

hi,
"Bald Eagle" <cre### [at] netscapenet> wrote:
> "jr" <cre### [at] gmailcom> wrote:
> > as I wrote, I'm game for collaboration. if you can express the spherical
> > bounding you're thinking off as "pseudo code" at least, I'm sure we could work
> > on something.
> ...
> > that's an interesting thought, reorienting the object. need to think about
> > that.
> (*) Well that's what I was getting at with the ellipsoid and the rotating
> calipers.
>
> Right now, you can imagine the the bounding box is determined in a very
> handsoff kinda way. If you took a book that was not axisaligned, and
> squeezed it with axisaligned calipers, it would "straighten out" until it was
> aligned with the minimal width parallel to the axis of measurement.
> ...
> It has to do with analyzing the orientation of the vectors  the trace ()
> results that you get from your "scan".
off the top of my head, write out the points/vectors to a CSV format file, then
either use your spreadsheetfu or describe the the necessary actions in kinda
pseudo code so we can discuss whether/how to implement as a script/compiled
utility.
> ...
> This goes by many names, but I found Singular Value Decomposition (SVD)
> but I guess there's Principal Component Analysis (PCA), Eigen Value
> Decomposition, etc. Which can be different but are more or less equivalent and
> are often used interchangeably.
>
> Over here (1/4 to 1/3 of the way down):
> https://blog.statsbot.co/singularvaluedecompositiontutorial52c695315254
> he says, "Suppose we have two, twodimensional vectors, x₁=(x₁,
> y₁), and x₂=(x₂, y₂). We can fit an ellipse with major
> axis, a, and minor axis, b, to these two vectors as shown in the figure."
>
> And then look here at the 7:00 mark:
> https://www.youtube.com/watch?v=_4jaLZCoLPI
>
>
https://www.youtube.com/watch?v=PFDu9oVAEg&list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab&index=14
quick viewed the vids. agree with 3Blue1Brown that "confusion" arises from
having a "shaky" understanding of the basics. :) (although a frown would be
more appropriate)
so, anything .. matrix you'd have to work through with me  bite size.
> ...
> "This is crazy, Bill."
> (No it's not, Thomas  the dried frog pills are _working_!!!)
chorus: "Oh no, they're not." :)
> Well, yes  and no. Because I can already see an application to your sphere
> slicing troubles in POVRay, the existing rootfinding problems that Bill
> Pokorny is grappling with, and SVD.
>
> If the problem with your sphere slicing arises from rootfinding troubles that
> POVRay experiences when trying to solve for rays that are parallel, or nearly
> so, to the object surface, then maybe if you added a "wiggle" to the object,
> solved for the root, and then unwiggled the intersection before rendering the
> result  then you'd get better renders with less holes.
I can "see" the concept, and like it. potential problem: registration, to get
exact realignment.
> So if we implemented it in source  them maybe it could be applied to solve a
> lot of longstanding, underlying problems. Or something like it.
I'm working myself up to trying Bill P's custom POVRay soon. but yes, support
in the program source sounds like the way forward.
> ...
regards, jr.
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