Re: Adding markers on the surface of a Plot3D?

*To*: mathgroup at smc.vnet.net*Subject*: [mg89356] Re: Adding markers on the surface of a Plot3D?*From*: "David Park" <djmpark at comcast.net>*Date*: Sat, 7 Jun 2008 02:57:03 -0400 (EDT)*References*: <g2b4o8$nm2$1@smc.vnet.net>

Here is a practice function. f[x_, y_] := x^2 - 2 x y^2 + y^2 The following draws only two mesh lines at specific values. MeshStyle is used to give a style to the lines. Plot3D[f[x, y], {x, 0, 1}, {y, 0, 1}, PlotStyle -> ColorData["Legacy"]["DarkSeaGreen"], Mesh -> {{.5}, {.5}}, MeshStyle -> Directive[Black, AbsoluteThickness[2]], Lighting -> "Neutral"] The following does the same thing, only now the style is embedded directly with each mesh line. Plot3D[f[x, y], {x, 0, 1}, {y, 0, 1}, PlotStyle -> ColorData["Legacy"]["DarkSeaGreen"], Mesh -> {{{.5, Directive[Black, AbsoluteThickness[2]]}}, {{.5, Directive[Black, AbsoluteThickness[2]]}}}, Lighting -> "Neutral"] The following draws a set of mesh lines in red and then draws two special mesh lines in thick black. Plot3D[f[x, y], {x, 0, 1}, {y, 0, 1}, PlotStyle -> ColorData["Legacy"]["DarkSeaGreen"], Mesh -> {{Sequence @@ Table[{x, Red}, {x, .1, .9, .1}], {.5, Directive[Black, AbsoluteThickness[2]]}}, {Sequence @@ Table[{x, Red}, {x, .1, .9, .1}], {.5, Directive[Black, AbsoluteThickness[2]]}}}, Lighting -> "Neutral"] The following uses Presentations to draw the special lines as extra curves. We can just combine all the various items in one Draw3DItems statement. Needs["Presentations`Master`"] Draw3DItems[ {Legacy@DarkSeaGreen, Draw3D[f[x, y], {x, 0, 1}, {y, 0, 1}], Black, AbsoluteThickness[2], ParametricDraw3D[{.5, y, f[.5, y] + .01}, {y, 0, 1}], ParametricDraw3D[{x, .5, f[x, .5] + .01}, {x, 0, 1}]}, NeutralLighting[.0, .5, .1], Axes -> True, BoxRatios -> {1, 1, 1/2}, ImageSize -> 350] The following displays the special mesh lines dynamically using a Slider2D. Manipulate[ Draw3DItems[ {Legacy@DarkSeaGreen, Draw3D[f[x, y], {x, 0, 1}, {y, 0, 1}], Black, AbsoluteThickness[1], ParametricDraw3D[{First[u], y, f[First[u], y] + .02}, {y, 0, 1}], ParametricDraw3D[{x, Last[u], f[x, Last[u]] + .02}, {x, 0, 1}]}, NeutralLighting[.0, .5, .1], Axes -> True, BoxRatios -> {1, 1, 1/2}, ImageSize -> 350], {u, {0, 0}, {1, 1}}] The following is a fancier presentation using a DynamicModule and a Grid containing the Slider2D and digital readout. Dynamic coordination of graphical and digital information is a wonderful method for exploring a mathematical relation. It's really like having your cake and eating it too. You can never get this on a dead static printed page. DynamicModule[{u = {.5, .5}}, Column[{ (* Digital control and readout *) Panel@Grid[{ {Item[Style["Dynamic Surface Marker", 16], Alignment -> Center], SpanFromLeft}, {Slider2D[Dynamic[u]], {x, y} == Dynamic[u]}, {SpanFromAbove, HoldForm[f[x, y]] == Dynamic[f @@ u]} }, ItemSize -> 10, Alignment -> Left], (* Graphics *) Draw3DItems[ {Legacy@DarkSeaGreen, Draw3D[f[x, y], {x, 0, 1}, {y, 0, 1}], Orange, Dynamic@Sphere[Flatten[{u, f @@ u}], .02]}, NeutralLighting[.0, .5, .1], Axes -> True, PlotRange -> {{0, 1}, {0, 1}, {0, 1}}, PlotRangePadding -> .05, BoxRatios -> {1, 1, 1/2}, ImageSize -> 350] }] ] -- David Park djmpark at comcast.net http://home.comcast.net/~djmpark/ "AES" <siegman at stanford.edu> wrote in message news:g2b4o8$nm2$1 at smc.vnet.net... > I'd like to highlight the two mesh lines that pass through a certain > central point -- let's call it the point {xc,yc} -- on a Plot3D by > thickening those two lines relative to the other mesh lines, or giving > them a distinctive color, or . . . > > Or put a dot on the surface at the point {xc, yc, f[xc,yc]} to identify > this location on the surface . . . > > Or run a vertical "post" up through that point using something like > Line[{xc, yc, 0}, {xc, yc, 2*f[xc,yc]}}] (with the part of the post > below the surface not being seen if you look at the surface from > above) . . . > > I think I've so far tested and confirmed every possible way in which > each of these tasks _can't_ be done . . . > > [And would someone want to help me understand _why_ the > Show[ - - - - -] command (followed by a semicolon) no longer works, or > can no longer be used, as one of a sequence of multiple expressions > within a longer cell? And why it can't even have a semicolon following > it as the last line in a cell? I just can't envision the logic of why > this was a necessary (or optional?) interface design decision -- isn't > Show[---] an expression?] >