000000 2^(2/3) (7026667556070696253202/244140625 - (1637971061985345024 g2^2)/78125 - (190911920799744 g2^4)/625 + √(4 (-(231106915244401/390625) - (107745652224 g2^2)/625)^3 + (7026667556070696253202/244140625 - (1637971061985345024 g2^2)/78125 - (190911920799744 g2^4)/625)^2))^(1/3)) + (203919 I 2^(1/3)Sqrt[3])/(125 (7026667556070696253202/244140625 - (1637971061985345024 g2^2)/78125 - (190911920799744 g2^4)/625 + √(4 (-(231106915244401/390625) - (107745652224 g2^2)/625)^3 + (7026667556070696253202/244140625 - (1637971061985345024 g2^2)/78125 - (190911920799744 g2^4)/625)^2))^(1/3)) - (70146909 2^(1/3)g2^2)/(625 (7026667556070696253202/244140625 - (1637971061985345024 g2^2)/78125 - (190911920799744 g2^4)/625 + √(4 (-(231106915244401/390625) - (107745652224 g2^2)/625)^3 + (7026667556070696253202/244140625 - (1637971061985345024 g2^2)/78125 - (190911920799744 g2^4)/625)^2))^(1/3)) + (70146909 I 2^(1/3) Sqrt[3] g2^2)/(625 (7026667556070696253202/244140625 - (1637971061985345024 g2^2)/78125 - (190911920799744 g2^4)/625 + √(4 (-(231106915244401/390625) - (107745652224 g2^2)/625)^3 + (7026667556070696253202/244140625 - (1637971061985345024 g2^2)/78125 - (190911920799744 g2^4)/625)^2))^(1/3)) - (1/(1536 2^(1/3)))((7026667556070696253202/244140625 - (1637971061985345024 g2^2)/78125 - (190911920799744 g2^4)/625 + √(4 (-(231106915244401/390625) - (107745652224 g2^2)/625)^3 + (7026667556070696253202/244140625 - (1637971061985345024 g2^2)/78125 - (190911920799744 g2^4)/625)^2))^(1/3)) - (1/(512 2^(1/3) Sqrt[3]))I (7026667556070696253202/244140625 - (1637971061985345024 g2^2)/78125 - (190911920799744 g2^4)/625 + √(4 (-(231106915244401/390625) - (107745652224 g2^2)/625)^3 + (7026667556070696253202/244140625 - (1637971061985345024 g2^2)/78125 - (190911920799744 g2^4)/625)^2))^(1/3))


And I wish to plot two parametric curves by parameterizing g2:

ParametricPlot[{{g2, g12}, {g2, g14}}, {g2, 0, 10}, PlotRange -> {{0, 6}, {0, 2.5}}, PlotStyle -> {Directive[Blue], Directive[Orange]}, LabelStyle -> 12, AspectRatio -> 1, PlotPoints -> 100, WorkingPrecision -> 20, Exclusions -> None, Frame -> True, FrameTicksStyle -> Directive[Thick, Black], PlotRangePadding -> None]


I arrive with: Where the blue curve is represents g12 and orange represents g14. I intend to shade the area bounded by the blue curve, orange curve and the x-y axes. How should I go about doing so?

• Why not define explicitly as functions of g2: g12[g2_] := (* stuff *); g14[g2_] := (* stuff *)? Commented Oct 18, 2018 at 0:18

This also works.

Plot[{g12, g14}, {g2, 0, 5.24}, PlotRange -> {{0, 6}, {0, 2.5}},
ImageSize -> Large, LabelStyle -> {12, Black, Bold}, AspectRatio -> 1,
WorkingPrecision -> 20, Frame -> True, Filling -> {1 -> Axis, 2 -> {Axis, White}}]


For some reason, it is necessary to adjust the upper limit on g2 to eliminate a faint vertical line.

EDIT: Changed PlotStyle and PlotRange

{maxg2, maxy} =
Ceiling[{g2, g12} /.
NSolve[{g12 == g14, g2 > 0}, g2, WorkingPrecision -> 20][[1]] //
N // Chop, 0.05]

(* {5.25, 2.1} *)

Show[
RegionPlot[{Re[g14] < y < Re[g12] && 0 < g2 < 6}, {g2, 0, maxg2}, {y,
0, maxy},
PlotStyle -> LightGreen,
PlotPoints -> 100,
BoundaryStyle -> None],
ParametricPlot[{{g2, g12}, {g2, g14}}, {g2, 0, 10},
PlotRange -> {{0, maxg2}, {0, maxy}},
PlotStyle -> {Directive[Blue], Directive[Orange]},
LabelStyle -> 12,
AspectRatio -> 1,
PlotPoints -> 100,
WorkingPrecision -> 20,
Exclusions -> None,
Frame -> True,
FrameTicksStyle -> Directive[Thick, Black],

• Thanks! Just a few follow up questions: It seems even with PlotRangePadding->None there still exists padding in the plot. Is there any way to remove the padding? Also how would I go about changing the color of the shade? (say Grey to Green) Edit: I figured out the color. I would just do PlotStyle->(color) Commented Oct 18, 2018 at 0:39