Re: Plotting questions

*To*: mathgroup at smc.vnet.net*Subject*: [mg19979] Re: [mg19949] Plotting questions*From*: "David Park" <djmp at earthlink.net>*Date*: Thu, 23 Sep 1999 23:26:25 -0400*Sender*: owner-wri-mathgroup at wolfram.com

Michael Chang wrote: >Hi again! > >Sorry, but in my rush, I sent out the *wrong* example regarding my plotting >difficulties in an earlier email (about 1 hour ago) today. > >I *meant* to use the following example: > >Suppose > >x(t)=(10^(1-g)-(1-g)*t)^(1/(1-g)) > >where 0.5<g<1 (say). > >I want to simulate this function x(t) for varying t ... specifically, > >0<=t<=10^(1-g)/(1-g) > >so that x(t) remains *real* for all t. For t > t_f := 10^(1-g)/(1-g), > >define x(t)=0. > >What I'd like to do is get a parametric 3d *surface* plot with g, t as two >axis, and x(t) as the third axis. I've struggled with this for a while, >but can't seem to do this using Plot3D (due to the fact that the range of >values for t *cannot* be given as a function of g ... i.e. I must use > >{t,0,10} (say), and *not* >{t,0,10^(1-g)/(1-g)} > >which is what I really want). > >I suspect that I have to change my definition of x(t) so that it knows >that if t>t_f, then x(t) should be 0, so that I can then use a fixed >plotrange for t, but I don't know how to do this ... > >Sorry for any confusion! > >Thanks again! > >Mike! > Michael, There is a package at my web site called DrawingCube which contains a routine for doing what you wish. I will show here the specific results of the routine and a plotting statement for your function which you can plot without the package. x[t_, g_] = (10^(1 - g) - (1 - g)*t)^(1/(1 - g)); This is a 3D parametric representation of your function which is necessary to produce the plot you wish: p[t_, g_] = {t, g, x[t, g]} {t, g, (10^(1 - g) - (1 - g)*t)^(1/(1 - g))} This is the routine in my package: ?IteratorSubstitution "IteratorSubstitution[expr, {var, lim1, lim2}, newvar:w] is used to transform \ a plot range iterator, which may contain variable limits, to one which \ contains constant limits. The plotting expr is transformed to the new \ variable and returned along with the new iterator." Using this on the parametric representation: IteratorSubstitution[{t, g, (10^(1 - g) - (1 - g)*t)^(1/(1 - g))}, {t, 0, 10^(1 - g)/(1 - g)}] {{-((10^(1 - g)*w)/(-1 + g)), g, (-10^(1 - g)*(-1 + w))^ (1/(1 - g))}, {w, 0, 1}} We can now plot the new parametric representation using g and w as the plotting parameters. We actually need a slightly restricted range of g to obtain a nice looking plot. ParametricPlot3D[{-((10^(1 - g)*w)/(-1 + g)), g, (-10^(1 - g)*(-1 + w))^(1/(1 - g))}, {g, 0.5, 0.95}, {w, 0, 1}, BoxRatios -> {1, 1, 1}, AxesLabel -> {t, g, "x[t,g]"}, AxesEdge -> {{-1, -1}, {1, -1}, {-1, -1}}, FaceGrids -> {{0, 0, -1}, {-1, 0, 0}, {0, 1, 0}}]; Try this out and see if it is what you intended. David Park djmp at earthlink.net http://home.earthlink.net/~djmp/