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From: Roger Stafford on 9 Jul 2010 13:25
Torsten Hennig <Torsten.Hennig(a)umsicht.fhg.de> wrote in message <1987639511.93716.1278674049147.JavaMail.root(a)gallium.mathforum.org>...
> In the notation of the link above, if
> v1 = (v11,v12), v2 = (v21,v22), pt = (pt1,pt2)
> then the point with the smallest distance to pt on
> the line through v1 and v2 lies on the line segment
> (v1v2) if the quantity
> lambda = ((v11-v21)*(v11-pt1)+(v12-v22)*(v12-pt2))/
> ((v11-v21)^2 + (v12-v22)^2)
> is between 0 and 1.
>
> Best wishes
> Torsten.
- - - - - - - -
Or equivalently, if the two angles CAB and CBA I referred to earlier are each no greater than pi/2, which can be tested by:

dot(C-A,B-A) >= 0 and dot(C-B,A-B) >= 0

Roger Stafford
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