# Different lower bound filling option

I recall my previous post Different style of filling in x direction. In particular, in the following code I have a new question:

colors = ColorData[97, "ColorList"][[{1, 1, 2, 3, 4}]]; linea =
Line[{{0.1, 0}, {0.1, 1200}}]; Show[
Plot[{ConditionalExpression[
1000 Abs[(-1000 + 1000 a)/(-2000 + 1000 a)], a <= .1],
ConditionalExpression[1000 Abs[(-1000 + 1000 a)/(-2000 + 1000 a)],
a >= .1], (500 Abs[(-3 + 2 a)/(-2 + a)])/Sqrt,
250 Sqrt
Abs[(4 + 3 Sqrt - 4 a - 4 Sqrt a +
2 Sqrt a^2)/((-2 + a) (-1 - Sqrt + Sqrt a))],
500 Abs[(
7 + 4 Sqrt - 8 a - 4 Sqrt a +
4 a^2)/((-2 + a) (-2 - Sqrt + 2 a))]}, {a, 0, 1},
PlotRange -> {{0, 1}, {0, 1200}}, Mesh -> {{0.1, 1}},
MeshShading -> {Dashed, Automatic, Dotted}, MeshStyle -> None,
Filling -> {1 -> {Axis, GrayLevel[.95]},
2 -> {Axis, GrayLevel[.75]}},
LabelStyle -> {FontFamily -> "Times New Roman", Plain,
FontSize -> 13},
Ticks -> {{0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1},
Automatic}, AxesOrigin -> {0, 0}, ImageSize -> Large,
Epilog -> {Directive[Black, Thick,
Dashing[{0, Small, Large, Small}]], linea,
Inset[Framed[
Style["\!$$\*SubscriptBox[\(V$$, $$22$$]\)",
FontFamily -> "Times New Roman", FontSize -> 13],
FrameStyle -> Directive[Black, Thin, Dashed]], {.5, 190}],
Inset[Framed[
Style["\!$$\*SubscriptBox[\(V$$, $$nn$$]\)",
FontFamily -> "Times New Roman", FontSize -> 13],
FrameStyle -> Directive[Black, Thin]], {.5, 1000}]}],
Graphics[{Dashed, Arrow[{{0.5, 240}, {0.5, 960}}]}]]


I would like to change filling option; in particular, I would like to fill from x axis to the lower bound of these 4 curves. How can I do this?

• Check Filling->{4->Axis} – David G. Stork Mar 22 '18 at 17:29

1. Redefine colors as colors = ColorData[97, "ColorList"][[;;4]];
2. Add two more functions ConditionalExpression[Min[functions1], a <= .1] and ConditionalExpression[Min[functions1], a >= .1]) to the end of the list of your four functions (functions1)
3. Use the Filling setting Filling -> {5 -> {Axis, GrayLevel[.95]}, 6 -> {Axis, GrayLevel[.75]}}
4. Use the PlotStyle setting PlotStyle -> Join[Thread[Directive[colors, Thickness[.005]]], {None, None}]
5. Add the option Exclusions -> None
colors = ColorData[97, "ColorList"][[;;4]];
functions1 = {1000 Abs[(-1000 + 1000 a)/(-2000 + 1000 a)],
(500 Abs[(-3 + 2 a)/(-2 + a)])/Sqrt,
250 Sqrt Abs[(4 + 3 Sqrt - 4 a - 4 Sqrt a +
2 Sqrt a^2)/((-2 + a) (-1 - Sqrt + Sqrt a))],
500 Abs[(7 + 4 Sqrt - 8 a - 4 Sqrt a + 4 a^2)/((-2 + a) (-2 - Sqrt + 2 a))]};
functions = Join[functions1, {ConditionalExpression[Min[functions1], a <= .1]
ConditionalExpression[Min[functions1], a >= .1]}];

linea =  Line[{{0.1, 0}, {0.1, 1200}}];
epilog = {linea, {Dashed, Arrow[{{0.5, 240}, {0.5, 960}}]},
Directive[Black, Thick, Dashing[{0, Small, Large, Small}]],
Inset[Framed[ Style[Subscript["V", "22"], Italic, FontFamily -> "Times New Roman",
FontSize -> 13],  FrameStyle -> Directive[Black, Thin, Dashed]], {.5, 190}],
Inset[Framed[Style[Subscript["V", "nn"], Italic, FontFamily -> "Times New Roman",
FontSize -> 13],  FrameStyle -> Directive[Black, Thin, Dashed]], {.5, 190}]};

Plot[functions, {a, 0, 1}, PlotRange -> {{0, 1}, {0, 1200}},
Mesh -> {{0.1, 1}}, MeshShading -> {Dashed, Automatic, Dotted},
MeshStyle -> None,
Filling -> {5 -> {Axis, GrayLevel[.95]},  6 -> {Axis, GrayLevel[.75]}},
LabelStyle -> {FontFamily -> "Times New Roman", Plain,  FontSize -> 13},
PlotStyle ->  Join[Thread[Directive[colors, Thickness[.005]]], {None, None}],
Ticks -> {{0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1}, Automatic},
AxesOrigin -> {0, 0}, ImageSize -> Large, Epilog -> epilog, Exclusions -> None] 