Re: ColorFunction and question about how to use it

*To*: mathgroup at smc.vnet.net*Subject*: [mg101668] Re: [mg101635] ColorFunction and question about how to use it*From*: "Kurt TeKolste" <ekt at fastmail.net>*Date*: Tue, 14 Jul 2009 05:33:18 -0400 (EDT)*References*: <200907120949.FAA16148@smc.vnet.net>*Reply-to*: ekt at fastmail.net

Sorry, but you're going to be embarrassed by this one: Correct the syntax from: Plot3D[x + y, {x, -2, 2}, {y, -2, 1}, ColorFunction -> Function[{x, y, z} -> Hue[z]]] to Plot3D[x + y, {x, -2, 2}, {y, -2, 1}, ColorFunction -> Function[{x, y, z} , Hue[z]]] You will see the expected rainbow of color Kurt TeKolste On Sun, 12 Jul 2009 01:49 -0400, "David" <david.b.a.epstein at googlemail.com> wrote: > Here is some Mathematica code > > In[1]:= Options[Plot3D] > > Out[1]= {AlignmentPoint -> Center, AspectRatio -> Automatic, > Axes -> True, AxesEdge -> Automatic, AxesLabel -> None, > AxesOrigin -> Automatic, AxesStyle -> {}, Background -> None, > BaselinePosition -> Automatic, BaseStyle -> {}, > BoundaryStyle -> GrayLevel[0], Boxed -> True, > BoxRatios -> {1, 1, 0.4}, BoxStyle -> {}, ClippingStyle -> Automatic, > ColorFunction -> Automatic, ColorFunctionScaling -> True, > ColorOutput -> Automatic, ContentSelectable -> Automatic, > ControllerLinking -> Automatic, ControllerMethod -> Automatic, > ControllerPath -> Automatic, CoordinatesToolOptions -> Automatic, > DisplayFunction :> $DisplayFunction, Epilog -> {}, > Evaluated -> Automatic, EvaluationMonitor -> None, > Exclusions -> Automatic, ExclusionsStyle -> None, FaceGrids -> None, > FaceGridsStyle -> {}, Filling -> None, FillingStyle -> Opacity[0.5], > FormatType :> TraditionalForm, ImageMargins -> 0., > ImagePadding -> All, ImageSize -> Automatic, LabelStyle -> {}, > Lighting -> Automatic, MaxRecursion -> Automatic, Mesh -> Automatic, > MeshFunctions -> {#1 &, #2 &}, MeshShading -> None, > MeshStyle -> Automatic, Method -> Automatic, > NormalsFunction -> Automatic, PerformanceGoal :> $PerformanceGoal, > PlotLabel -> None, PlotPoints -> Automatic, > PlotRange -> {Full, Full, Automatic}, PlotRangePadding -> Automatic, > PlotRegion -> Automatic, PlotStyle -> Automatic, > PreserveImageOptions -> Automatic, Prolog -> {}, > RegionFunction -> (True &), RotationAction -> "Fit", > SphericalRegion -> False, Ticks -> Automatic, TicksStyle -> {}, > ViewAngle -> Automatic, ViewCenter -> Automatic, > ViewMatrix -> Automatic, ViewPoint -> {1.3, -2.4, 2.}, > ViewRange -> All, ViewVector -> Automatic, ViewVertical -> {0, 0, 1}, > WorkingPrecision -> MachinePrecision} > > > In[2]:= > Plot3D[x + y, {x, -2, 2}, {y, -2, 1}, > ColorFunction -> Function[{x, y, z} -> Hue[z]]] > > Plot3D[x + y, {x, -2, 2}, {y, -2, 1}] > ----------------------------------------------------------------------------- > The first Plot3D command gives me only black and white. Why is that? > Otherwise it looks fine. > The second Plot3D command gives me the graph in a uniform blue. Why is > that? Apart from the colour, the two graphs look the same. > > What I am actually trying to do is more complicated, but I need to > understand the simplest situations first: I have a given real valued > function f of two variables. I can show that there are exactly two > {x,y} locations at which the two partial derivatives of f are > simultaneously zero. I would like to demonstrate this through Plot3D, > for example by plotting the sum of the squares of the two partial > derivatives. The function surface should be mostly transparent, but > the surface would be coloured (say red) whenever the sum of squares > lies in the closed interval [0,epsilon], with the value of the > positive number epsilon under user control. Transparency would enable > one to see the zeros even if the surface is in the way. > > My many attempts to achieve this have all failed. > > Thanks for any help. > > David > -- Kurt ekt at fastmail.net

**References**:**ColorFunction and question about how to use it***From:*David <david.b.a.epstein@googlemail.com>

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**Re: ColorFunction and question about how to use it**

**ColorFunction and question about how to use it**

**Re: ColorFunction and question about how to use it**