How can I customize the style of a discretization of a Region?

Question

This works as expected:

BoundaryDiscretizeRegion[RegionUnion[Triangle[], Rectangle[{0.5, 0}, {1, 1}]]]

Now, suppose I want to change the fill color to green and the edge color to red. How would I do that?

(I tried using RegionPlot, but that didn't work)

Answer 1

BoundaryDiscretizeRegion takes most of the options available to Graphics:

Complement[
    Options[Graphics][[All, 1]],
    Options[BoundaryDiscretizeRegion][[All, 1]]
]

{ColorOutput, ContentSelectable, CoordinatesToolOptions, FormatType, \ ImageSizeRaw, PreserveImageOptions}

This means, that you should be able to use Graphics options to control the appearance of the discretization. Rather than just giving you the options to use, I will show you how to find out what options are available for this purpose. The box form of Graphics is GraphicsBox, and the options for GraphicsBox are:

Options[GraphicsBox]

{AlignmentPoint -> Center, AspectRatio -> Automatic, Axes -> False, AxesLabel -> None, AxesOrigin -> {Automatic, Automatic}, AxesStyle -> {}, Background -> None, BaseStyle -> {}, BaselinePosition -> Automatic, ColorOutput -> Automatic, ContentSelectable -> Automatic, CoordinatesToolOptions :> Automatic, DefaultAxesStyle -> "GraphicsAxes", DefaultBaseStyle -> "Graphics", DefaultFrameStyle -> "GraphicsFrame", DefaultFrameTicksStyle -> "GraphicsFrameTicks", DefaultGridLinesStyle -> "GraphicsGridLines", DefaultLabelStyle -> "GraphicsLabel", DefaultTicksStyle -> "GraphicsTicks", Epilog -> {}, FormatType -> TraditionalForm, Frame -> False, FrameLabel -> None, FrameStyle -> {}, FrameTicks -> Automatic, FrameTicksStyle -> {}, GridLines -> None, GridLinesStyle -> {}, ImageMargins -> 0., ImageMarkers -> None, ImagePadding -> All, ImageSize -> Automatic, ImageSizeRaw -> Automatic, ImageSizeRules -> Automatic, LabelStyle -> {}, Method -> {}, PlotLabel -> None, PlotRange -> All, PlotRangeClipping -> False, PlotRangePadding -> Automatic, PlotRegion -> {{0., 1.}, {0., 1.}}, PreserveImageOptions -> Automatic, Prolog -> {}, RotateLabel -> True, Ticks -> Automatic, TicksStyle -> {}}

In particular, note the DefaultBaseStyle option:

Options[GraphicsBox, DefaultBaseStyle]

{DefaultBaseStyle -> "Graphics"}

The DefaultBaseStyle points to the style "Graphics". This style has the following settings:

CurrentValue[{StyleDefinitions, "Graphics"}]

{CellMargins -> {{4, Inherited}, {Inherited, Inherited}}, CellGroupingRules -> "GraphicsGrouping", StripStyleOnPaste -> False, PageBreakWithin -> False, GeneratedCell -> True, CellAutoOverwrite -> True, ShowCellLabel -> False, DefaultFormatType -> DefaultOutputFormatType, ContextMenu -> {MenuItem["Cu&t Graphics Selection", "Cut"], MenuItem["&Copy Graphics Selection", "Copy"], MenuItem["&Paste into Graphic", FrontEnd`Paste[After]], Delimiter, MenuItem["&Drawing Tools", FrontEndExecute[{FrontEnd`NotebookOpen[ FrontEnd`FindFileOnPath["DrawingTools.nb", "PrivatePathsSystemResources"]]}]], MenuItem["&Get Coordinates", FrontEndExecute[FrontEnd`Select2DTool["GetCoordinates"]]], Delimiter, MenuItem["G&roup", "Group"], MenuItem["&Ungroup", "Ungroup"], Delimiter, MenuItem["Move to &Front", "MoveToFront"], MenuItem["Move to &Back", "MoveToBack"], MenuItem["Move For&ward", "MoveForward"], MenuItem["Move Bac&kward", "MoveBackward"]}, "AutoStyleOptionsHighlightMisspelledWords" -> False, LanguageCategory -> "NaturalLanguage", FormatType -> StandardForm, ShowStringCharacters -> False, NumberMarks -> False, CounterIncrements -> "Graphics", ImageMargins -> {{43, Inherited}, {Inherited, 0}}, Arrowheads -> 0.04, Dashing -> None, CapForm -> "Square", JoinForm -> {"Miter", 3.25}, LineColor -> GrayLevel[0], LineOpacity -> 1, EdgeColor -> GrayLevel[0], EdgeOpacity -> 1, EdgeThickness -> Medium, EdgeDashing -> None, EdgeCapForm -> "Square", EdgeJoinForm -> {"Miter", 3.25}, FrontFaceColor -> GrayLevel[0], BackFaceColor -> GrayLevel[0], FrontFaceOpacity -> 1, BackFaceOpacity -> 1, GraphicsColor -> GrayLevel[0], PointSize -> Absolute[3], Thickness -> Medium, Opacity -> 1, DrawEdges -> False, StyleMenuListing -> None, FontFamily -> "Arial", FontSize -> 10, FontWeight -> "Plain", FontColor -> GrayLevel[0], FontOpacity -> 1}

You see options controlling LineColor, EdgeColor, etc., and you can play with changing these settings to see what their effects are. To change the fill color and the edge color of your discretization, you could use:

BaseStyle -> {FrontFaceColor -> Green, EdgeColor -> Red, EdgeThickness -> .02}

Using this BaseStyle in your discretization produces:

BoundaryDiscretizeRegion[
    RegionUnion[Triangle[], Rectangle[{0.5, 0}, {1, 1}]],
    BaseStyle -> {FrontFaceColor -> Green, EdgeColor -> Red, EdgeThickness -> .02}
]

Answer 2

You could use the option MeshCellStyle.

BoundaryDiscretizeRegion[
  RegionUnion[Triangle[], Rectangle[{0.5, 0}, {1, 1}]], 
  MeshCellStyle -> {1 -> Directive[Thick, Red], 2 -> Green}
]