Re: "infinite" line through 2 3D points
- To: mathgroup at smc.vnet.net
- Subject: [mg67934] Re: "infinite" line through 2 3D points
- From: dh <dh at metrohm.ch>
- Date: Thu, 13 Jul 2006 06:53:48 -0400 (EDT)
- References: <e8vtd3$ski$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Hi Daniel,
There is no such thing like a free lunch,you simply have to calculate
the intersection.
All heights intersects in one point ph. We calculate this point by
noting that the line from any triangle point pi to ph={x1,x2,x3} is
perpendicular to the adjacent triangle side:
ph={x1,x2,x3};
ph= ph/. Solve[{
(ph-p1).(p2-p3)==0,
(ph-p2).(p3-p1)==0,
(ph-p3).(p1-p2)==0},
{x1,x2,x3}]
next we need the feet points:fi of the heigths:
fi lies on traingle side i,e.g. f1=p1+t(p2-p1) for some t, and
fi-ph is perpendicular to the traingle side i:
f1 = p2 + t(p2 - p3) /.
Solve[(p2 + t(p2 - p3) - ph).(p2 - p3) == 0, t][[1]]
f2 = p3 + t(p3 - p1) /.
Solve[(p3 + t(p3 - p1) - ph).(p3 - p1) == 0, t][[1]]
f3 = p1 + t(p1 - p2) /.
Solve[(p1 + t(p1 - p2) - ph).(p1 - p2) == 0, t][[1]]
Daniel
daniel_of_vienna wrote:
> Dear Experts,
>
> I've got a set of 3D points, which result in a movie, the points
> describes two triangles, which are moving in 3D in time (frame). Now I
> needed to draw the "height" of the triangles, which lines shall
> intersect somewhere outside of the triangles. Now I konw, how to draw a
> line betweeen two points, but how do I "lengthten" them in one
> direction?
>
> I hope, I was clear so far :DDD
> Thanx,
> Daniel
>