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Originally posted by argentus
Perhaps I'm really a very disturbed person who has deluded himself into thinking he's found a happy and provocative place to think and share and be inspired by the thoughts of others.
I've been giving a great deal of thought on how exactly to answer this ...
Originally posted by argentus
that'd have a bit more punch, methinks, if you were still wearing the Powder avatar
Did you know there's a UFO Hunter marathon on the History Channell???
There IS!
Curiously, it doesn't seems as disappointing as the first time I saw it. This time through, I notice that nearly everyone utilizes a midwest/western U.S. hat brim bend. That's the hat brim bend of trust, y'know, unlike that southern fold. ewg.
Originally posted by argentus
I mean, am I just fooling myself? Are my sideways attempts at humor a joke upon myself? Do any of you regret friending me?
I find that lately, when I go into "My ATS", there is a long string of threads that I've posted on, and nothing further happens.
Originally posted by argentus
Don't want to take a chance of shortening the flow of an important story.
Anisotropic curve shortening flow is a geometric evolution of a curve and is equivalent to the gradient flow of anisotropic interface energy. We develop a numerical scheme for this nonlinear and degenerate problem, which is based on the fact that the evolution problem can be written formally as a linear partial differential equation on the interface itself. The scheme requires the solution of a tridiagonal complex linear system in each time step. We prove optimal error estimates in adequate norms for the semidiscrete scheme and provide numerical test computations. The scheme can also be applied to crystalline energies. *
The geometry of a space curve is described in terms of a Euclidean invariant frame field, metric, connection, torsion and curvature. Here the torsion and curvature of the connection quantify the curve geometry. In order to retain a stable and reproducible description of that geometry, such that it is slightly affected by non-uniform protrusions of the curve, a linearised Euclidean shortening flow is proposed. (Semi)-discretised versions of the flow subsequently physically realise a concise and exact (semi-)discrete curve geometry. Imposing special ordering relations the torsion and curvature in the curve geometry can be retrieved on a multi-scale basis not only for simply closed planar curves but also for open, branching, intersecting and space curves of non-trivial knot type. In the context of the shortening flows we revisit the maximum principle, the semi-group property and the comparison principle normally required in scale-space theories. We show that our linearised flow satisfies an adapted maximum principle, and that its Green's functions possess a semi-group property. We argue that the comparison principle in the case of knots can obstruct topological changes being in contradiction with the required curve simplification principle. Our linearised flow paradigm is not hampered by this drawback; all non-symmetric knots tend to trivial ones being infinitely small circles in a plane. Finally, the differential and integral geometry of the multi-scale representation of the curve geometry under the flow is quantified by endowing the scale-space of curves with an appropriate connection, and calculating related torsion and curvature aspects. This multi-scale modern geometric analysis forms therewith an alternative for curve description methods based on entropy scale-space theories. *
We argue that the comparison principle in the case of knots can obstruct topological changes being in contradiction with the required curve simplification principle.
Originally posted by tribewilder
reply to post by GypsK
.............*listening, but hearing nothing but the sound of Dutch crickets*............
[atsimg]http://files.abovetopsecret.com/images/member/86ebdb1ed181.gif[/atsimg]
[edit on 10/31/2009 by tribewilder]