OneCAD/docs/perf.md

# Design loading

## Parallel STEP body preparation (2026-10-12)

Profiling an original 48-cylinder STEP fixture before changing the importer measured
3.17 ms parsing, 6.06 ms reconstructing B-reps and 45.58 ms preparing/orienting bodies.
The five complete imports had a median of 59.21 ms. The expensive orientation mesh,
rather than the text parser, was the first parallelization target for #287.

Desktop import now prepares consecutive independent solids in a representation with
up to eight workers. Each batch contains at most 64 solids. Parsing, B-rep reconstruction,
assembly traversal, first-use unit resolution, naming and result collection remain ordered.
Mapped items end a batch. Fewer than four solids use the serial path; wasm always uses it.
Thread creation failure falls back to serial work, and kernel/worker failures remain
per-body errors reported by the importer.

Windows x64, AMD Ryzen AI Max+ 395 (16 cores / 32 logical processors), optimized `ci`
profile, no concurrent build: three fresh test processes per fixture, five alternating
serial/parallel pairs in each process. These are complete uncached kernel imports,
including parsing and body preparation; fixture generation/export and later desktop
display meshing are outside the timer. Both paths use the same input text and code.

| Original generated fixture | Bodies | Serial median | 8 workers median | Reduction |
|---|---:|---:|---:|---:|
| Cylinders, radius 5 mm, height 12 mm | 48 | 57.54 ms | 17.38 ms | 69.8% |
| Cylinders, radius 5 mm, height 12 mm | 512 | 896.31 ms | 313.06 ms | 65.1% |
| Tori, major radius 20 mm, minor radius 4 mm | 48 | 269.05 ms | 51.90 ms | 80.7% |
| Boxes, 10 × 15 × 12 mm | 512 | 247.97 ms | 90.15 ms | 63.6% |
| Boxes, 10 × 15 × 12 mm | 4 | 1.49 ms | 1.02 ms | 31.5% |
| One cylinder (serial fallback) | 1 | 1.22 ms | 1.29 ms | serial fallback |

There are 15 samples per cell. The single-cylinder modes run identical serial code; their
0.07 ms median difference is within the overlapping 1.11–1.57 / 1.13–1.52 ms ranges. The 512-cylinder runs ranged from 567.40–983.61 ms
serial and 197.72–345.51 ms parallel; scheduling/thermal variation is material. These
synthetic results do not establish a speedup for every assembly or complete desktop Open.
In particular, parts containing only one solid are not parallelized across assembly nodes.
Cross-part scheduling, parallel B-rep reconstruction and later display meshes remain open.

Reproduce after compiling, without other builds running:

```sh
cargo test -p solidcraft-kernel --profile ci benchmark_independent_step_solids --no-run
SOLIDCRAFT_STEP_BENCH_COUNT=512 SOLIDCRAFT_STEP_BENCH_KIND=cylinder \
  cargo test -p solidcraft-kernel --profile ci benchmark_independent_step_solids \
  -- --ignored --nocapture --test-threads=1
```

Use `torus` or `box` for the other fixtures and repeat in three fresh processes.
`SOLIDCRAFT_STEP_BENCH_FIXTURE` optionally writes the original STEP for native inspection.
No timing threshold runs in CI. Regressions compare serial and threaded imports with
different worker counts: exact display meshes, measures, body/face source identities,
names, colours/opacity, units, rotated assembly placements, duplicates and partial failures
across the batch boundary. The public analytic/FreeCAD reference suite also checks STEP
export/import; its current results are reported in docs/oracle.md.
## Design storage: container and binary payloads (#303, phase one)

Design containers avoid formatting/parsing imported mesh coordinates as JSON numbers.
The metadata serializer replaces embedded fields before creating JSON values, without
cloning the full document or duplicating its schema. Binary coordinates retain `f64`
precision, indices retain `u32`, and SHA-256 deduplicates identical payloads. The reader
checks archive budgets, CRCs, hashes, exact lengths, finite coordinates and index bounds.

