Abstract
It is shown that from d projections of a k-flat into ( k+1)-dimensional linear subspaces one can still reconstruct the k-flat. Furthermore, we show that a k-flat and a j-flat intersect in d-space if and only if they intersect in ( d k+ j+1 ) linear subspaces of dimension ( k+ j+1) (and which are independent, of the k-flat and the j-flat). An application of these projection results is k-dimensional simplex searching for a set I of n points in d-dimensional space with a structure of size O( n k+1+ ε ) and O(log n) query time, for arbitrarily small positive ε. A second application is ray shooting in axis-parallel boxes in d-dimensional space, with a structure of size O( n 2+ ε ) and O(log n) query time.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
