Re: Epilog with 3 dimensional graphics primitives

• To: mathgroup at smc.vnet.net
• Subject: [mg83720] Re: Epilog with 3 dimensional graphics primitives
• From: dh <dh at metrohm.ch>
• Date: Thu, 29 Nov 2007 06:18:37 -0500 (EST)
• References: <fijg30\$hcg\$1@smc.vnet.net>

```
Hi Barrow,

Epilog only takes 2D primitives.

Using Opacity you can make an object transparent. Note that this acts on

the whole objects that follow. If only part of an object should be

transparent, you will need to draw the object in two pieces. Here is an

example where the top of the torus is opaque:

r1={Cos[u],Sin[u],0};

r2=0.5 {{Sin[u],Cos[u],0},{-Cos[u],Sin[u],0},{0,0,1}}.{0,Cos[v],Sin[v]};

g1=ParametricPlot3D[ r1+r2,{u,0,2\[Pi]},{v,-\[Pi],0}];

g2=ParametricPlot3D[ r1+r2,{u,0,2\[Pi]},{v,0,\[Pi]}];

Show[g1,Graphics3D[Opacity[0.5]],g2,PlotRange->All]

Instead of a relatively slow opaque surface, you may also simple draw

the grid, what is much faster, mainly during rotation:

Show[g1,Graphics3D[Normal[g2][[1,2]]],PlotRange->All]

hope this helps, Daniel

Barrow wrote:

> Dear all,

>    I wanna plot a torus on which shows the definition of parameters.

> That is, there is a torus ((R+r*Cos[u])Cos[v],(R

> +r*Sin[u])*Sin[v],r*Sin[u]), I wanna show the definitions of u and v.

> So I have to draw some circles, lines on the torus. My idea is:

>

> ParametricPlot3D[{(5 + 2 Cos[u]) Cos[v], (5 + 2 Cos[u]) Sin[v], 2

> Sin[u]}, {u,0,2Pi},{v,0,2Pi}, Epilog->{Line and Circle here}]

>

> There are two problems. The first is that, I tried to put in the

> Epilog above some 3D graphics primitive, e.g. Point[{0,0,0}]. But it

> doesn't work! It seems that only 2D graphics primitives can be put

> inside the Epilog.

>

> The second problem is that, I wanna show the definitions of u and v,

> so the torus should be "transparent" in some section to show the lines

> and circles (i.e. to show the definitions of u and v), how can I do

> that? i.e. to make some portion of the torus being transparent?

>

>  Thank you all!    Sincerely Barrow

>

```

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