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MathGroup Archive 2012

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3d artifacts

  • To: mathgroup at smc.vnet.net
  • Subject: [mg127201] 3d artifacts
  • From: Roger Bagula <roger.bagula at gmail.com>
  • Date: Sat, 7 Jul 2012 05:30:06 -0400 (EDT)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com

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.



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