       Re: Mathematica Functions

• To: mathgroup at smc.vnet.net
• Subject: [mg6675] Re: [mg6608] Mathematica Functions
• From: jpk at max.mpae.gwdg.de
• Date: Wed, 9 Apr 1997 09:15:40 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```> Subject: [mg6675] [mg6608] Mathematica Functions
>
>
> I just got Mathmatica 3.0, and I would like to use its power to find the
> equation of a circle on a plane.  I can graph the plane, but then
> I would like to graph a circle, not a 3-d sphere, on that plane.  If
> anybody has an idea or knows some Mathematica functions that might help,
>
> Thank-you, Jason Frederick.
>

Hi Jason,

suppose You have a plane equation

a x + b y + c z ==d

and a circle with  radius  R and a center {xc,yc,zc}.
The first think You require is that the center point {xc,yc,zc} is on the
plane i. e. TrueQ[ a xc + b yc + c zc==d].

To draw the cirlce You need two vectors e2 and e3 with

Dot[e2,{a,b,c}]==0
Dot[e3,{a,b,c}]==0

and

Dot[e2,e3]==0
Dot[e2,e2]==1
Dot[e3,e3]==1

where {a,b,c} is the normal vector of the plane. You can simply construct the
vectors with Gram-Schmidt orthogonalisation form {a,b,c} and two unit vectors
as long as none of the unit {u1,u2} vectors is  a multiple of {a,b,c}.

Onec You have found the vectors e1 and e2 You can draw a parametric curve

{xc,yc,zc}+e2*Cos[t]+e3*Sin[t]

for t in [0,2Pi) that lies on the plane.

Hope that helps
Jens

```

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