Euclidian projection on ellipsoid and conic

Version 1.4.0.0 (31 ko) par Bruno Luong
Projecting a point on ellipsoid or conic in n-dimensional space
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Mise à jour 25 mai 2010

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Find the projection of point P in R^n on the ellipsoid

E = { x = x0 + U*(z.*radii) : |z| = 1 }, where U is orthogonal matrix of the orientation of E, radii are the axis lengths, and x0 is the center.

Or on generalized conic E = { x : x'*A*x + b'*x + c = 0 }.

The projection is the minimization problem:
min | x - P | (or max | x - P|) for x in E.

Method: solve the Euler Lagrange equation with respect to the Lagrange multiplier, which can be written as polynomial equation (from an idea by Roger Stafford)

Citation pour cette source

Bruno Luong (2024). Euclidian projection on ellipsoid and conic (https://www.mathworks.com/matlabcentral/fileexchange/27711-euclidian-projection-on-ellipsoid-and-conic), MATLAB Central File Exchange. Récupéré le .

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EllipsePrj/

Version Publié le Notes de version
1.4.0.0

Fix a bug, Introducing an adjustable tolerance value for parabola detection
1.3.0.0

Cosmetic changes + Script for test example for 2D conic projection
1.2.0.0

Extend to generalized conic (ellipsoid, paraboloid, hyperboloid, etc...)
1.0.0.0