Reproduce the storage measurements with an optimized `ci` IO test executable:

```sh
cargo test -p solidcraft-io --profile ci benchmark_ -- --ignored --nocapture --test-threads=1
```

The benchmarks generate an original 100,000-vertex/100,000-triangle mesh and a STEP
containing 512 disjoint 10 mm boxes. Fixtures are written under `CARGO_TARGET_DIR`
(or the crate's `target` directory). Each compares nine encoding/decoding samples;
atomic-save samples include encoding, temporary-file flush, replacement and `.bak`
creation and alternate JSON/container ordering. Documents are compared after decoding.
These are storage measurements, separate from timeline evaluation or first-frame latency.

On Windows x64, based on upstream `e6e0a7e` before STEP parallelism (#312), three
consecutive optimized runs without concurrent compilation gave
the following medians of the three nine-sample medians (milliseconds, fast mode):

| Fixture / operation | JSON | Container |
|---|---:|---:|
| Mesh size, bytes | 15,139,115 | 3,600,828 |
| Mesh encode | 23.336 | 6.094 |
| Mesh decode | 57.175 | 2.962 |
| Mesh atomic save | 52.924 | 14.856 |
| STEP size, bytes | 1,998,793 | 1,950,056 |
| STEP encode | 1.507 | 1.473 |
| STEP decode | 1.479 | 1.318 |
| STEP atomic save | 7.213 | 7.087 |

Three alternating fresh-process `solidcraft-cli bench-open` runs of each STEP encoding
returned the same 512 bodies and 6,144 triangles. Median read-plus-parse was 2.274 ms
for JSON and 2.151 ms for the container; median evaluation was 218.559/236.915 ms and
display meshing 203.160/197.790 ms respectively. Geometry dominates and these variable
results do not establish an end-to-end STEP opening improvement. Fresh processes do
not imply a cold operating-system file cache, and these are not desktop first-frame times.

Fast mode stores STEP and mesh payloads directly. Explicit `"compression":"compact"`
compresses them at Deflate level one; it is a space/CPU tradeoff. In the initial
512-box STEP experiment, compression reduced 1,998,793 JSON bytes to 578,659 package
bytes but increased median encoding from 1.68 to 5.02 ms and decoding from 1.76 to
4.18 ms. That regression is why compression is not the default. PNG/JPEG are stored
directly in either policy; small parametric metadata uses Deflate level one.

Plain JSON remains a supported Save As/export format; `.json` saves keep JSON and
scripts may explicitly select either format. The CLI detects packages before attempting
JSON parsing. Desktop/browser recovery and browser downloads also use the container.
See [the versioned container format](design-container.md) for layout and bounds.

This phase does not restore evaluated B-reps, skip STEP import, or make cold geometry
rebuilds instant. A matching cache key is not enough to trust unvalidated geometry.
Evaluated B-rep/state restoration remains further work in #303. The provisional saved
display described below is separate from #287's import parallelism.

## Provisional saved display (#303)

Desktop Open can show an experimental saved picture while the existing file worker rebuilds geometry.
It requires an explicit `preview: true` engine Save/Save As call. Ordinary saves omit
display caches to avoid the measured overhead; native evaluated B-rep caching remains open.
The cache contains only already warm evaluated display meshes, capped at 8 MiB, 1,024
bodies and 100,000 triangles. Larger or cold models save without it. Cached geometry is
never used for editing, measurements or picking. Source/document fingerprints and
payload validation reject stale or malformed caches; cancellation and document/revision
checks prevent a background result from replacing newer work.

The cached picture is prepared on the file worker from the same file snapshot as the
normal Open command. It adds work before reconstruction, rather than bypassing it, so
measure preview readiness and full editing readiness separately. Cached display also
adds file size and save work; the storage-only results above exclude that optional data.

