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What Method options are allowed for DensityPlot and ContourPlot? I am unable to find this information either in MMA documentation or in SE. Thanks.

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    $\begingroup$ Related: How to extract a list of available Method-s $\endgroup$ – Karsten 7. Dec 21 '14 at 4:23
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    $\begingroup$ @Karsten7,@Nasser, I tried the approach you recommended but received no Options for "DensityPlot" or "ContourPlot", even though with "NIntegrate" it worked fine. Suggestions? $\endgroup$ – bbgodfrey Dec 21 '14 at 5:41
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    $\begingroup$ AbsoluteOptions[ DensityPlot[Sin[x] Sin[y], {x, -4, 4}, {y, -3, 3}], Method ] gives {Method -> {"DefaultBoundaryStyle" -> Automatic, "DefaultPlotStyle" -> Automatic, "ScalingFunctions" -> None}} $\endgroup$ – Karsten 7. Dec 21 '14 at 5:56
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As far as I know there is no documented list of Method options for ContourPlot and DensityPlot. If you want to experiment there is a large list of strings in Charting`CommonDump`$VisualizationMethodOptions to have a look at. Some of these are option settings, some are option values. Most seem to have no effect on a simple ContourPlot and probably apply to different visualization functions or only apply in specific circumstances.

For an example here are a couple that affect the creation of the mesh:

GraphicsRow[
 ContourPlot[Sin[x y], {x, -2, 2}, {y, -2, 2},
    Mesh -> All, PlotPoints -> 5, Method -> {#}] & /@
  {Automatic, "Subdivision" -> "Loop", "PolygonReduction" -> 100}]

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This is the complete list:

{"ScalingFunctions", "PlotRandomSeed", "DraftRendering", "ArrayPlot", 
"InvertNormalsDirection", "BoundaryOffset", "Refinement", 
"MeshBoundaryValues", "StepsJoined", "SurfaceStitch", 
"UnboundedPolygons", "InterpolateMesh", "DownsampleWindow", 
"FilterMeshAll", "OriginalCoordinates", "ReturnMeshObject", 
"ReturnRawMeshObject", "MeshMaxRecursion", "ContourMaxRecursion", 
"DelaunayDomainScaling", "PolygonReverse", "VertexAliasTolerance", 
"Average", "Fan", "Seidel", "Constrained", "GradientAligned", 
"MeshRegions", "PathPolygons", "SimplifyPaths", 
"PackGraphicsComplex", "SnapContourVertex", "PlotTheme", 
"VertexColorsPalette", "VectorBackgroundPadding", "ReturnImage", 
"Closed3DRegion", "PolygonColoring", "Equalized", "EqualizeColor", 
"ColorFunctionData", "Valence", "Laplace", "Conformal", 
"RGBColorSpace", "GrayColorSpace", "ParallelPlotEvaluate", 
"ParallelPlotMethod", "ParallelPlotParameters", "LightingMethod", 
"DiffuseReflection", "AspectBasedShading", "Contrast", "Brightness", 
"Saturation", "SpatialResolution", "ElevationDefault", 
"IlluminationModel", "AngularDistanceRadius", "UseNumericalFunction", 
"NumericalFunction", "FlattenFunctions", "SuppressMessages", 
"MessagesHead", "MappingFunctions", "DomainMappingFunctions", 
"LegacyColorFunctionProcessing", "ContourShadingPrefixFunction", 
"ContoursPrefixFunction", "UseCaching", "CutMeshLines", 
"FillBoundaryLines", "Ungroup", "CloseMeshThickness", 
"ClipNoneMeshShading", "ClipAtPlotRange", "ClipMeshOverlay", 
"ClipBoundaryLines", "Subdivision", "CellDecomposition", "Divisions", 
"ControlValue", "VertexTolerance", "MaxBoundaryEdgeLength", 
"CellCuboids", "Dihedral", "Gaussian", "GradientNorm", "Loop", 
"Contouring", "Curvature", "ContourLevel", "PlanarRectangular", 
"Triangular", "Quad", "QuadTriangular", "Length", "Area", 
"Perimeter", "BhatiaLawrence", "AverageNormal", "WeightedNormal", 
"Barycenter", "Cotangents", "Circumcenter", "Incenter", "Inradius", 
"Circumradius", "InteriorAngles", "Dual", "OFF", "NOFF", "Frenet", 
"NaturalNeighbour", "InverseDistance", "Kriging", "MaxMemoryUse", 
"Intersect", "FullLattice", "MarchingCubes", "AdvancedMarchingCubes", 
"AdaptiveTriangular", "Octree", "OctreeCubes", "Algebraic", 
"Cubical", "Tetra", "Seeds", "Linear", "Bisect", "NoiseDelta", 
"ContourSpacing", "MeshSpacing", "Quantile", "CurveLength", 
"ArcLength", "DataLineMesh", "DataPointMesh", "GraphicsIndex", 
"SymbolicPiecewiseSubdivision", "pw", "PiecewiseTimeConstraint", 
"SymbolicPointsTimeConstraint", "Singularities", "Isolated", 
"SingularCurves", "SingularMaxRecursion", "ExclusionsOffset", 
"PolygonReduction", "Polygons", "PolygonContraction", 
"PointPlacement", "QuadricWeighting", "CompactnessRatio", 
"MeshPenalty", "BoundaryWeight", "EndPoint", "EndOrMidPoint", 
"LinearPoint", "OptimalPoint", "UniformWeight", "AreaWeight", 
"AngleWeight", "AverageWeight", "AreaAverageWeight", "NormalWeight", 
"VerticesGoal", "EdgesDistanceGoal", "MinArea", 
"PreserveInteriorFaces", "SegmentPartition", "SegmentLengthGoal", 
"LegendsFunction", "Legend", "Extrapolation", "Interpolation", 
"PointsToSpheres", "Caps", "ConnectEnds", "StreamlinesMethod", 
"StreamlinesSamplingStep", "StreamlinesInsertionStep", 
"StreamlinesParameterLimit", "StreamlinesNDSolve", 
"StreamlinesNumericalFunction", "LICLines", "LICMinHits", 
"LICMaxLines", "AccuracyGoal", "PrecisionGoal", "HSBChannel", 
"LICModulate", "NewtonFlow", "PerturbateFrame", "PerturbateSeeds", 
"ParseGlyphStyle", "LinePath", "LineArrow", "GlyphPath", 
"Directional", "DirectionalScaled", "Velocity", "VelocityScaled", 
"ControlPoints", "BSplineCurve", "BezierCurve", "NURBSCurve", 
"XSplineCurve", "BSplineShape", "BezierShape", "NURBSShape", 
"XSplineShape", "SharedMemoryReference", "Method", "Automatic", 
"None", "All", "True", "False"}
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    $\begingroup$ How did you obtain this list? Thanks. $\endgroup$ – bbgodfrey Dec 22 '14 at 0:01
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One should not be confused with method or option.

