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MathGroup Archive 2004

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Re: Conditional Plots

  • To: mathgroup at smc.vnet.net
  • Subject: [mg50487] Re: Conditional Plots
  • From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
  • Date: Tue, 7 Sep 2004 05:43:48 -0400 (EDT)
  • Organization: Universitaet Leipzig
  • References: <chblrt$rme$1@smc.vnet.net>
  • Reply-to: kuska at informatik.uni-leipzig.de
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,

something like

Clear[BlendSplit]
BlendSplit[{{p1_, f1_}, {_, f2_}}, _] /; Sign[f1] == Sign[f2] := {p1,
f1}

If[$VersionNumber < 5.0,
  BlendSplit[{{p1_, f1_}, {p2_, f2_}}, blend_] :=
    
    Module[{func, t, sol, crossp},
        func = blend @@ (p1*(1 - t) + p2*t);
        sol = t /. FindRoot[Evaluate[func], {t, {0, 1}}];
       crossp = p1*(1 - sol) + p2*sol;
      Sequence @@ {{p1, f1}, {crossp, 0}, {p2, f2}}
      ],
  (* Else *)

  BlendSplit[{{p1_, f1_}, {p2_, f2_}}, blend_] :=
    
    Module[{func, t, sol, crossp},
        func = blend @@ (p1*(1 - t) + p2*t);
        sol = First[t /. FindRoot[Evaluate[func], {t, {0, 1}}]];
       crossp = p1*(1 - sol) + p2*sol;
      Sequence @@ {{p1, f1}, {crossp, 0}, {p2, f2}}
      ]
  ]

BlendPoly[Polygon[pnts_], blend_] :=
  Module[{feval, p1, p2, addp1, i, n},
      feval = {#, blend @@ #} & /@ pnts;
      feval = 
      BlendSplit[##, blend] & /@ Transpose[{feval, RotateLeft[feval]}];
     If[And @@ (Last[#] > 0 & /@ feval),
        Return[Polygon[pnts]],
      ];
     p1 = First /@ Select[feval, Last[#] >= 0 &];
     Polygon[p1]
    ]


gg = Graphics3D[
    Plot3D[Sin[(x + y)*y], {x, -2Pi, 2Pi}, {y, -2Pi, 2Pi}, PlotPoints ->
60]];


Show[Graphics3D[
    Cases[gg, _Polygon, Infinity] /.
        
      p_Polygon :> BlendPoly[p, Function[{x, y, z},
                                          - ( x^2 + y^2 - 4)]], 
    PlotRange -> All]
  ]


??

Regards
  Jens


matt wrote:
> 
> Dear all,
> 
> Í´m trying to produce a 3D plot with a 2D ploygon (within unit circle)
> as its base. Equivalently, I want my 3D surface to sit inside (be
> bounded by) a cylinder with n-gon cross section.
> 
> How can I trim off the edges?
>  I´ve tried to use
> If[ (condition), Plot, Blah] but it doesn´t seem to work.....


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