
Re: find a point relative to three other points
Posted:
Feb 2, 2014 10:47 AM


> > 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
The solution is much simpler
D = E + h/F*F .
Best regards, Avni