A method in the sense of Mathematica (See: Method)

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Options in the sense of Mathematica (See: Options)

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For DensityPlot or ContourPlot you can query for Options with ??DensityPlot or with ??ContourPlot:

enter image description here

The Link provided by @Karsten 7. (answer by @Nasser), is a really fabulous strategy to "unearth" the methods to a function.

For example (algorithm omitted) with:

r = getList2["NDSolve"];
Grid[r, Frame -> All, Alignment -> Left]

all "Methods" approved for NDSolve are listed:

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Edit

Since DensityPlot, ContourPlot and others have the same options as Graphics those rules are applicable (see Graphics and see "The following Method options can be given" ibid. For Functions Mathematica states:

With the default setting Method->Automatic, the Wolfram Language will automatically try to pick the best method for a particular computation.

See Method.

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  • $\begingroup$ I agree that "the link provided by @Karsten 7. (answer by @Nasser), is a really fabulous strategy to "unearth" the methods to a function." However, although it works well for "NDSolve" and "NIntegrate", it returns no useful information for "DensityPlot" or "ContourPlot". $\endgroup$ – bbgodfrey Dec 21 '14 at 18:39
  • $\begingroup$ True, but with ??ContourPlot you will retrieve all Options aviable, hence "Method" is only applicable to Functions with Method. $\endgroup$ – user9660 Dec 21 '14 at 18:45
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    $\begingroup$ indeed, ??ContourPlot, like Options[ContourPlot], returns a long list of options, including Method->Automatic. I wish to know what those methods are. (@Karsten7 identifies some of them in an earlier comment.) I should add that @Nasser provides two functions, getList and getList2. Neither returns information for "DensityPlot" or "ContourPlot". $\endgroup$ – bbgodfrey Dec 21 '14 at 19:02

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