Re: tracing lines on surface-graphics

• To: mathgroup at smc.vnet.net
• Subject: [mg25603] Re: tracing lines on surface-graphics
• From: "Allan Hayes" <hay at haystack.demon.co.uk>
• Date: Wed, 11 Oct 2000 03:50:41 -0400 (EDT)
• References: <8rtst2\$dpo@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```
"Alan Wetherby" <roommate222 at my-deja.com> wrote in message
news:8rtst2\$dpo at smc.vnet.net...
> Hi - I can't find an obvious way to trace a line on a surface-graphics
> object. I've plotted f(x,y) and got the surface I want, and now I want
> to add a curve, say: x varies according to the plotted range, y=1+x/2,
> z=f(x,y) --so it lies on the surface I've plotted. I've turned the mesh
> off because it's too dense, given the number of points I'm plotting,
> but I want to add a couple of such lines - another option would be to
> trace every 20th mesh-line or something like that, but that doesn't
> seem to be possible either.
>
> Thanks for any help -- Alan
>
>
> Sent via Deja.com http://www.deja.com/
>

f[x_, y_] := x^2 + y^3

sg = Plot3D[f[x, y], {x, -1, 1}, {y, -1, 1}, PlotPoints -> 6];

ln = ParametricPlot3D[{x, x/2, f[x, x/2], {Thickness[.01], Hue[0]}}, {x, -1,
1}];

Show[sg, ln]

We have to lift the line a little to stop parts of it being hidden by the
surface.

ln2 = ln =
ParametricPlot3D[{x, x/2,
f[x, x/2] + .1, {Thickness[.01], Hue[0]}}, {x, -1, 1}]

Show[sg, ln2];

For surfaces given by ParametricPlot3D we have to be more subtle. Two
possibilities are: 1) pulling the line towards the view point and 2)
approximating it by line segments across the triangles that, in spite of
appearence, make up the displayed polygons.

Controlling the number of mesh lines shown is the objective of a package by
Hartmut Wolf and myself that will appear in the next issue of Mathematica in
Education and Research.

--
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

```

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