Re: 3D-plot over a triangle

*To*: mathgroup at smc.vnet.net*Subject*: [mg65032] Re: [mg65021] 3D-plot over a triangle*From*: "David Park" <djmp at earthlink.net>*Date*: Sun, 12 Mar 2006 23:57:49 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

Pluton, Here is your plot. I used ParametricPlot3D to draw the surface. Needs["Graphics`Colors`"] f[s_, t_] := 4s t ParametricPlot3D[{s, w - s w, -4 (-1 + s) s w}, {s, 0, 1}, {w, 0, 1}, PlotPoints -> 15, BoxRatios -> {1, 1, 1/2}, AxesLabel -> {s, t, f}, PlotLabel -> SequenceForm[f[s, t], " on a Triangular Domain"], ViewPoint -> {2.292, -1.483, 2.000}, Background -> Linen, ImageSize -> 450]; Notice that I used a reparametrization of the function, and of t so that the plot statement now uses fixed iterators. (Plot does not allow dependent iterators such as are allowed in Integrate.) How did I get the reparametrization? By using the IteratorSubstitution routine from the DrawGraphics package. It replaces t by a new variable w that has a fixed iteration range. Needs["DrawGraphics`DrawingMaster`"] IteratorSubstitution[{s, t, f[s, t]}, {t, 0, 1 - s}] {{s, w - s w, -4 (-1 + s) s w}, {w, 0, 1}} The first item above is the new parametrization of the surface in terms of s and w, and the second item is the w iterator. David Park djmp at earthlink.net http://home.earthlink.net/~djmp/ From: pluton [mailto:plutonesque at gmail.com] To: mathgroup at smc.vnet.net Hi there, I want to plot the following function f = 4*s*t over a triangle defined by s going from 0 to 1 and t from 0 to 1-s. I tried Plot3D[4st, {s, 0, 1}, {t, 0, 1-s}]; but it does not work. Any suggestion ? Thank you, Pluton