For an engine-level save benchmark, first generate the original 512-box STEP fixture
with the ignored IO benchmark, then run the warmed-session benchmark:

```sh
cargo test --workspace --profile ci benchmark_step_storage -- --ignored --nocapture --test-threads=1
cargo test --workspace --profile ci benchmark_warm_design_save_with_preview -- --ignored --nocapture --test-threads=1
```

Set `CARGO_TARGET_DIR` to the workspace's absolute target directory in both commands.
The engine benchmark alternates nine JSON/container atomic saves, includes the optional
display cache, and verifies both preview decoding and authoritative document identity.
Three runs on Windows, with no concurrent build or test suite, measured median atomic
JSON saves of 7.679/7.610/7.630 ms and container-with-preview saves of
10.319/10.633/10.541 ms. Preview decoding took 0.964/0.961/1.130 ms; the container
was 2,510,490 bytes. This optional preview costs save time on this STEP fixture.
An actual desktop sensor-enclosure opening on e8a8e0f prepared its saved picture in
24.320 ms; geometry reconstruction, display warmup and thumbnail preparation took
8,913.212 ms. The same preview experiment is now explicitly opt-in; full geometry
readiness still requires reconstruction.
For actual desktop opening phases, launch with `SOLIDCRAFT_PROFILE_OPEN=1`: `ready_ms`
reports saved-picture preparation, while the normal phase log reports reconstruction,
display warmup and thumbnail completion. Neither log measures the exact GPU first frame.

## Analytic extrusion source preparation

New-body extrusion certificates now prepare the sketch's bounded analytic segments once
per certification pass instead of allocating segments and resolving their points for each
generated cap boundary and side face. Saved designs run this same code during cold rebuilds.
Exact containment tolerances, ambiguous-source rejection and the certification work budget
are unchanged. Prepared segments borrow an immutable evaluated sketch and are not retained
across edits.

The reproducible microbenchmark is:

```sh
cargo test -p solidcraft-doc --profile ci benchmark_prepared_extrude_sources -- --ignored --nocapture
```

Three Windows x64 optimized `ci` runs, during other compilation, compared the previous
segment reconstruction loop and the prepared matcher in the same process. For 1,000
analytic lines and 1,000 generated face segments, median time fell from **45.90 ms to
12.30 ms** (73% less, about 3.7x faster). Preparation is included and every returned source
identity is compared. This measures certification only, not complete extrusion, file-open
latency or Boolean operations; it does not establish an end-to-end loading speedup.
Remaining cold geometry rebuild and import costs are tracked in
[#255](https://github.com/bherbruck/solidcraft/issues/255); certification work is
[#254](https://github.com/bherbruck/solidcraft/issues/254).

## Cold geometry rebuilds after 0.3.1

Three alternating cold-process comparisons on the same Windows machine and optimized
`ci` profile, with no concurrent build, compare the unchanged 0.3.1 source with the
straight-line projection and exact surface-refinement reuse changes:

| Saved design | Before, median evaluation | After | Reduction |
|---|---:|---:|---:|
| Public sensor enclosure, 21 features, 52 KB | 11.96 s | 8.85 s | 26.0% |
| Local Pi case assembly, 25 features, 2,990 bodies | 14.75 s | 11.57 s | 21.6% |

These are geometry rebuild times, not complete desktop opening times. The public fixture
can be generated with `solidcraft-cli run examples/acceptance/sensor_enclosure.json
--save sensor.solidcraft --quiet`, then measured with `solidcraft-cli bench-open
sensor.solidcraft`. Each benchmark starts a new process; this does not measure a warm
timeline-cache hit. The local assembly is private and is not part of the repository.

Straight segments now use guarded algebraic closest-point projection instead of sampling
65 points and running Newton iterations. Other curve types retain their existing behavior.
Curved-face refinement reuses derivative and midpoint evaluations with exact finite input
keys and bounded, local caches. It keeps the original tolerance, seam and singularity
checks, refinement passes, and triangle limits.

Identity assembly placements retain the definition body's shared display-mesh cache.
Changed placements continue to build separate meshes in their own coordinates. Face-name
preparation remains eager during placement: deferring it merely shifted expensive work to
thumbnails and the first face query, so that approach was excluded.

