       Re: ParametricPlot3D from 5.2 to 6.0

• To: mathgroup at smc.vnet.net
• Subject: [mg80547] Re: ParametricPlot3D from 5.2 to 6.0
• From: Francois LE COAT <lecoat at atari.org>
• Date: Sun, 26 Aug 2007 02:56:00 -0400 (EDT)
• References: <fagtvh\$91l\$1@smc.vnet.net> <faj4au\$8io\$1@smc.vnet.net> <16249230.1187867994319.JavaMail.root@m35> <falspp\$gij\$1@smc.vnet.net>

```Hi,

If I use this form with the "star" 3D surface, that's because
it is generated with the help from my Eureka 2.12 software. If
you look at the documentation <http://eureka.atari.org/eureka.htm>
the system of axis is "right handed" like it is used in French
mathematics, at the opposite of Mathematica's system of axis being
"left handed".

Some other 3D shapes are there <http://eureka.atari.org/vrml/>

Regards,

--
Fran=E7ois LE COAT
Author of Eureka 2.12 (2D Graph Describer, 3D Modeller)
<http://eureka.atari.org/>
<http://fon.gs/eureka/>

DrMajorBob wrote :
> 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"]
>
> Francois LE COAT wrote :
>> 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]
>>
>> 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.gif=
>>>> using Mathematica v. <= 5.2. With Mathematica 6.0 the interpolati=
on
>>>> method order seems to have changed. I didn't managed to obtain a
similar
>>>> rendering with the "star" 3D surface.
>>>>
>>>> Can someone help to find how to describe the "star" the same way
again ?

```

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