Re: Not drawing lines at polygon edges, in ParametricPlot3D

• To: mathgroup at smc.vnet.net
• Subject: [mg21953] Re: Not drawing lines at polygon edges, in ParametricPlot3D
• From: "Allan Hayes" <hay at haystack.demon.co.uk>
• Date: Sat, 5 Feb 2000 22:22:20 -0500 (EST)
• References: <87ged9\$1ok@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Aram,

NO EDGES:
We can  use a fourth, "styling", coordinate to give any list of directives
to the polygons as functions of the coordinate x and y (a single directive
can be given without listing it):

f[x_, y_] = 2 - x^2 - y^2;

pg1 = ParametricPlot3D[{x, y, f[x, y], EdgeForm[]}, {x, -1, 1}, {y, -1, 1},
PlotPoints -> 5];

More generally

pg2 = ParametricPlot3D[{x, y, f[x, y],
{EdgeForm[Thickness[ .02], Hue[1 - f[x, y]/2]],
Hue[f[x, y]/2]}}, {x, -1, 1}, {y, -1, 1},
Lighting -> False, PlotPoints -> 5];

TRANSPARENT (WireFrame)

We can use a standard package (look for WireFrame in HelpBrowser > Master
Index)

<< Graphics`Shapes`

?WireFrame

"WireFrame[graphics3D] replaces all polygons in the three-dimensional \
graphics object by outlines."

Show[WireFrame[pg2]];

Oddly, the edges pick up the colors from the polygons face colors and
EdgeForm[...] is lost.
We could do our own programming:

pg2[[1]]

Show[pg2 /.
{___, EdgeForm[d___], ___, Polygon[pts_]} :> {d,
Line[Append[pts, First[pts]]]}]

--
Allan
---------------------
Allan Hayes
Mathematica Training and Consulting
Leicester UK
www.haystack.demon.co.uk
hay at haystack.demon.co.uk
Voice: +44 (0)116 271 4198
Fax: +44 (0)870 164 0565

"Aram Schiffman" <aram at sirius.com> wrote in message
news:87ged9\$1ok at smc.vnet.net...
> As the subject header says ... how can I render a ParametricPlot3D, but
not
> have the lines drawn at the polygon edges? I've tried every obvious (to
me)
> option, but no dice.
>
> Also, can I make my 3D object transparent, in ParametricPlot3D?
>