Both saved fixtures retain exactly the same body names, face/edge/vertex/shell counts,
bounds, volumes, and surface areas. Focused tests compare cached and uncached refinement
coordinates and normals bit for bit on periodic, singular and transformed surfaces.

For desktop phase profiling, set `SOLIDCRAFT_PROFILE_OPEN=1` before launching the app.
Interactive Open reports geometry, placement, tessellation, thumbnail and total worker
times to stderr without logging the source path. Thumbnails were about 0.1 seconds of
the slow assembly's open and were not the main bottleneck. Further cold Boolean and
import costs remain; these changes do not make all documents open instantly.

### Prepared assembly geometry and selection

Prepared world geometry is now keyed by the document, evaluated model and exact placement
context instead of the session revision. Selecting a face or edge, changing visibility,
or moving the view no longer discards already prepared assembly bodies and meshes.
Geometry edits, pending occurrence moves, authoring context changes, undo/redo and timeline
rollback still invalidate the cache. Scratch sessions share prepared geometry while their
inputs match, and adopting a computed session retains its warm cache.

On the private 2,990-body Pi assembly, a matched Linux desktop control probe reduced an
edge-selection round trip from 9.24 s to 0.57 s. Initial opening stayed essentially unchanged
(33.54 s to 33.32 s); this fixes a separate selection stall, not cold geometry evaluation.
Three fresh Windows desktop runs with the corrected cache measured a median 15.87 s to
ready: 13.04 s geometry, 2.20 s placement, 0.53 s meshing and 0.07 s thumbnails. These used
the optimized `ci` profile and actual Vulkan rendering, with isolated settings and caches.
Linux and Windows timings are separate measurements and must not be compared as a speedup.

`solidcraft-cli bench-open design.solidcraft` reports JSON lines for file reading,
JSON decoding and migrations (including input-name repair), timeline evaluation, individual
features, and world placement/display meshing. `--parse-only` stops before geometry evaluation.
The parse timer includes document validation and repair, not just the JSON parser.

Windows x64, optimized `ci` profile, measured during other builds:

| Design | Parse/repair | Evaluate | Display meshes |
|---|---:|---:|---:|
| 19-feature enclosure, 34 KB | 1.2 ms | 14.9 s | 6 ms |
| 25-feature assembly, 15.2 MB, 2,990 bodies | 21 ms | 12.5 s | 2.1 s |
| Generated 1,000 independent boxes, 185 KB | 5 ms | 0.82 s | 0.15 s |
| Generated 5,000 boxes in five grids, 10 features | 0.45 ms | 17.6 s | 0.81 s |

The enclosures spend most of evaluation in joins and cuts, not parsing. Designs save feature
definitions; opening them rebuilds their geometry. Those times remain after the repair fix.

A separate generated timeline with missing input names reproduced minutes in the reader:

| Timeline (geometry rolled back) | Parse/repair before | After |
|---|---:|---:|
| 2,000 boxes, 6,000 unnamed inputs | 78.1 s | 10–20 ms |
| 5,000 boxes, 15,000 unnamed inputs | interrupted after 131 s, still repairing | 26–46 ms |

Previously, each missing input restarted the `d1`, `d2`, … search, scanning the document for
every candidate. This approaches cubic work as unnamed inputs accumulate. Loading now reserves
names once and assigns missing names with an advancing cursor. Existing names, names on later
features, parameter collisions and reuse of surplus names retain the previous behavior.
Regression tests compare the old and bulk repairs and load a 5,000-feature unnamed timeline.

