Re: Graphics3D[Plot3D[]] vs. ParametricPlot3D[]

• To: mathgroup at smc.vnet.net
• Subject: [mg26359] Re: Graphics3D[Plot3D[]] vs. ParametricPlot3D[]
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Wed, 13 Dec 2000 02:41:19 -0500 (EST)
• Organization: Universitaet Leipzig
• References: <90v56g\$6tq@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Hi,

you can split a quadrilateral into triangles
by creating two triangles with

+----+
|   /|
|  / |
| /  |
|/   |
+----+

or

+----+
|\   |
| \  |
|  \ |
|   \|
+----+

if you have such a nonplanar quadrilateral
the result look different. If specify quadrilaterals
you leave it to the rendering system to break
the  quadrilaterals into triangles and it is
no wonder that the result can be different.

Regards
Jens

Gianluca Gorni wrote:
>
> Hello!
>
> I would have thought that
>
>      Graphics3D[ Plot3D[ f, {x,0,1},{y,0,1}] ]
>
> gave the same result as
>
>      ParametricPlot3D[ {x,y,f}, {x,0,1},{y,0,1}].
>
> Well, almost, but I have just discovered that
> there is a subtle difference that has maddened me
> while I was trying to build a routine that worked for both
> Plot3D and ParametricPlot3D objects.
>
> Try
>
> f = (y + x - 1)^2;
>
> Graphics3D[
>     Plot3D[f, {x, 0, 1}, {y, 0, 1}, PlotPoints -> 2,
>       ViewPoint -> {2, -2, 1}, BoxRatios -> Automatic]][[1, 1]]
>
> Out ->  Polygon[{{0., 1., 0.}, {0., 0., 1.}, {1., 0., 0.}, {1., 1., 1.}}]
>
> while
>
> ParametricPlot3D[{x, y, f}, {x, 0, 1}, {y, 0, 1}, PlotPoints -> 2,
>      ViewPoint -> {2, -2, 1}, BoxRatios -> Automatic][[1, 1]]
>
> Out ->  Polygon[{{0., 0., 1.}, {1., 0., 0.}, {1., 1., 1.}, {0., 1., 0.}}]
>
> You can see: the vertices of the polygons are the same as above,
> but they are "rotated". Since this is a highly nonplanar polygon, the
> two versions look quite different when displayed.
>
> Maybe someone from wri can explain why they built the
> conversion of SurfaceGraphics to Graphics3D this way.
>
> Best regards,
>
>               Gianluca Gorni
>
> --
>
>  +---------------------------------+
>  | Gianluca Gorni                  |
>  | Universita` di Udine            |
>  | Dipartimento di Matematica      |
>  |   e Informatica                 |
>  | via delle Scienze 208           |
>  | I-33100 Udine UD                |
>  | Italy                           |
>  +---------------------------------+
>  | Ph.: (39) 0432-558422           |
>  | Fax: (39) 0432-558499           |
>  | mailto:gorni at dimi.uniud.it      |
>  | http://www.dimi.uniud.it/~gorni |
>  +---------------------------------+

```

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