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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 1, 2014 7:44 PM

> 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

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