# Viewport performance

Measured with the control channel (`ui.inspect` `frame_ms`: CPU time of one UI frame, which
includes picking under the cursor) on the sample plate patterned 20 × 20 (400 bodies, about
600k triangles), 1600 × 1000 window under Xvfb, release build. Hover: 60 cursor moves across
the model; orbit: a right-drag.

| | hover median | hover p90 | orbit median |
|---|---|---|---|
| before | 18.7 ms | 37.5 ms | 21.0 ms |
| after | 1.9 ms | 2.4 ms | 2.6 ms |
| after, Browser hidden | 0.4 ms | — | 0.4 ms |

What changed:
- **Picking culls by bounding box.** Per-body boxes are cached until the model changes. The
  face raycast skips bodies whose box the ray misses or enters behind the nearest hit so far.
  Edge and vertex tests skip bodies whose box, projected on screen, is not under the cursor.
- **Picks are reused** while the cursor, camera and model are unchanged, and **no picking runs
  while the view moves** (orbit, pan, zoom).
- **The model extent is cached** (it sets the view's depth range and was recomputed from every
  mesh several times per frame).

With 49 bodies the frame was already 2.8 ms (hover) before these changes. The remaining frame
time with the Browser shown is mostly the Browser listing every body row. GPU ID-buffer picking
was not needed at this size.

## Browser

Same model and method (400 bodies, Bodies folder open, 60 hover moves over the viewport):

| | median | p90 |
|---|---|---|
| Browser shown, before | 1.95 ms | 2.71 ms |
| Browser shown, after | 0.72 ms | 1.19 ms |
| Browser hidden | 0.30 ms | 0.72 ms |

What changed: rows scrolled out of view only reserve their height. They register no widgets
and paint nothing (no text layout, icons or eye/fold buttons), so the cost follows the rows on
screen rather than the rows in the tree. Scrolling, Find in Browser and drag and drop still see
every row's place.

# Recompute performance

`solidcraft-cli bench-edit <script> <param> "(<old>) * 1.02"` builds a design from its script
(timing the build), then times a parameter edit, setting the parameter back to its old
expression, undo and redo. Each cell is before → after the evaluation cache, with the number of
features recomputed in parentheses. Release build, on a machine shared with other build jobs (load average about 45; the
times vary by ±50 % run to run, so compare the recompute counts and the zeros). "Early" edits a parameter of the
first sketch or feature, "late" one of the last feature.

| Design | Edit | Build | Edit | Set back | Undo | Redo |
|---|---|---|---|---|---|---|
| sample plate, 20 × 20 pattern | early (`width`) | 7587 ms (10) → 1764 ms (10) | 7969 ms (10) → 1691 ms (10) | 7557 ms (10) → 0 ms (0) | 6534 ms (0) → 0 ms (0) | 4570 ms (0) → 0 ms (0) |
| sample plate, 20 × 20 pattern | late (`d9`) | 7870 ms (10) → 1699 ms (10) | 3944 ms (1) → 812 ms (1) | 4039 ms (1) → 0 ms (0) | 1464 ms (0) → 0 ms (0) | 1398 ms (0) → 0 ms (0) |
| oracle 58 phone stand | early (`d1`) | 163 ms (6) → 140 ms (6) | 228 ms (5) → 140 ms (5) | 171 ms (5) → 0 ms (0) | 158 ms (0) → 0 ms (0) | 130 ms (0) → 0 ms (0) |
| oracle 58 phone stand | late (`d4`) | 144 ms (6) → 195 ms (6) | 118 ms (1) → 118 ms (1) | 145 ms (1) → 0 ms (0) | 149 ms (0) → 0 ms (0) | 187 ms (0) → 0 ms (0) |
| oracle 59 enclosure base | late (`d8`) | 11582 ms (11) → 11179 ms (11) | 5772 ms (1) → 5742 ms (1) | 5606 ms (1) → 0 ms (0) | 6023 ms (0) → 0 ms (0) | 6119 ms (0) → 0 ms (0) |
| oracle 60 pipe flange | early (`d1`) | 8137 ms (7) → 8348 ms (7) | 7569 ms (6) → 10143 ms (6) | 8354 ms (6) → 0 ms (0) | 8607 ms (0) → 0 ms (0) | 10034 ms (0) → 0 ms (0) |
| oracle 60 pipe flange | late (`d6`) | 7661 ms (7) → 11990 ms (7) | 67 ms (1) → 361 ms (1) | 69 ms (1) → 0 ms (0) | 84 ms (0) → 0 ms (0) | 66 ms (0) → 0 ms (0) |
| oracle 61 shaft keyway | early (`d1`) | 1723 ms (6) → 3016 ms (6) | 1785 ms (5) → 2745 ms (5) | 1760 ms (5) → 2323 ms (5) | 1667 ms (0) → 0 ms (0) | 1719 ms (0) → 0 ms (0) |
| oracle 61 shaft keyway | late (`d4`) | 1905 ms (6) → 2247 ms (6) | 1734 ms (1) → 2101 ms (1) | 1682 ms (1) → 0 ms (0) | 1719 ms (0) → 0 ms (0) | 1876 ms (0) → 0 ms (0) |
| oracle 62 heat sink | early (`d1`) | 382 ms (6) → 643 ms (6) | 362 ms (5) → 697 ms (5) | 233 ms (5) → 568 ms (5) | 245 ms (0) → 0 ms (0) | 360 ms (0) → 0 ms (0) |
| oracle 62 heat sink | late (`d5`) | 479 ms (6) → 688 ms (6) | 270 ms (1) → 657 ms (1) | 321 ms (1) → 0 ms (0) | 413 ms (0) → 0 ms (0) | 283 ms (0) → 0 ms (0) |
| oracle 63 hinge knuckle | early (`d1`) | 1305 ms (8) → 1671 ms (8) | 1329 ms (7) → 2397 ms (7) | 1971 ms (7) → 0 ms (0) | 1705 ms (0) → 0 ms (0) | 1321 ms (0) → 0 ms (0) |
| oracle 63 hinge knuckle | late (`d4`) | 1430 ms (8) → 2072 ms (8) | 1387 ms (1) → 2073 ms (1) | 1480 ms (1) → 0 ms (0) | 1192 ms (0) → 0 ms (0) | 1035 ms (0) → 0 ms (0) |

