
Re: find a point relative to three other points
Posted:
Feb 1, 2014 7:44 PM


> Dear all, > > I want to obtain the 3dimensional 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?
Hi Hajizadeh,
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) (xe1)/f1 = (ye2)/f2 = (ze3)/f3 ,
(2) (xe1)^2+(ye2)^2+(ze3)^2 = h^2 ,
where h = r/d*sqrt(d^2r^2),
E=[e1, e2, e3] = (r^2*A + (d^2r^2)*C)/d^2 , F=[f1, f2, f3] = (CA)x((AB)x(CB)) .
Best regards, Avni

