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Topic: find a point relative to three other points
Replies: 2   Last Post: Feb 2, 2014 10:47 AM

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 Avni Pllana Posts: 546 Registered: 12/6/04
Re: find a point relative to three other points
Posted: Feb 2, 2014 10:47 AM

> > Dear all,
> >
> > I want to obtain the 3-dimensional coordinate of
> > point d. I know the following information:
> > - Point d should be placed in the plane formed by
> > (point a, point b, point c)
> > - I have the distance between point c, point d
> > - The line formed by (point c, point d) is
> > perpendicular to the line formed by (point a, point
> > d)
> > - Points a, c, d are placed on the circumference of

> a
> > circle
> > With this information, I want to obtain the 3d
> > coordinate of point d with Matlab software. I want

> to
> > obtain a system of linear equations to make it easy
> > for Matlab if possible. Could anyone help me with
> > writing this code or system of equations?

>
>
> let us represent points a,b,c,d with their position
> vectors A,B,C,D. Let D=[x,y,z]. Let E be the
> orthogonal projection of D on line AC. Let |CD|=r and
> |AC|=d. Now we have following equations:
>
> (1) (x-e1)/f1 = (y-e2)/f2 = (z-e3)/f3 ,
>
> (2) (x-e1)^2+(y-e2)^2+(z-e3)^2 = h^2 ,
>
> where h = r/d*sqrt(d^2-r^2),
>
> E=[e1, e2, e3] = (r^2*A + (d^2-r^2)*C)/d^2 ,
> F=[f1, f2, f3] = (C-A)x((A-B)x(C-B)) .
>
>
>
> Best regards,
> Avni

The solution is much simpler

D = E + h/|F|*F .

Best regards,
Avni

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