## Distance of a point to an Ellipsoid

I am working on a Matlab sim and I need to find the shorted distance of a point to an Elliposid surface.

The point is defined as [X,Y,Z].
Elliposid center is defined as [Xc,Yc,Zc]

Ellipsoid is defined as
A B C
E F G
H I J

(I dont if thats sufficient information for ellipsoid, assuming its having standard equation.)
 PhysOrg.com science news on PhysOrg.com >> Leading 3-D printer firms to merge in $403M deal (Update)>> LA to give every student an iPad;$30M order>> CIA faulted for choosing Amazon over IBM on cloud contract
 Recognitions: Gold Member Science Advisor Staff Emeritus I really don't know what you mean by saying the ellipsoid is "given" by that array of letters but if you have an equation for the ellipsoid the most direct thing to do is write the equation for the line between the given point and the center of the ellipsoid. Put the parametric equations for the line, in terms of the parameter, t, say, into the equation of the ellipse to get a single quadratic equation for t. Put that t into the parametric equations to find the point. That quadratic equation will have two solutions. One gives the point on the ellipsoid closest to the given point, the other the point farthest away.

 Similar discussions for: Distance of a point to an Ellipsoid Thread Forum Replies Calculus & Beyond Homework 16 General Math 2 Differential Geometry 0 Differential Geometry 0 General Math 6