Zu dieser Karteikarte gibt es einen kompletten Satz an Karteikarten. Kostenlos!

We can represent a plane by

if
and a point by

Then, the distance from to the plane is given by


Given a set of planes , we want to find a point which minimizes the squared distances to all planes:






The matrices are called fundamental error quadrics and are computed as


From this definition, we see that the error quadrics of two sets of planes , can simply be merged into one error quadric by adding them:


Solution Approach 1
In order to find a minimum solution for , we can find the eigenvector to the smallest eigenvalue of .

Solution Approach 2


By computing

we obtain the linear system



Which is easier to solve than computing the eigenvectors and eigenvalues of .