Graphics3D[Plot3D[]] vs. ParametricPlot3D[]

• To: mathgroup at smc.vnet.net
• Subject: [mg26269] Graphics3D[Plot3D[]] vs. ParametricPlot3D[]
• From: Gianluca Gorni <gorni at dimi.uniud.it>
• Date: Sun, 10 Dec 2000 00:19:42 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```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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