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130 Commits 7 Branches 2 Tags 954 KiB
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Author SHA1 Message Date
Aaron Fenyes
8a77cd7484 Irisawa hexlet: drop unviable approach 
The approach in the deleted file can't work, because the "sun" and
"moon" spheres can't be placed arbitrarily.
 2024-07-18 03:21:46 -07:00
Aaron Fenyes
a26f1e3927 Add Irisawa hexlet example 
Hat tip Romy, who sent me the article on sangaku that led me to this
problem.
 2024-07-18 03:16:57 -07:00
Aaron Fenyes
19a4d49497 Clean up example formatting 2024-07-18 01:48:05 -07:00
Aaron Fenyes
71c10adbdd Overlapping pyramids: drop outdated comment 2024-07-18 01:12:49 -07:00
Aaron Fenyes
33c09917d0 Correct scope of guess constants 2024-07-18 01:05:13 -07:00
Aaron Fenyes
b24dcc9af8 Report success correctly when step limit is reached 2024-07-18 01:04:40 -07:00
Aaron Fenyes
b040bbb7fe Drop old code from examples 2024-07-18 00:50:48 -07:00
Aaron Fenyes
9007c8bc7c Circles in triangle: jiggle the guess 2024-07-18 00:49:09 -07:00
Aaron Fenyes
a7f9545a37 Circles in triangle: correct frozen variables 
Since the self-product of the point at infinity is left unspecified, the
first three components can vary without violating any constraints. To
keep the point at infinity where it's supposed to be, we freeze all of
its components.
 2024-07-18 00:43:00 -07:00
Aaron Fenyes
3764fde2f6 Clean up formatting of notes 2024-07-18 00:27:10 -07:00
Aaron Fenyes
24dae6807b Clarify notes on tangency 2024-07-18 00:16:23 -07:00
Aaron Fenyes
74c7f64b0c Correct sign of normal in plane utility 
Clarify the relevant notes too.
 2024-07-18 00:03:12 -07:00
Aaron Fenyes
d0340c0b65 Correct point utility again 
The balance between the light cone basis vectors was wrong, throwing the
point's coordinates off by a factor of two.
 2024-07-17 23:37:28 -07:00
Aaron Fenyes
69a704d414 Use notes' sign convention for light cone basis 2024-07-17 23:07:34 -07:00
Aaron Fenyes
01f44324c1 Tetrahedron radius ratio: find radius ratio 2024-07-17 22:45:17 -07:00
Aaron Fenyes
96ffc59642 Tetrahedron radius ratio: tweak guess 
Jiggle the vertex guesses. Put the circumscribed sphere guess on-shell.
 2024-07-17 19:01:34 -07:00
Aaron Fenyes
a02b76544a Tetrahedron radius ratio: add circumscribed sphere 2024-07-17 18:55:36 -07:00
Aaron Fenyes
6e719f9943 Tetrahedron radius ratio: correct vertex guesses 2024-07-17 18:27:58 -07:00
Aaron Fenyes
d51d43f481 Correct point utility 2024-07-17 18:27:22 -07:00
Aaron Fenyes
6d233b5ee9 Tetrahedron radius ratio: correct signs 2024-07-17 18:08:36 -07:00
Aaron Fenyes
5abd4ca6e1 Revert "Give spheres positive radii in examples" 
This reverts commit 4728959ae0, which
actually gave the spheres negative radii! I got confused by the sign
convention differences between the notes and the engine.
 2024-07-17 17:49:43 -07:00
Aaron Fenyes
ea640f4861 Start tetrahedron radius ratio example 
Add the vertices of the tetrahedron to the `sphere-in-tetrahedron`
example.
 2024-07-17 17:33:32 -07:00
Aaron Fenyes
4728959ae0 Give spheres positive radii in examples 
This changes the meaning of `indep_val` in the overlapping pyramids
example, so we adjust `indep_val` to get a nice-looking construction.
