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MathGroup Archive 1999

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Re: Smarter 3D listplot clipping

  • To: mathgroup at smc.vnet.net
  • Subject: [mg15963] Re: Smarter 3D listplot clipping
  • From: Martin Kraus <mkraus at theorie3.physik.uni-erlangen.de>
  • Date: Fri, 19 Feb 1999 03:26:52 -0500
  • Organization: Regionales Rechenzentrum Erlangen, Germany
  • References: <7ag4ib$b0i@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Dan Truong wrote:
> 
> In Short:
> A question for Graphics3D/ListPlot3D knowledgeable people...
> I want the Ideal clipping below, not regular
> mathematica clipping.
> 
> > Before:
> >     ___
> >  __/\__\
> >  \_\/
> >
> > Regular Clipping:
> >     ___
> >    /\__\
> >    \/
> >
> > Ideal: (how to do that?)
> >     ___
> >     \__\
> >

I do not think that this is ideal. 
For each clipped point you have to delete 
4 polygons. Thus, the holes in your plot will be
pretty large.

> Work setting:
> I have to display 3D plots for non square arrays.

Then the function ListSurfacePlot3D from the 
Graphics`Graphics3D` package would be more appropriated.
(See my adaption of Tom Wickham-Jones tutorial at:
http://theorie3.physik.uni-erlangen.de/~mkraus/tutorial/tutorial2_3.html)

> I use a square array, but zero values are meaningless.
> When I plot the curve however zero values change the
> look of the curve (making it harder to read).
> I want to clip-out zero samples ideally: Zero samples
> should not change the curves. Regular clipping however
> clip the curve when it reaches zero, which means the
> drop (see Reg. figure) is visible, clipping only the flat
> zero values (Before figure). I don't want the drops towards
> clipped regions drawn at all (3rd fig).
> Note: I am stacking multiple ListPlot3D in the same figure
> (that's why erratic drops bug me, since the surfaces
> do not have any reason to cross), so the ListPlots are
> already converted to Graphics3D. I also use the neat colorization
> scheme given by jtischer on the forum a couple of weeks ago.
> 
> Has someone found a solution to this problem?
> 
> Would it be possible in Graphics3D to search for all polygons
> with a corner having z < clipped region, and to remove those?
> (I expect it to be harder to do while in ListPlot format (?) )
> If so, how could this be done (ie enumerate all polygons in a
> Graphics3D object and delete those we wish),

Here we go:

array=Table[If[Random[]>0.1,Sin[i/2.]*Cos[j/2.]+1,0],{i,1,20},{j,1,20}];
(* generates a table of values with "holes" *)

polys=Table[
    Polygon[{{j,i,array[[i,j]]},{j,i+1,array[[i+1,j]]},{j+1,i+1,
         
array[[i+1,j+1]]},{j+1,i,array[[i,j+1]]}}],{i,1,Length[array]-1},{j,
      1,Length[array[[1]]]-1}];
(* generates the list of polygons *)

clippedpolys=
  DeleteCases[polys,Polygon[l_List]/;Count[l,{_,_,z_/;(z<=0.)}]>0,2];
(* deletes the polygons which include points with z <= 0. *)

Show[Graphics3D[clippedpolys]];
(* shows the rest of the polygons *)

> and could it be implemented as a function like:
> 
>  clippedFig3D = True3DClip[fig3D];
>  Show[clippedFig3D];
> 
> Dan-

Sure, that could be done! ;)

Hope that helps

Martin Kraus


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