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.
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 in-source 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.