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RE: ListPlot vs ListPlot3D
*To*: mathgroup at smc.vnet.net
*Subject*: [mg28935] RE: [mg28884] ListPlot vs ListPlot3D
*From*: "Wolf, Hartmut" <Hartmut.Wolf at t-systems.de>
*Date*: Sat, 19 May 2001 22:27:52 -0400 (EDT)
*Sender*: owner-wri-mathgroup at wolfram.com
Please see below:
> -----Original Message-----
> From: Otto Linsuain [SMTP:linsuain+ at andrew.cmu.edu]
To: mathgroup at smc.vnet.net
> Sent: Thursday, May 17, 2001 10:23 AM
> To: mathgroup at smc.vnet.net
> Subject: [mg28884] ListPlot vs ListPlot3D
>
>
> Dear Mathematica experts, I was wondering if there is a way of plotting
> a 3D graph using a rectangular array of z-values USING THE CORRESPONDING
> VALUES OF X AND Y.
>
> Here is what I mean:
>
> with a 2D plot, one can do:
>
> ListPlot[ {y1,y2,y3,.........yn} ] and this will give a graph of the
> points
>
> {y1,1} ,{y2,2}, {y3,3},....{yn,n}, i.e. it will use the integers
> 1,2,3,...n as the x values.
>
> One can, however, write
>
> ListPlot[ { {x1,y1}, {x2,y2}, {x3,y3}, ... {xn,yn} }]
>
> and get a graph with user-specified values for x and y.
>
> There doesn't seem to be an analogous thing for ListPlot3D. The values
> of x and y seem to be always {1,1}, {1,2},{2,1},{2,2},.......{n,n}
>
> Any ideas? Thanks in advance. Otto Linsuain.
>
[Hartmut Wolf]
Otto,
let me make up an example: Let's assume we have a regular, but not evenly
spaced grid for xy-values:
xgrid=Table[Pi*Sin[x],{x,0,Pi/2,Pi/2/14}];
ygrid=Table[Pi/2*Sin[y],{y,-Pi/2,Pi/2, Pi/14}];
xygrid=Outer[List,xgrid,ygrid];
and z-values for say function Sin[x]*Cos[y] sampled at the grid.
tt=Apply[Sin[#1]Cos[#2]& ,xygrid,{2}]//N;
If we plot it with ListPlot3D we certainly get a distorted view
gg=ListPlot3D[Transpose[tt]]
- SurfaceGraphics -
What we have to do, is to shift the integer grid of ListPlot3D to the real,
true xy-Grid of the problem. We cannot do that with SurfaceGraphics, so we
convert that to a Graphics3D object.
gg1=Graphics3D[gg];
Show[gg1];
So far display is unchanged, but now we can put the points onto the real
grid:
gg2=gg1/.Polygon[points_] :>
Polygon[points/. {x_,y_,z_} :> xgrid[[Round[x]]],
ygrid[[Round[y]]],z}]
- Graphics3D -
Show[gg2]
- Graphics3D -
Compare that with
Plot3D[Sin[x]Cos[y],{x,0,Pi},{y,-Pi/2,Pi/2}]
- SurfaceGraphics -
and we watch the same 3D-shape, however at different grids. So we have got
the "real" plot, sampled at our own regular, yet not-equally spaced grid by
only use of the original data. And the axes come out correctly too.
This method of transformation also may be used to get a more dense sampling
at regions of special interest (e.g. at rapid variation). The grid still has
to stay regular though.
-- Hartmut
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