Path: FormationFlying/Collision
% Distance from a point to the edge of an ellipsoid. Finds the distance (and the corresponding point) from a distant point to the closest point on an ellipsoid. An ellipsoid is defined as (x-xc)'*inv(P)*(x-xc), where x - point on the ellipsoid P - ellipsoid definition xc - center of ellipsoid d - distance from x0 to x x0 - outside point This form accepts the singular value decomposition of P. -------------------------------------------------------------------------- Form: [d,x] = DistantPtToEll(U,S,xc,x0,laguerre) -------------------------------------------------------------------------- ------ Inputs ------ U (3,3) Unitary matrix from SVD of P S (3,3) Singular value matrix from SVD of P xc (3,1) Ellipsoid center x0 (3,1) Outside point laguerre (1,1) Flag to use Laguerre for roots instead of eig ------- Outputs ------- d (1) Distance x (3,1) Point on the ellipsoid --------------------------------------------------------------------------
FormationFlying: Collision/Laguerre
Back to the FormationFlying Module page