7 Changed example
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Edit 2: Updated with a non-convex polygon

reg = With[{pts = RandomReal[{-3, 3}, {15, 2}]},
   Polygon@SortBy[pts, Apply[ArcTan, # - Mean[pts]] &]];

You could make a texture and use RegionPlot:

RegionPlot[
 reg,
 PlotStyle -> Texture[ExampleData[{"ColorTexture", "MultiSpiralsPattern"}]]]

Mathematica graphics

Update

Vector graphics through ContourShading:

ClearAll[f];
f[x_, y_] := x - y;
ContourPlot[f[x, y], {x, y} ∈ reg,
 Contours -> 20, ContourShading -> {Blue, LightRed}, 
 ContourStyle -> None]

Mathematica graphics

A self-intersecting polygon:

reg = Polygon[RandomReal[{-3, 3}, {15, 2}]];
ContourPlot[f[x, y], {x, y} ∈ reg,,
 Contours -> Flatten[Table[{c, c + 0.05}, {c, -6, 6, 0.3}]],
 ContourShading -> {Blue, LightRed}, ContourStyle -> None]]

Mathematica graphicsMathematica graphics

Edit 2: Updated with a non-convex polygon

reg = With[{pts = RandomReal[{-3, 3}, {15, 2}]},
   Polygon@SortBy[pts, Apply[ArcTan, # - Mean[pts]] &]];

You could make a texture and use RegionPlot:

RegionPlot[
 reg,
 PlotStyle -> Texture[ExampleData[{"ColorTexture", "MultiSpiralsPattern"}]]]

Mathematica graphics

Update

Vector graphics through ContourShading:

ClearAll[f];
f[x_, y_] := x - y;
ContourPlot[f[x, y], {x, y} ∈ reg,
 Contours -> 20, ContourShading -> {Blue, LightRed}, 
 ContourStyle -> None]

Mathematica graphics

ContourPlot[f[x, y], {x, y} ∈ reg,,
 Contours -> Flatten[Table[{c, c + 0.05}, {c, -6, 6, 0.3}]],
 ContourShading -> {Blue, LightRed}, ContourStyle -> None]]

Mathematica graphics

Edit 2: Updated with a non-convex polygon

reg = With[{pts = RandomReal[{-3, 3}, {15, 2}]},
   Polygon@SortBy[pts, Apply[ArcTan, # - Mean[pts]] &]];

You could make a texture and use RegionPlot:

RegionPlot[
 reg,
 PlotStyle -> Texture[ExampleData[{"ColorTexture", "MultiSpiralsPattern"}]]]

Mathematica graphics

Update

Vector graphics through ContourShading:

ClearAll[f];
f[x_, y_] := x - y;
ContourPlot[f[x, y], {x, y} ∈ reg,
 Contours -> 20, ContourShading -> {Blue, LightRed}, 
 ContourStyle -> None]

Mathematica graphics

A self-intersecting polygon:

reg = Polygon[RandomReal[{-3, 3}, {15, 2}]];
ContourPlot[f[x, y], {x, y} ∈ reg,,
 Contours -> Flatten[Table[{c, c + 0.05}, {c, -6, 6, 0.3}]],
 ContourShading -> {Blue, LightRed}, ContourStyle -> None]]

Mathematica graphics

6 Responded to comment
source | link

You could make a texture and use RegionPlotEdit 2: Updated with a non-convex polygon

RegionPlot[
reg ConvexHullMesh[RandomReal[= With[{pts = RandomReal[{-3, 3}, {2015, 2}]]]},
   Polygon@SortBy[pts, Apply[ArcTan, # - Mean[pts]] &]];

You could make a texture and use RegionPlot:

RegionPlot[
 reg,
 PlotStyle -> Texture[ExampleData[{"ColorTexture", "MultiSpiralsPattern"}]]]

Mathematica graphicsMathematica graphics

Update

Vector graphics through ContourShading:

ClearAll[f];
f[x_, y_] := x - y;
reg = ConvexHullMesh[RandomReal[{-3, 3}, {15, 2}]];
ContourPlot[f[x, y], {x, y} ∈ reg,
 Contours -> 20, ContourShading -> {Blue, LightRed}, 
 ContourStyle -> None]

Mathematica graphicsMathematica graphics

reg = ConvexHullMesh[RandomReal[{-3, 3}, {15, 2}]];
ContourPlot[f[x, y], {x, y} ∈ reg,,
 Contours -> Flatten[Table[{c, c + 0.05}, {c, -6, 6, 0.3}]],
 ContourShading -> {Blue, LightRed}, ContourStyle -> None]]

Mathematica graphicsMathematica graphics

You could make a texture and use RegionPlot:

RegionPlot[
 ConvexHullMesh[RandomReal[{-3, 3}, {20, 2}]],
 PlotStyle -> Texture[ExampleData[{"ColorTexture", "MultiSpiralsPattern"}]]]

Mathematica graphics

Update

Vector graphics through ContourShading:

ClearAll[f];
f[x_, y_] := x - y;
reg = ConvexHullMesh[RandomReal[{-3, 3}, {15, 2}]];
ContourPlot[f[x, y], {x, y} ∈ reg,
 Contours -> 20, ContourShading -> {Blue, LightRed}, 
 ContourStyle -> None]

