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Re: 3d artifacts
Posted:
Jul 9, 2012 5:24 AM
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Resent since this hasn't shown up.
On Sat, Jul 7, 2012 at 8:14 AM, Bob Hanlon <hanlonr357@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@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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