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Re: 3d artifacts

  • To: mathgroup at smc.vnet.net
  • Subject: [mg127223] Re: 3d artifacts
  • From: Bob Hanlon <hanlonr357 at gmail.com>
  • Date: Mon, 9 Jul 2012 05:24:10 -0400 (EDT)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com
  • Delivered-to: mathgroup-newout@smc.vnet.net
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  • References: <201207070930.FAA20625@smc.vnet.net>

Resent since this hasn't shown up.

On Sat, Jul 7, 2012 at 8:14 AM, Bob Hanlon <hanlonr357 at gmail.com> wrote:
> Use Exclusions or define the functions with Piecewise
>
> g[t_] = -Pi/2 + Mod[t, Pi];
>
> f[t_] = If[-Pi/2 <= t <= Pi/2,
>    (1 - Cos[2 t])/2, (-1 + Cos[2 t])/2];
>
> ParametricPlot3D[{f[t] g[t], g[t]^2, f[t]},
>  {t, -Pi, Pi}, Exclusions -> {-Pi/2, Pi/2}]
>
> f[t_] = Piecewise[
>    {{(1 - Cos[2 t])/2, -Pi/2 <= t <= Pi/2}},
>    (-1 + Cos[2 t])/2];
>
> ParametricPlot3D[{f[t] g[t], g[t]^2, f[t]},
>  {t, -Pi, Pi}]
>
> ww[t_] := If[0 <= t < 2 Pi,
>    {Cos[t], Sin[t], Sin[2 t]},
>    If[2 Pi <= t <= 4 Pi,
>     {Sin[2 t], 15/10 Cos[t]/(1 + Sin[t]^2), Sin[t]/(1 + Sin[t]^2)},
>     {Cos[t], Sin[t], Sin[2 t]}]];
>
> ParametricPlot3D[ww[t], {t, 0, 4 Pi},
>  Exclusions -> {2 Pi, 4 Pi}]
>
> ww[t_] := Piecewise[
>    {{{Cos[t], Sin[t], Sin[2 t]},
>      0 <= t < 2 Pi},
>     {{Sin[2 t], 15/10 Cos[t]/(1 + Sin[t]^2), Sin[t]/(1 + Sin[t]^2)},
>      2 Pi <= t <= 4 Pi}},
>    {Cos[t], Sin[t], Sin[2 t]}];
>
> ParametricPlot3D[ww[t], {t, 0, 4 Pi}]
>
>
> Bob Hanlon
>
>
> On Sat, Jul 7, 2012 at 5:30 AM, Roger Bagula <roger.bagula at gmail.com> wrote:
>> In the two part defintion:
>>
>> f[t_] = If [ t >= -Pi/2 && t <= Pi/2, (1 - Cos[2*t])/2, (-1 + Cos[2*t])/2];
>> g[t_] = -Pi/2 + Mod[t, Pi];
>> ParametricPlot3D[{f[t]*g[t], g[t]*g[t], f[t]}, {t, -Pi, Pi}]
>>
>> A "handle" appears between the two parts of the curve.
>> I got the same effect when I tried to get a
>> patched manifold for the Whitehead Link:
>>
>> x = Cos[t];
>> z = Sin[t];
>> y = 2*Cos[t]*Sin[t];
>> w = {x, y, z};
>> {z1, y1} = 1/(1 + Sin[t]^2) {15/10 Cos[t], Sin[t] };
>> x1 = 2*Cos[t]*Sin[t];
>> w1 = {x1, y1, z1};
>> (* patched manifold function for Whitehead link*)
>> ww[t_] :=
>>   If[t >= 0 && t < 2*Pi, {Cos[t], Sin[t], Sin[2*t]},
>>    If[t >= 2*Pi && t <= 4*Pi, {Sin[2*t], 15/10 Cos[t]/(1 + Sin[t]^2),
>>      Sin[t]/(1 + Sin[t]^2)}, {Cos[t], Sin[t], Sin[2*t]}]];
>> ParametricPlot3D[ww[t], {t, 0, 4*Pi + 0.01}]
>>
>> I'd like to remove that artifact handle
>> by some simple method.
>>



-- 
Bob Hanlon



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