 2024-07-17 17:22:33 -07:00
Aaron Fenyes
2038103d80 Write examples directly in light cone basis 2024-07-17 15:37:14 -07:00
Aaron Fenyes
bde42ebac0 Switch engine to light cone basis 2024-07-17 14:30:43 -07:00
Aaron Fenyes
e6cf08a9b3 Make tetrahedron faces planar 2024-07-15 23:54:59 -07:00
Aaron Fenyes
7c77481f5e Don't constrain self-product of frozen vector 2024-07-15 23:39:05 -07:00
Aaron Fenyes
1ce609836b Implement frozen variables 2024-07-15 22:11:54 -07:00
Aaron Fenyes
b185fd4b83 Switch to backtracking Newton's method in Optim 
This performs much better than the trust region Newton's method for the
actual `circles-in-triangle` problem. (The trust region method performs
better for the simplified problem produced by the conversion bug.)
 2024-07-15 15:52:38 -07:00
Aaron Fenyes
94e0d321d5 Switch back to BigFloat precision in examples 2024-07-15 14:31:30 -07:00
Aaron Fenyes
53d8c38047 Preserve explicit zeros in Gram matrix conversion 
In previous commits, the `circles-in-triangle` example converged much
more slowly in BigFloat precision than in Float64 precision. This
turned out to be a sign of a bug in the Float64 computation: converting
the Gram matrix using `Float64.()` dropped the explicit zeros, removing
many constraints and making the problem much easier to solve. This
commit corrects the Gram matrix conversion. The Float64 search now
solves the same problem as the BigFloat search, with comparable
performance.
 2024-07-15 14:08:57 -07:00
Aaron Fenyes
7b3efbc385 Clean up backtracking gradient descent code 
Drop experimental singularity handling strategies. Reduce the default
tolerance to within 64-bit floating point precision. Report success.
 2024-07-15 13:15:15 -07:00
Aaron Fenyes
25b09ebf92 Sketch backtracking Newton's method 
This code is a mess, but I'm committing it to record a working state
before I start trying to clean up.
 2024-07-15 11:32:04 -07:00
Aaron Fenyes
3910b9f740 Use Newton's method for polishing 2024-07-11 13:43:52 -07:00
Aaron Fenyes
d538cbf716 Correct improvement threshold by using unit step 
Our formula for the improvement theshold works when the step size is
an absolute distance. However, in commit `4d5ea06`, the step size was
measured relative to the current gradient instead. This commit scales
the base step to unit length, so now the step size really is an absolute
distance.
 2024-07-10 23:31:44 -07:00
Aaron Fenyes
4d5ea062a3 Record gradient and last line search in history 2024-07-09 15:00:13 -07:00
Aaron Fenyes
5652719642 Require triangle sides to be planar 2024-07-09 14:10:23 -07:00
Aaron Fenyes
f84d475580 Visualize neighborhoods of global minima 2024-07-09 14:01:30 -07:00
Aaron Fenyes
77bc124170 Change loss function to match gradient 2024-07-09 14:00:24 -07:00
Aaron Fenyes
023759a267 Start "circles in triangle" from a very close guess 2024-07-08 14:21:10 -07:00
Aaron Fenyes
610fc451f0 Track slope in gradient descent history 2024-07-08 14:19:25 -07:00
Aaron Fenyes
93dd05c317 Add required package to "sphere in tetrahedron" example 2024-07-08 14:19:05 -07:00
Aaron Fenyes
9efa99e8be Test gradient descent for circles in triangle 2024-07-08 12:56:28 -07:00
Aaron Fenyes
828498b3de Add sphere and plane utilities to engine 2024-07-08 12:56:14 -07:00
Aaron Fenyes
736ac50b07 Test gradient descent for sphere in tetrahedron 2024-07-07 17:58:55 -07:00
Aaron Fenyes
ea354b6c2b Randomize guess in gradient descent test 
Randomly perturb the pre-solved part of the guess, and randomly choose
the unsolved part.
 2024-07-07 17:56:12 -07:00
Aaron Fenyes
d39244d308 Host Ganja.js locally 2024-07-06 21:35:09 -07:00
Aaron Fenyes
7e94fef19e Improve random vector generator 2024-07-06 21:32:43 -07:00
Aaron Fenyes
abc53b4705 Sketch random vector generator 
This needs to be rewritten: it can fail at generating spacelike vectors.
 2024-07-02 17:16:31 -07:00
Aaron Fenyes
17fefff61e Name gradient descent test more specifically 2024-07-02 17:16:19 -07:00