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From: Osama T. Masoud <masoud@cs...>  20051022 19:24:07

Any particular reason the intersection of two conics operator returns only real solutions? It seems limiting conisering that a lot of the projective geometry algorithms depend on complex solutions (e.g., every two circles intersect at the circular points [1 i 0] and [1 i 0]). Since the class is templated, one idea would be that if the return type is vcl_complex, complex solutions are returned as well. osama On Wed, 12 Oct 2005, Peter Vanroose wrote: > > vgl has an elegant alogithm that computes the point on the conic > > closest to a given point. > > Anyone knows of a reference to that (paper/book)? > > As the insource documentation states, this is standard plane > projective geometry: > > "The nearest point must have a polar line which is orthogonal to its > connection line with the given point; all points with this property > form a conic." > > You can find theory and applications of polar points and lines in any > text book on projective geometry. > The actual implementation in vgl was not borrowed from any such text > book: I just implemented it based on the ideas of polar line/point, and > using the algorithm to intersect two conics. > (By the way, that intersection algorithm is also a straightforward > consequence of standard projective geometry, viz. bundles of conics.) > >  Peter. > 