3170a933e4
Clean up example of three mutually tangent spheres
2024-02-15 17:16:37 -08:00
f2000e5731
Test different sign patterns for cosines
...
It seems like there are real solutions if and only if the product of the
cosines is positive.
2024-02-15 16:25:09 -08:00
ba365174d3
Find real solutions for three mutually tangent spheres
...
I'm not sure why the solver wasn't working before. It might've been just
an unlucky random number draw.
2024-02-15 16:16:06 -08:00
ae5db0f9ea
Make results reproducible
2024-02-15 16:00:46 -08:00
8d8bc9162c
Store elements in arrays to keep order stable
...
This seems to restore reproducibility.
2024-02-15 15:42:26 -08:00
291d5c8ff6
Study mutually tangent spheres with two fixed
2024-02-15 13:28:01 -08:00
e41bcc7e13
Explore the performance wall
...
Three points on two spheres is too much.
2024-02-13 04:02:14 -05:00
31d5e7e864
Play with two points on two spheres
...
Guess conditions that make the scaling constraint impossible to satisfy.
2024-02-12 22:48:16 -05:00
a450f701fb
Try displaying a chain of spheres
...
For three mutually tangent spheres, I couldn't find real solutions.
2024-02-12 21:14:07 -05:00
6cf07dc6a1
Evaluate and display elements
2024-02-12 20:34:12 -05:00
1f173708eb
Move random cut routine into engine
2024-02-10 17:39:26 -05:00
6f18d4efcc
Test lots of uniformly distributed hyperplanes
2024-02-10 15:10:48 -05:00
621c4c5776
Try uniformly distributed hyperplane orientations
...
Unit normals are uniformly distributed over the sphere.
2024-02-10 15:02:26 -05:00
b3b7c2026d
Separate the algebraic and numerical parts of the engine
2024-02-10 14:50:50 -05:00
af1d31f6e6
Test a scale constraint
...
In all but a few cases (for example, a single point on a plane), we
should be able to us the radius-coradius boost symmetry to make the
average co-radius—representing the "overall scale"—roughly one.
2024-02-10 14:21:52 -05:00
8e33987f59
Systematically try out different cut planes
2024-02-10 13:46:01 -05:00
06872a04af
Say how many sample solutions we found
2024-02-10 01:06:06 -05:00
becefe0c47
Try switching to compiled system
2024-02-10 00:59:50 -05:00
34358a8728
Find witnesses on random rational hyperplanes
...
Choose hyperplanes that go through the trivial solution.
2024-02-09 23:44:10 -05:00
95c0ff14b2
Show explicitly that all coefficients are 1 in first cut equation
2024-02-09 17:09:43 -05:00
f97090c997
Try a cut that goes through the trivial solution
...
The previous cut was supposed to do this, but I was missing some parentheses.
2024-02-08 01:58:12 -05:00
45aaaafc8f
Seek sample solutions by cutting with a hyperplane
...
The example hyperplane yields a single solution, with multiplicity six. You can
find it analytically by hand, and homotopy continuation finds it numerically.
2024-02-08 01:53:55 -05:00
43cbf8a3a0
Add relations to center and orient the construction
2024-02-05 00:10:13 -05:00
21f09c4a4d
Switch element abbreviation from "elem" to "elt"
2024-02-04 16:08:13 -05:00
a3f3f6a31b
Order spheres before points within each coordinate block
...
In the cases I've tried so far, this leads to substantially smaller
Gröbner bases.
2024-02-01 16:13:22 -05:00
65d23fb667
Use module names as filenames
...
You're right: this naming convention seems to be standard for Julia
modules now.
2024-01-30 02:49:33 -05:00
4e02ee16fc
Find dimension of solution variety
2024-01-30 02:45:14 -05:00
6349f298ae
Extend AbstractAlgebra ideals to rational coefficients
...
The extension should also let us work over finite fields of prime order,
although we don't need to do that.
2024-01-29 19:11:21 -05:00
0731c7aac1
Correct relation equations
2024-01-29 12:41:07 -05:00
59a527af43
Correct Minkowski product; build chain of three spheres
2024-01-29 12:28:57 -05:00
c29000d912
Write a simple solver for the hitting set problem
...
I think we need this to find the dimension of the solution variety.
2024-01-28 01:34:13 -05:00
86dbd9ea45
Order variables by coordinate and then element
...
In other words, order coordinates like
(rₛ₁, rₛ₂, sₛ₁, sₛ₂, xₛ₁, xₛ₂, xₚ₃, yₛ₁, yₛ₂, yₚ₃, zₛ₁, zₛ₂, zₚ₃)
instead of like
(rₛ₁, sₛ₁, xₛ₁, yₛ₁, zₛ₁, rₛ₂, sₛ₂, xₛ₂, yₛ₂, zₛ₂, xₚ₃, yₚ₃, zₚ₃).
In the test cases, this really cuts down the size of the Gröbner basis.
2024-01-27 14:21:03 -05:00
463a3b21e1
Realize relations as equations
2024-01-27 12:28:29 -05:00
4d5aa3b327
Realize geometric elements as symbolic vectors
2024-01-26 11:14:32 -05:00
b864cf7866
Start drafting engine prototype
2024-01-24 11:16:24 -05:00
Glen Whitney
c48d685ad6
doc: Extend comments on coordinatization; add a theory.md notes file
2023-11-07 17:06:19 -08:00
Glen Whitney
15159302c3
doc: Add Aaron's observations on inversive coords
2023-11-06 11:47:53 -08:00
Glen Whitney
daed435826
doc: Add a few implementation goals to README
2023-11-01 13:08:20 -07:00
Glen Whitney
2cfcfacb5a
doc: Add new notes directory with design notes
2023-11-01 12:58:08 -07:00
fce8be5b56
Adjust lighting and camera for decent initial rendering of polyhedra
...
Note that the version of three.js also incidentally bumped, since it's set
to take the latest
2019-12-31 07:20:33 -08:00
Glen Whitney
9c2038e3c9
Enable mouse rotate, pan, and zoom with TrackballControls
2019-12-12 14:04:11 -05:00
Glen Whitney
c7f2feab1f
First pass at coordinate axes
2019-12-12 02:44:33 -05:00
Glen Whitney
413a8b5b81
Switch to good old make to reduce redundancies in build
2019-12-12 00:33:59 -05:00
Glen Whitney
2c17758987
0.1.1
2019-12-11 13:21:01 -05:00
Glen Whitney
6717a76f21
Copy only the production dependencies to the site directory
2019-12-11 13:20:31 -05:00
Glen Whitney
5fef463aba
0.1.0
2019-12-11 12:43:50 -05:00
Glen Whitney
c3995d6fcb
Set up testing with Ava
2019-12-11 12:07:43 -05:00
Glen Whitney
eb81cee609
Generate documentation by assembling markdown and litcoffee files
2019-12-09 20:52:42 -05:00
Glen Whitney
83318c7884
Set up npm run build to build dyna3
2019-12-09 12:08:05 -05:00
Glen Whitney
660f42b31f
Automatically generate externals.js from package-lock.json
...
This commit adds a utility to parse package-lock.json and write the proper
contents of externals.js to standard output. In addition, if the utility
(src/helpers/pkglock_to_externals.litcoffee) is invoked with a --doc option,
it instead emits a Markdown bulleted list of all of the external dependencies.
2019-12-08 23:22:52 -05:00
Aaron Fenyes
Glen Whitney