       RE: Conic sections

• To: mathgroup at smc.vnet.net
• Subject: [mg43492] RE: [mg43448] Conic sections
• From: "David Park" <djmp at earthlink.net>
• Date: Thu, 18 Sep 2003 05:38:55 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```Needs["Graphics`ParametricPlot3D`"];
Needs["Graphics`Animation`"]

gr1 = CylindricalPlot3D[r, {r, -1, 1}, {theta, 0, 2 Pi},
DisplayFunction -> Identity] ;

frame[al_] :=
Show[gr1,
ParametricPlot3D[{-x, y, Tan[al] (x - 1) + .5 },
{x, -1, 1}, {y, -1, 1},
DisplayFunction -> Identity],
PlotRange -> {-1, 1},
Ticks -> None,
DisplayFunction -> \$DisplayFunction]

Animate[frame[x], {x, -1.5, 1.5, 0.125}]
SelectionMove[EvaluationNotebook[], All, GeneratedCell]
FrontEndTokenExecute["OpenCloseGroup"]; Pause[0.5];
FrontEndExecute[{FrontEnd`SelectionAnimate[200, AnimationDisplayTime -> 0.1,
AnimationDirection -> ForwardBackward]}]

David Park

From: Narasimham G.L. [mailto:mathma18 at hotmail.com]
To: mathgroup at smc.vnet.net

In an (unsuccessful) attempt to depict each frame as part of an
animation of cone/plane intersections (circle, ellipse, parabola,
hyperbola), instead of Showing [( gr1,gr2)n] ( n frames) , the
following program  Shows   [gr1,(gr2)n] (single frame) :

Needs["Graphics`ParametricPlot3D`"];
gr1=CylindricalPlot3D[r, {r, -1, 1},{theta, 0,2 Pi}] ;
gr2=Table[
ParametricPlot3D[{-x,y, Tan[al] (x-1)+.5 },
{x, -1, 1},{y,-1,1}],{al,-1.5,1.5,.5}];
Show[gr1,gr2];

This has the undesirable effect of the required cone section being
obscured by the next succeeding intersection plane. How is it done in
separate frames in a DO loop or Table?  TIA    G.L.Narasimham

```

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