Re: Light and surface colors

*To*: mathgroup at smc.vnet.net*Subject*: [mg58717] Re: Light and surface colors*From*: Daniele Lupo <danwolf_no_spam_please_ at libero.it>*Date*: Fri, 15 Jul 2005 14:13:59 -0400 (EDT)*References*: <db7nrj$ms5$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Il Fri, 15 Jul 2005 07:16:03 +0000 (UTC), David Park ha scritto: > I tried to send you a Mathematica notebook with the code for this but your > server rejected it because of a full mailbox. This is because you must toggle _no_spam_please_... > > To make a shaded plot with regular Mathematica graphics we could use > ParametricPlot3D with the 4th argument in the parametrization. The 4th > argument gives graphics directives for plotting the surface. We don't have > to turn the Lighting off if we give SurfaceColor instead of a raw color. > > We redefine the pressure for the parameters of the ellipsoid. > > ellipsoid[a_, b_, c_][u_, v_] := {a Cos[v]Cos[u], b Cos[v]Sin[u], c Sin[v]} > pressure[x_, y_, z_] := x^2 + y^2 + Sin[4z]; > pressure[u_, v_] = > pressure[x, y, z] /. Thread[{x, y, z} -> ellipsoid[7, 5, 4][u, v]] > 49*Cos[u]^2*Cos[v]^2 + 25*Cos[v]^2*Sin[u]^2 + Sin[16*Sin[v]] > > Then define the parametrization for the ellipsoid with the function on it. > > ellipsoidfunction[a_, b_, c_][u_, v_] := {a Cos[v]Cos[u], b Cos[v]Sin[u], > c Sin[v], {EdgeForm[], SurfaceColor[Hue[pressure[u, v]/50]]}} .... I must study better this code... So, if I understood, you've created the color function with a parametrization, using u, v instead of x, y, z, creating in this way pressure[u_,v_], but I can't understand if this line 49*Cos[u]^2*Cos[v]^2 + 25*Cos[v]^2*Sin[u]^2 + Sin[16*Sin[v]] is in the definition or if it's an Output. I think the sendond, right? Because I can't understand why you use it in the definition of that function... And I did not know that I'm able to specify colors directives directly in the ellipsoid function: I've used them always as graphic command options... I think that this is the solution key for my problem, right? In this case, I can specify colors in the function, instead that in the ParametricPlot3D command, resolving the conflich between Ligthing and surface color in my original problem > > Then we can plot. > > ParametricPlot3D[ellipsoidfunction[7, 5, 4][u, v], {u, 0, 2*Pi}, > {v, -Pi/2, Pi/2}, > PlotPoints -> 100, > ImageSize -> 450]; I think to understand your work. Thanks for you effort!!! > > There are three problems with this plot. 1) The regular Mathematica lighting > tends to interfer with the colors on the surface. I think that creating light with GrayLevel can resolve this problem > 2) The Hue color function > is not easy to interpret. What is high pressure and what is low pressure? Yes, I know it, but this color was only a try. I'll find a better color function.... > 3) > It doesn't give a very accurate indication of what the shape of the contours > are. They are not quite as regular as one might expect. I know, but I am not be able to draw contour lines in the surface... > > My second solution uses DrawGraphics (from my web site below). It trims a > grid of polygons in the uv-plane to the contour regions and then maps the > resulting grids to the ellipsoidal surface. It uses the TwoColorScale > function to give a color scale that gives shades of blue for values below 25 > and shades of red for colors above 25. It is much easier to interpret > two-color plots - they are similar to cartographic maps. The NeutralLighting > option is used to turn down the color saturation of the regular lighting so > it doesn't interfer with the surface colors. I'll try it... > > Needs["DrawGraphics`DrawingMaster`"] > > colorfun = > TwoColorScale[{-0.29, 25, 49.7}, {ColorMix[RoyalBlue, Black][0.5], > RoyalBlue, ColorMix[RoyalBlue, White][0.8], ColorMix[Red, > White][0.8], > Red, ColorMix[Red, Black][0.5]}]; > > CUT > > Background -> Linen, > ImageSize -> 450]; This seems good... Unfortunately, in these days I've two tests at university, but I'll study your package when I can. Thanks again Daniele

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**Re: Light and surface colors**

**Re: Light and surface colors**