       graphics problem

• To: mathgroup at thnext.mit.edu
• Subject: graphics problem
• From: Robert Singleton <bobs at thnext.mit.edu>
• Date: Wed, 21 Oct 92 19:06:37 PDT

```I have a graphics problem of sorts. I want to graph a hyperboloid of
one sheet with an arc drawn across it. However, when the arc goes
around the hyperboloid I would still like to see it  rather than have
it eclipsed. How do I do this? There was a similar question the other
day about partial transparency. Unfortunately I didn't understand the
reply (which was from twj at wri.com -- obviously a Mathematica expert).

Here is a little more detail:

Define:

Z0[tau_,w_]:=-Tan[w]
Z1[tau_,w_]:= Sin[tau]/Cos[w]
Z2[tau_,w_]:= Cos[tau]/Cos[w]

where -Pi<tau<Pi and -Pi/2<w<Pi/2. This alo parametrizes the
hyperboloid:

grHy=ParametricPlot3D[{Z1[tau,w],Z2[tau,w],Z0[tau,w]},
{tau,-Pi,Pi},{w,-1.,1.}]

I can also parametarize the hyperboloid as follows:

z0[r_,t_]:=(1 - r^2 + t^2)/(2*r)
z1[r_,t_]:=t/r
z2[r_,t_]:=(1 + r^2 - t^2)/(2*r)

where r,t are any real numbers. (These are lower case z's). I am
interested in putting the r=3 curve on "grHy". This is what I do:

grArc=ParametricPlot3D[{z1[3.0,t],z2[3.0,t],z0[3.0,t]},
{t,-4.16,4.16}]

Show[grHy,grArc,ViewPoint->{2.245, 1.552, 2.000}]

This gives me an arc running across the hyperboloid, but
unfortunately part of it is eclipsed. What should I do
to see the arc on both sides? Thanks very much.

Robert Singleton
bobs at thnext.mit.edu

```

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