       Re: 3d artifacts

• To: mathgroup at smc.vnet.net
• Subject: [mg127361] Re: 3d artifacts
• From: Roger Bagula <roger.bagula at gmail.com>
• Date: Fri, 20 Jul 2012 03:49:32 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• Delivered-to: mathgroup-newout@smc.vnet.net
• Delivered-to: mathgroup-newsend@smc.vnet.net
• References: <201207070930.FAA20625@smc.vnet.net> <jte808\$ss6\$1@smc.vnet.net>

```Bob Hanlon
You and Park both thought exceptions would work.
Once add an tube function Parametric3D
no longer performs the Exceptions it appears.
I tried a tube program  that usually works
and then my triaxial tubes topological product method:
Clear[ww, x, t, p, f, g]
ww[t_, p_] :=
If[t >= 0 &&
t < 2*Pi, {(10 + Cos[p])*Cos[t], (10 + Cos[p + 2*Pi/3])*
Sin[t], (10 + Cos[p - 2*Pi/3])*Sin[2*t]},
If[t >= 2*Pi &&
t <= 4*Pi, {(10 + Cos[p])*
Sin[2*t], (10 + Cos[p + 2*Pi/3])*15/
10 Cos[t]/(1 + Sin[t]^2), (10 + Cos[p - 2*Pi/3])*
Sin[t]/(1 + Sin[t]^2)}, {(10 + Cos[p])*
Cos[t], (10 + Cos[p + 2*Pi/3])*Sin[t], (10 + Cos[p - 2*Pi/3])*
Sin[2*t]}]];
ParametricPlot3D[ww[t, p], {t, 0, 4*Pi + 0.01}, {p, 0, 2*Pi},
Exclusions -> {2 Pi, 4 Pi}, Boxed -> False, Axes -> False,
ColorFunction -> "GreenBrownTerrain", MeshFunctions -> {#3 &},
PlotPoints -> {35, 100}]
ParametricPlot3D[ww[t, p], {t, 0, 4*Pi + 0.01}, {p, 0, 2*Pi},
Exclusions -> Range[0, 4 \[Pi], \[Pi]/4], Boxed -> False,
Axes -> False, ColorFunction -> "GreenBrownTerrain",
MeshFunctions -> {#3 &}, PlotPoints -> {35, 100}]
(* bicuspoid manifold definition*)
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[{(10 + Cos[p])*f[t]*g[t], (10 + Cos[p + 2*Pi/3])*
g[t]*g[t], (10 + Cos[p - 2*Pi/3])*f[t]}, {t, -Pi, Pi}, {p, 0,
2*Pi}, Exclusions -> Range[-\[Pi], \[Pi], \[Pi]/4], Boxed -> False,
Axes -> False, ColorFunction -> "GreenBrownTerrain",
MeshFunctions -> {#3 &}, PlotPoints -> {35, 100}]
ParametricPlot3D[{(10 + Cos[p])*f[t]*g[t], (10 + Cos[p + 2*Pi/3])*
g[t]*g[t], (10 + Cos[p - 2*Pi/3])*f[t]}, {t, -Pi, Pi}, {p, 0,
2*Pi}, Exclusions -> {-Pi/2, Pi/2}, Boxed -> False, Axes -> False,
ColorFunction -> "GreenBrownTerrain", MeshFunctions -> {#3 &},
PlotPoints -> {35, 100}]

On Monday, July 9, 2012 2:24:24 AM UTC-7, Bob Hanlon wrote:
> Resent since this hasn&#39;t shown up.

```

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