# How can I fill the inverted region of this?

How can I fill the inverted region of this? I want to fill the region outside of this shape t instead.

ListLinePlot[{{-1, 1}, {1, 1}, {10,
10}, {10, -10}, {1, -1}, {-1, -1}, {-10, -10}, {-10, 10}, {-1, 1}},
PlotStyle -> Directive[Red, Dashed, Thickness[0.008]],
Filling -> {1 -> Axis}, FillingStyle -> Lighter[Gray, 0.85]]


pts = {{-1, 1}, {1, 1}, {10,
10}, {10, -10}, {1, -1}, {-1, -1}, {-10, -10}, {-10, 10}, {-1, 1}}


Using Prolog:

ListLinePlot[pts, PlotStyle -> Directive[Red, Dashed, Thickness[0.008]]
, Filling -> {1 -> Axis}, FillingStyle -> Lighter[White, 0.85]
, Prolog -> {GrayLevel[0.9]
(*, Rectangle[{-10,-10},{10,10}]*)
, Rectangle @@ {
{
Min[#[[All, 1]]], Min[#[[All, 2]]]}
, {Max[#[[All, 1]]], Max[#[[All, 2]]]
}
} &@pts
}
]


• Use RegionDifference to construct the outer region.
pts = {{-1, 1}, {1, 1}, {10,
10}, {10, -10}, {1, -1}, {-1, -1}, {-10, -10}, {-10, 10}, {-1, 1}};
outreg = TransformedRegion[Rectangle @@ CoordinateBoundingBox[pts],
ScalingTransform[{1.2, 1.2}, Mean[pts]]];
inreg = Polygon[pts];
clip = RegionDifference[outreg, inreg];
Graphics[{{Lighter[Gray, 0.5],
clip}, {EdgeForm[Directive[Red, Dashed, Thickness[0.008]]],
FaceForm[], inreg}}, AspectRatio -> 1/GoldenRatio, Axes -> True]


• Use Polygon[outpts -> {inpts}] to get holes.
pts = {{9, 11}, {11, 11}, {20, 15}, {9, -5}, {11, 9}, {9, 9}, {-10,
0}, {0, 20}, {9, 11}};
inpts = Most@pts;
{{xmin, xmax}, {ymin, ymax}} = {MinMax[pts[[;; , 1]]],
MinMax[pts[[;; , 2]]]};
outpts = {{xmin, ymin}, {xmax, ymin}, {xmax, ymax}, {xmin, ymax}};
clip = Polygon[outpts -> {inpts}];
Graphics[{Lighter[Gray, 0.5], clip,
Directive[Red, Dashed, Thickness[0.008]], Line[pts]},
AspectRatio -> 1/GoldenRatio, Axes -> True, PlotRangePadding -> .8]


Fill with white and make the background gray:

ListLinePlot[{{-1, 1}, {1, 1}, {10,
10}, {10, -10}, {1, -1}, {-1, -1}, {-10, -10}, {-10, 10}, {-1, 1}},
PlotStyle -> Directive[Red, Dashed, Thickness[0.008]],
Filling -> {1 -> Axis}, FillingStyle -> White,
Background -> Lighter[Gray, 0.85]]


coords = {{-1, 1}, {1, 1}, {10, 10}, {10, -10}, {1, -1}, {-1, -1},
{-10, -10}, {-10, 10}, {-1, 1}};

Graphics[{Lighter[Gray, 0.5], Rectangle @@ (Scaled /@ {{0, 0}, {1, 1}}),
EdgeForm[{Red, Dashed, AbsoluteThickness[3]}], White, Polygon @ coords},
AspectRatio -> 1/GoldenRatio, Axes -> True]


Graphics[{Directive[Red, Dashed, AbsoluteThickness[4]], Line @ coords,
Lighter[Gray, 0.5], FilledCurve[Line /@
{Scaled /@ {{0, 0}, {0, 1}, {1, 1}, {1, 0}, {0, 0}}, coords}]},
AspectRatio -> 1/GoldenRatio, Axes -> True]


The even-odd rule for FilledCurve can be used:

Module[{shape = {Line[{{-1, 1}, {1, 1}, {10, 10}, {10, -10}, {1, -1},
{-1, -1}, {-10, -10}, {-10, 10}, {-1, 1}}]},
universe = {Line[{{-100, 100}, {100, 100}, {100, -100}, {-100, -100},
{-100, 100}}]},
bounds = {{-10.5, 10.5}, {-11, 11}}},
Graphics[{Lighter[Gray, .75], FilledCurve[{shape, universe}], Dashed,
Red, Thickness[.008], JoinedCurve[shape]},
AspectRatio -> (1/GoldenRatio), Axes -> True, PlotRange -> bounds,
ImageSize -> 360]]