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Add the kaleidocycle

Vectornaut 2025-05-27 09:16:21 +00:00
parent 1d30ac652a
commit 7c034db3f1
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Test-problems.md

@ -54,7 +54,7 @@ What are the diameters of the other chain spheres?
#### Coverage
As of pull request #84, the function [`engine::examples::realize_irisawa_hexlet`](../src/commit/2adf4669f47ab8f2bff8d64ac011a2bd09f632fa/app-proto/src/engine.rs#L526-L573) sets up and solves this problem for use in the unit test [`irisawa_hexlet_test`](../src/commit/2adf4669f47ab8f2bff8d64ac011a2bd09f632fa/app-proto/src/engine.rs#L715-L727) and the example [`irisawa-hexlet.rs`](https://code.studioinfinity.org/StudioInfinity/dyna3/src/commit/2adf4669f47ab8f2bff8d64ac011a2bd09f632fa/app-proto/examples/irisawa-hexlet.rs).
As of pull request #84, the function [`engine::examples::realize_irisawa_hexlet`](../src/commit/2adf4669f47ab8f2bff8d64ac011a2bd09f632fa/app-proto/src/engine.rs#L518-L573) sets up and solves this problem for use in the unit test [`irisawa_hexlet_test`](../src/commit/2adf4669f47ab8f2bff8d64ac011a2bd09f632fa/app-proto/src/engine.rs#L715-L727) and the example [`irisawa-hexlet.rs`](https://code.studioinfinity.org/StudioInfinity/dyna3/src/commit/2adf4669f47ab8f2bff8d64ac011a2bd09f632fa/app-proto/examples/irisawa-hexlet.rs).
You can also set up and solve the problem by hand. A good way to do this is to first impose all the tangencies and then start fixing diameters. Right now, the engine isn't very robust, so you'll have to adjust the spheres as you set up the problem to help the engine satisfy each additional constraint.
@ -79,6 +79,16 @@ O’Hara has described the configuration space of hexagons in 3-space which are
According to Dan Piker, the configuration space of right-angled equilateral heptagons also has at least one one-dimensional component.
### Kaleidocycle
#### Statement
A kaleidocycle has seven degrees of freedom: six from the Euclidean motions and one from twisting.
#### Coverage
As of pull request #84, the function [`engine::examples::realize_kaleidocycle`](../src/commit/2adf4669f47ab8f2bff8d64ac011a2bd09f632fa/app-proto/src/engine.rs#L575-L618) sets up a kaleidocycle using distance constraints between points and finds its tangent space. The unit test [`tangent_test_kaleidocycle`](../src/commit/2adf4669f47ab8f2bff8d64ac011a2bd09f632fa/app-proto/src/engine.rs#L814-L881) confirms that the tangent space includes the twist motion. The example [`kaleidocycle.jl`](../src/commit/2adf4669f47ab8f2bff8d64ac011a2bd09f632fa/app-proto/examples/kaleidocycle.rs) finds the twist motion.
### Generalized conic: multifocal ellipsoid
#### Source