Mathematica graphics

reg = ConvexHullMesh[RandomReal[{-3, 3}, {15, 2}]];
ContourPlot[f[x, y], {x, y} ∈ reg,,
 Contours -> Flatten[Table[{c, c + 0.05}, {c, -6, 6, 0.3}]],
 ContourShading -> {Blue, LightRed}, ContourStyle -> None]]

Mathematica graphics

Edit 2: Updated with a non-convex polygon

reg = With[{pts = RandomReal[{-3, 3}, {15, 2}]},
   Polygon@SortBy[pts, Apply[ArcTan, # - Mean[pts]] &]];

You could make a texture and use RegionPlot:

RegionPlot[
 reg,
 PlotStyle -> Texture[ExampleData[{"ColorTexture", "MultiSpiralsPattern"}]]]

Mathematica graphics

Update

Vector graphics through ContourShading:

ClearAll[f];
f[x_, y_] := x - y;
ContourPlot[f[x, y], {x, y} ∈ reg,
 Contours -> 20, ContourShading -> {Blue, LightRed}, 
 ContourStyle -> None]

Mathematica graphics

ContourPlot[f[x, y], {x, y} ∈ reg,,
 Contours -> Flatten[Table[{c, c + 0.05}, {c, -6, 6, 0.3}]],
 ContourShading -> {Blue, LightRed}, ContourStyle -> None]]

Mathematica graphics

5 Responded to comment
source | link

You could make a texture and use RegionPlot:

RegionPlot[
 ConvexHullMesh[RandomReal[{-3, 3}, {20, 2}]],
 PlotStyle -> Texture[ExampleData[{"ColorTexture", "MultiSpiralsPattern"}]]]

Mathematica graphics

Update

Vector graphics through ContourShading:

ClearAll[f];
f[x_, y_] := x - y;
reg = ConvexHullMesh[RandomReal[{-3, 3}, {15, 2}]];
ContourPlot[f[x, y], {x, -3, 3}, {y,} -3, 3}reg,
 Contours -> 20, ContourShading -> {Blue, LightRed}, 
 ContourStyle -> None,
 RegionFunction -> Function[{x, y}, {x, y} ∈ reg]]None]

Mathematica graphics

reg = ConvexHullMesh[RandomReal[{-3, 3}, {15, 2}]];
ContourPlot[f[x, y], {x, -3, 3y}, {y, -3reg, 3},
 Contours -> Flatten[Table[{c, c + 0.05}, {c, -6, 6, 0.3}]],
 ContourShading -> {Blue, LightRed}, ContourStyle -> None,
 RegionFunction -> Function[{x, y}, {x, y} ∈ reg]]None]]

Mathematica graphics

You could make a texture and use RegionPlot:

RegionPlot[
 ConvexHullMesh[RandomReal[{-3, 3}, {20, 2}]],
 PlotStyle -> Texture[ExampleData[{"ColorTexture", "MultiSpiralsPattern"}]]]

Mathematica graphics

Update

Vector graphics through ContourShading:

ClearAll[f];
f[x_, y_] := x - y;
reg = ConvexHullMesh[RandomReal[{-3, 3}, {15, 2}]];
ContourPlot[f[x, y], {x, -3, 3}, {y, -3, 3},
 Contours -> 20, ContourShading -> {Blue, LightRed}, 
 ContourStyle -> None,
 RegionFunction -> Function[{x, y}, {x, y} ∈ reg]]

Mathematica graphics

reg = ConvexHullMesh[RandomReal[{-3, 3}, {15, 2}]];
ContourPlot[f[x, y], {x, -3, 3}, {y, -3, 3},
 Contours -> Flatten[Table[{c, c + 0.05}, {c, -6, 6, 0.3}]],
 ContourShading -> {Blue, LightRed}, ContourStyle -> None,
 RegionFunction -> Function[{x, y}, {x, y} ∈ reg]]

Mathematica graphics

You could make a texture and use RegionPlot:

RegionPlot[
 ConvexHullMesh[RandomReal[{-3, 3}, {20, 2}]],
 PlotStyle -> Texture[ExampleData[{"ColorTexture", "MultiSpiralsPattern"}]]]

Mathematica graphics

Update

Vector graphics through ContourShading:

ClearAll[f];
f[x_, y_] := x - y;
reg = ConvexHullMesh[RandomReal[{-3, 3}, {15, 2}]];
ContourPlot[f[x, y], {x, y}  reg,
 Contours -> 20, ContourShading -> {Blue, LightRed}, 
 ContourStyle -> None]

Mathematica graphics

reg = ConvexHullMesh[RandomReal[{-3, 3}, {15, 2}]];
ContourPlot[f[x, y], {x, y}  reg,,
 Contours -> Flatten[Table[{c, c + 0.05}, {c, -6, 6, 0.3}]],
 ContourShading -> {Blue, LightRed}, ContourStyle -> None]]

Mathematica graphics

4 Responded to comment
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3 Rollback to Revision 1
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2 Responded to comment
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1
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