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Vectornaut:regulators-always-valid
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Vectornaut:tangent-space
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3 commits
uniform-pr ... main

Author SHA1 Message Date
Vectornaut
46324fecc6 Use workaround to keep representation coordinates in order (#46) 
This fixes #41 by rendering representation vectors with a static list view rather than an `Indexed` view. The Sycamore maintainer has confirmed that `Indexed` is always supposed to display list items in order, so I think #41 is likely caused by a bug in `Indexed`. We should consider reverting this pull request when the bug is fixed.

Co-authored-by: Aaron Fenyes <aaron.fenyes@fareycircles.ooo>
Reviewed-on: glen/dyna3#46
Co-authored-by: Vectornaut <vectornaut@nobody@nowhere.net>
Co-committed-by: Vectornaut <vectornaut@nobody@nowhere.net>
 2025-02-08 06:08:36 +00:00
Vectornaut
25017176fd Adjust normalization step of nudge routine (#43) 
The brach to be merged partially addresses issue #42 by changing the way we normalize element representations after stepping them in a straight line through configuration space during a nudge. On the main branch, we rescale the whole representation vector. On the branch to be merged, we instead contract the representation vector toward the last coordinate axis by rescaling the spatial and curvature components.

### Improvement in leakage

This change reduces the directional leakage described in #42. For a quantitative comparison, I used the [reproduction prodcedure](issues/42#user-content-leakage) from that issue, holding **W** until the second coordinate of Deimos had increased by 4 units (from 0.6 to 4.6). During this motion, the third coordinate changed by 0.158 units on the main branch, but only 0.007 units on the branch to be merged. In other words, this pull request decreased drift by roughly a factor of 20.

### Neutral changes in oscillation and jitter

This change makes oscillation and jitter happen differently during the reproduction procedures from #42, but I wouldn't describe them as being better or worse.

Co-authored-by: Aaron Fenyes <aaron.fenyes@fareycircles.ooo>
Reviewed-on: glen/dyna3#43
Co-authored-by: Vectornaut <vectornaut@nobody@nowhere.net>
Co-committed-by: Vectornaut <vectornaut@nobody@nowhere.net>
 2025-02-06 22:53:41 +00:00
Vectornaut
817a446fad Switch to Euclidean-invariant projection onto tangent space of solution variety (#34) 
This pull request addresses issues #32 and #33 by projecting nudges onto the tangent space of the solution variety using a Euclidean-invariant inner product, which I'm calling the *uniform* inner product.

### Definition of the uniform inner product

For spheres and planes, the uniform inner product is defined on the tangent space of the hyperboloid $\langle v, v \rangle = 1$. For points, it's defined on the tangent space of the paraboloid $\langle v, v \rangle = 0,\; \langle v, I_\infty \rangle = 1$.

The tangent space of an assembly can be expressed as the direct sum of the tangent spaces of the elements. We extend the uniform inner product to assemblies by declaring the tangent spaces of different elements to be orthogonal.

#### For spheres and planes

If $v = [x, y, z, b, c]^\top$ is on the hyperboloid $\langle v, v \rangle = 1$, the vectors
$$\left[ \begin{array}{c} 2b \\ \cdot \\ \cdot \\ \cdot \\ x \end{array} \right],\;\left[ \begin{array}{c} \cdot \\ 2b \\ \cdot \\ \cdot \\ y \end{array} \right],\;\left[ \begin{array}{c} \cdot \\ \cdot \\ 2b \\ \cdot \\ z \end{array} \right],\;\left[ \begin{array}{l} 2bx \\ 2by \\ 2bz \\ 2b^2 \\ 2bc + 1 \end{array} \right]$$
form a basis for the tangent space of hyperboloid at $v$. We declare this basis to be orthonormal with respect to the uniform inner product.

The first three vectors in the basis are unit-speed translations along the coordinate axes. The last vector moves the surface at unit speed along its normal field. For spheres, this increases the radius at unit rate. For planes, this translates the plane parallel to itself at unit speed. This description makes it clear that the uniform inner product is invariant under Euclidean motions.

