       Parametric cylinder plots round in one instance and elliptical in

• To: mathgroup at smc.vnet.net
• Subject: [mg101392] Parametric cylinder plots round in one instance and elliptical in
• From: Bill <WDWNORWALK at aol.com>
• Date: Sat, 4 Jul 2009 06:44:28 -0400 (EDT)

```Ref: Parametric cylinder plots round in one instance and elliptical in another

Hi:

I have the following Mathematica 6.0.1 code:

ParaCyl[ {x1_, y1_, z1_}, {x2_, y2_, z2_}, r_] := ParametricPlot3D[{

r*Cos[s] + x1 + t*(x2 - x1),
r*Sin[s] + y1 + t*(y2 - y1),
z1 + t*(z2 - z1)},

{s, 0, 2*Pi}, {t, 0, 1}, Mesh -> False, Axes -> True,
AxesLabel -> {"x", "y", "z"},
PlotRange -> {{-10, 10}, {-10, 10}, {-10, 10}},
ViewPoint -> {9, 10, 8}]

(*I used the following which looks good wrt roundess:*)

ParaCyl[ {0, 0, 0}, {0, 0, 7}, 5]
(*Plot looks good.*)

Show[%, ViewPoint -> Top]
(*Plot looks round, as expected. *)

(*I change the next plot to:*)
ParaCyl[ {2, 3, 4}, {6, 7, 8}, 5]
(*Plot: Cylinder looks elliptical. Expected a round cylinder.*)

Show[%, ViewVector -> {{12, 13, 14}, {7, 8, 9}}]
(*This is a look down the throat of the elliptical looking cylinder.*)

Question: How can I code this to show a round cylinder, regardless of cylinder orientation?