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Old 2016-06-01, 14:23   #1
Xyzzy
 
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Default June 2016

https://www.research.ibm.com/haifa/p.../June2016.html
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Old 2016-06-03, 01:28   #2
a1call
 
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I can solve this for maximum filled volume. But I am stumped on the variable volume optimization.
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Old 2016-06-03, 17:33   #3
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This is how I figure the solution.

Notes:

* The actual angles are unreadable (I hope)
* Instructions for viewing X-Eyed 3-D images can be found on the web:
http://www.starosta.com/3dshowcase/ihelp.html
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Old 2016-06-04, 14:29   #4
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Well my submission is not showing up, which probably means there is a better (more accurate) optimization possible. I did a successive approximation style search by checking the Center-of-Mass' offset by checking 16 successive fill levels (2^4). There were 2 offsets to the right (towards the edge), one above and one below the center of the icosahedrons. The one below was larger so I made a more precise locating by further successive approximation(all manually).
I assume to find an optimization with a greater Center-of-Mass offset, one could write a script to check COMs for a much higher number of fill percentages. But That would be too much work for me.
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Old 2016-06-04, 16:44   #5
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I examined Centers-of-Mass at 64 different heights of filled volume. I don't think there can be a better optimization than what I already had.
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Old 2016-06-22, 02:05   #6
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There are some names up. For the record I had to resubmit the answer with a higher precision/accuracy.

* The fully loaded container will always have its COM at the same point in the center of the symmetrical geometry.

* A partially loaded container however is not (necessarily) symmetrical

* Unlike a fully loaded container whose COM remains constant at any tilt angle, a partially filled container will have its COM shift dynamically as the container is tilted and hence the geometry transforms.
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Old 2016-06-29, 01:26   #7
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Hi, I have just submitted a solution but it is very close to the deadline and it sometimes takes a while to find out if your solution is correct or not. Could someone who has already got a correct solution PM me so I can give them my numerical solution and check if it correct or if I have made a mistake somewhere?
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Old 2016-07-04, 13:59   #8
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https://www.research.ibm.com/haifa/p.../June2016.html
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Old 2016-07-05, 02:12   #9
LaurV
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Ha! Looking through that guy's paper, I would actually call that "an elegant solution"!!
I don't know how this problem could be solved more elegant, beside some animation/movie. You can't skip the formulas part anyhow. We also solved this "by hand", using AutoCad and got the right tilt and fill, but were too lazy to put it in a nice form. We were thinking to a small lisp program to show it in acad and capture the animation, but we were too busy to write it (or too stupid to write it fast, in the limit of the available time).
Something like "tilt it in this direction, section the thing a little, project the mass center, section the thing a little bit more, etc, if the center of the mass projects inside of the base, tilt a bit more, etc, then change the tilt direction by one degree and start from the beginning (only 36° due to symmetry of the tilting direction); record the max angle in all cases, send the minimum angle and the section (volume) to the guys. But we only dreamed to do this, all the month... never did it...

Last fiddled with by LaurV on 2016-07-05 at 02:18
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Old 2016-07-05, 03:46   #10
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Quote:
Originally Posted by LaurV View Post
Ha! Looking through that guy's paper, I would actually call that "an elegant solution"!!
Which one?
Link #1 is not a valid PDF file --
Quote:
(See attached file: TippingCanister.pdf)
Link #2 is in fact elegant (but is not a solution)!
Quote:
Brian Mirtich's paper from 1996 "Fast and Accurate Computation of Polyhedral Mass Properties" (http://www.math.uiuc.edu/~redavid2/PW/TimsPaper.pdf)
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Old 2016-07-05, 07:59   #11
LaurV
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Your "linker" is confused. (or linkator? or pdf viewer? hehe). The first link is a valid pdf link, with a nice Wolfram Mathematica solution.
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