Re: Slicing a surface

*To*: mathgroup at smc.vnet.net*Subject*: [mg97386] Re: Slicing a surface*From*: "Sjoerd C. de Vries" <sjoerd.c.devries at gmail.com>*Date*: Thu, 12 Mar 2009 02:19:23 -0500 (EST)*References*: <gp7vrq$1c7$1@smc.vnet.net>

Perhaps you could use Solve. Example: some x[s,t],y[s,t],z[s,t] functions as you described: p1 = ParametricPlot3D[{s + t^2, 3 s t, t - s }, {s, -1, 1}, {t, -1, 1}] finding a solution for a fixed z: In[156]:= Assuming[ {x \[Element] Reals, y \[Element] Reals, z \[Element] Reals}, Solve[{x == s + t^2, y == 3 s t, z == t - s, z == 0}, {x},= {s, t}]] Out[156]= {{x -> 1/3 (-Sqrt[3] Sqrt[y] + y)}, {x -> 1/3 (Sqrt[3] Sqrt[y] + y)}} Plot the contour together with the surface: p2 = ParametricPlot3D[{1/3 (-Sqrt[3] Sqrt[y] + y), y, 0}, {y, -3, 3}, PlotStyle -> Red]; p3 = ParametricPlot3D[{1/3 (Sqrt[3] Sqrt[y] + y), y, 0}, {y, -3, 3}, PlotStyle -> Red] Show[{p3, p2, p1}, PlotRange -> All] and now in 2D: Plot[{1/3 (Sqrt[3] Sqrt[y] + y), -(1/3) (Sqrt[3] Sqrt[y] + y)}, {y, -3, 3}] Cheers -- Sjoerd On Mar 11, 11:22 am, SotonJames <james.fre... at soton.ac.uk> wrote: > Hi, > > I've generated a surface in Mathematica 6 by solving some simultaneous eq= uations for three variables (x[s,t], y[s,t] and z[s,t]) and parametric plot= ting the variables against each other, with s and t the surface parameters.= I want to get a one-dimensional cross-section of the surface, ie a slice t= hrough constant z, but I don't know how to do this. Taking a constant s or = t is the best I can do, but isn't nearly the same. I'd like the line cross-= section to be displayed as a flat 2D graph, rather than be embedded in the = original 3D space. > > Any suggestions on how to do this? > > Many thanks in advance, > > James