#### For points

If $v = [x, y, z, b, c]^\top$ is on the paraboloid $\langle v, v \rangle = 0,\; \langle v, I_\infty \rangle = 1$, the vectors
$$\left[ \begin{array}{c} 2b \\ \cdot \\ \cdot \\ \cdot \\ x \end{array} \right],\;\left[ \begin{array}{c} \cdot \\ 2b \\ \cdot \\ \cdot \\ y \end{array} \right],\;\left[ \begin{array}{c} \cdot \\ \cdot \\ 2b \\ \cdot \\ z \end{array} \right]$$
form a basis for the tangent space of paraboloid at $v$. We declare this basis to be orthonormal with respect to the uniform inner product.

The meanings of the basis vectors, and the argument that the uniform inner product is Euclidean-invariant, are the same as for spheres and planes. In the engine, we pad the basis with $[0, 0, 0, 0, 1]^\top$ to keep the number of uniform coordinates consistent across element types.

### Confirmation of intended behavior

Two new tests confirm that we've corrected the misbehaviors described in issues #32 and #33.

Issue | Test
---|---
#32 | `proj_equivar_test`
#33 | `tangent_test_kaleidocycle`

Co-authored-by: Aaron Fenyes <aaron.fenyes@fareycircles.ooo>
Reviewed-on: glen/dyna3#34
Co-authored-by: Vectornaut <vectornaut@nobody@nowhere.net>
Co-committed-by: Vectornaut <vectornaut@nobody@nowhere.net>
 2025-01-31 19:34:33 +00:00
2 changed files with 24 additions and 19 deletions
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19
app-proto/src/assembly.rs
View file

@ -5,7 +5,7 @@ use std::{collections::BTreeSet, sync::atomic::{AtomicU64, Ordering}};
use sycamore::prelude::*;
use web_sys::{console, wasm_bindgen::JsValue}; /* DEBUG */
use crate::engine::{realize_gram, local_unif_to_std, ConfigSubspace, PartialMatrix, Q};
use crate::engine::{realize_gram, local_unif_to_std, ConfigSubspace, PartialMatrix};
// the types of the keys we use to access an assembly's elements and constraints
pub type ElementKey = usize;
@ -371,8 +371,8 @@ impl Assembly {
}
}
// step each element along the mass shell geodesic that matches its
// velocity in the deformation found above
// step the assembly along the deformation. this changes the elements'
// normalizations, so we restore those afterward
/* KLUDGE */
// since our test assemblies only include spheres, we assume that every
// element is on the 1 mass shell
@ -380,9 +380,16 @@ impl Assembly {
elt.representation.update_silent(|rep| {
match elt.column_index {
Some(column_index) => {
let rep_next = &*rep + motion_proj.column(column_index);
let normalizer = rep_next.dot(&(&*Q * &rep_next));
rep.set_column(0, &(rep_next / normalizer));
// step the assembly along the deformation
*rep += motion_proj.column(column_index);
// restore normalization by contracting toward the last
// coordinate axis
let q_sp = rep.fixed_rows::<3>(0).norm_squared();
let half_q_lt = -2.0 * rep[3] * rep[4];
let half_q_lt_sq = half_q_lt * half_q_lt;
let scaling = half_q_lt + (q_sp + half_q_lt_sq).sqrt();
rep.fixed_rows_mut::<4>(0).scale_mut(1.0 / scaling);
},
None => {
console::log_1(&JsValue::from(

24
app-proto/src/outline.rs
View file

@ -64,11 +64,16 @@ fn ElementOutlineItem(key: ElementKey, element: assembly::Element) -> View {
move |sel| if sel.contains(&key) { "selected" } else { "" }
);
let label = element.label.clone();
let rep_components = element.representation.map(
|rep| rep.iter().map(
|u| format!("{:.3}", u).replace("-", "\u{2212}")
).collect()
);
let rep_components = move || {
element.representation.with(
|rep| rep.iter().map(
|u| {
let u_str = format!("{:.3}", u).replace("-", "\u{2212}");
view! { div { (u_str) } }
}
).collect::<Vec<_>>()
)
};
let constrained = element.constraints.map(|csts| csts.len() > 0);
let constraint_list = element.constraints.map(
|csts| csts.clone().into_iter().collect()
@ -129,14 +134,7 @@ fn ElementOutlineItem(key: ElementKey, element: assembly::Element) -> View {
}
) {
div(class="element-label") { (label) }
div(class="element-representation") {
Indexed(
list=rep_components,
view=|coord_str| view! {
div { (coord_str) }
}
)
}
div(class="element-representation") { (rep_components) }
div(class="status")
}
}