       Re: Re: ParametricPlot3D from 5.2 to 6.0

• To: mathgroup at smc.vnet.net
• Subject: [mg80527] Re: [mg80498] Re: ParametricPlot3D from 5.2 to 6.0
• From: DrMajorBob <drmajorbob at bigfoot.com>
• Date: Fri, 24 Aug 2007 02:02:32 -0400 (EDT)
• References: <fagtvh\$91l\$1@smc.vnet.net> <faj4au\$8io\$1@smc.vnet.net> <16249230.1187867994319.JavaMail.root@m35>

```It matters little in THIS case, but Set is faster than SetDelayed, the
functions are not needed, and I see no reason to switch x and y or change
signs, so on principal I'd write it as

rho = Max[1 - 3 Sin[2 p] Sin[5 t + Pi/2], 0];
x = rho Sin[p] Cos[t];
y = rho Sin[p] Sin[t];
z = rho Cos[p];
ParametricPlot3D[{x, y, z}, {t, 0, 2 \[Pi]}, {p, 0, \[Pi]},
PlotPoints -> {11, 5}, Mesh -> All, MaxRecursion -> 0,
PlotRange -> All, NormalsFunction -> None]

Anyway, I like the more accurate "flower petal" version:

ParametricPlot3D[{x, y, z}, {t, 0, 2 \[Pi]}, {p, 0, \[Pi]},
PlotRange -> All, PerformanceGoal -> "Quality"]

Bobby

On Thu, 23 Aug 2007 05:22:34 -0500, Francois LE COAT <lecoat at atari.org>
wrote:

> Hi,
>
> Thanks. I finally found the following form, thanks to Brett Champion
>
> xmin := 0
> xmax := 2*Pi
> ymin := 0
> ymax := Pi
> ro[t_, p_] := Max[1 - 3*Sin[2*p]*Sin[5*t + Pi/2], 0]
> xxx[t_, p_] := ro[t, p]*Sin[p]*Cos[t]
> yyy[t_, p_] := ro[t, p]*Sin[p]*Sin[t]
> zzz[t_, p_] := ro[t, p]*Cos[p]
> ParametricPlot3D[{yyy[t, p], -xxx[t, p], zzz[t, p]}, {t, xmin, xmax},
>   {p,ymin, ymax}, PlotPoints -> {11, 5}, Mesh -> All, MaxRecursion -> 0,
>   PlotRange -> All, NormalsFunction -> None]
>
> Regards,
>
> --
> Fran=E7ois LE COAT
> Author of Eureka 2.12 (2D Graph Describer, 3D Modeller)
> <http://eureka.atari.org/>
> <http://fon.gs/eureka/>
>
> Jens-Peer Kuska wrote :
>> try:
>>
>> xmin := 0
>> xmax := 2*Pi
>> ymin := 0
>> ymax := Pi
>> ro[t_, p_] := Max[1 - 3*Sin[2*p]*Sin[5*t + Pi/2], 0]
>> xxx[t_, p_] := ro[t, p]*Sin[p]*Cos[t]
>> yyy[t_, p_] := ro[t, p]*Sin[p]*Sin[t]
>> zzz[t_, p_] := ro[t, p]*Cos[p]
>> ParametricPlot3D[{yyy[t, p], -xxx[t, p], zzz[t, p]}, {t, xmin,
>>    xmax}, {p, ymin, ymax}, PlotPoints -> {11, 5}, MaxRecursion -> 0,
>>   PlotRange -> All, PerformanceGoal -> "Speed"]
>>
>> Francois LE COAT wrote :
>>> With the following notebook <http://eureka.atari.org/vrml/etoile.nb>=

>>> I had the following rendering <http://eureka.atari.org/vrml/etoilm.g=
if=
>>
>>> using Mathematica v. <= 5.2. With Mathematica 6.0 the interpolatio=
n
>>> method order seems to have changed. I didn't managed to obtain a sim=
il=
> ar
>>> rendering with the "star" 3D surface.
>>>
>>> Can someone help to find how to describe the "star" the same way aga=
in=
>  ?
>
>

-- =

DrMajorBob at bigfoot.com

```

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