What changed: every feature evaluation is cached by a key made of the feature's own inputs
(definition and parameter values), the document context it may read (construction planes,
sheet metal and plastic rules, components) and a digest of the model it starts from, in which
each body is identified by the evaluation that produced it (bodies a feature passes through
unchanged keep their identity). The same feature on the same inputs is never evaluated twice:
setting a value back, undo, redo, a preview followed by the same command, and the repeated
evaluations while a script builds the design all reuse earlier results. The cache is shared by a
model and its copies (previews, scratch sessions) and keeps the last 4096 results.

An edit still recomputes the edited feature and every later feature whose starting model
changed; in these parts every later feature works on the edited body, so early edits recompute
almost everything, as they must. `cached_evaluation_matches_from_scratch` checks that cached and
from-scratch evaluation give the same models (bodies, volumes and areas to 1e-6, topology,
errors) through edits, suppression, roll-back, undo and redo. Setting a sketch dimension back
can still recompute (oracle 61, 62): solving the sketch moves its points by rounding noise, so
its inputs are not exactly the old ones. Oracle 59's first parameter edit fails (a recipe
expression the bench's `* 1.02` can't scale) and is left out.


## Desktop loading and recent thumbnails (2026-10-10)

The Arduino Uno enclosure (19 features, 34 KB) and Raspberry Pi 5 case (24 features,
61 KB) each decode in about 1 ms. A release build spends roughly 12.1 s and 8.2 s,
respectively, evaluating their geometry on this Windows machine. Changing the document
encoding does not eliminate these boolean operations.

Interactive Open, recent-file clicks, drag/drop and STEP/mesh insertion now execute on a
worker, including preparation of the world-space bodies and display meshes. The existing
design stays available until the result is ready; a failed or cancelled job cannot replace
it. Insertion preserves the file, saved state, earlier undo history and view settings.
Timeline copies share their lazy mesh cell, and adopting a prepared session keeps its warm
world-space cache instead of transforming and tessellating its components again on the UI.
A STEP body's missing-face check reuses its orientation tessellation when the tolerances
match and its orientation was not reversed.

Live desktop tests (`ci` profile, with other builds/tests running) opened the Arduino and
Pi case in 15.2 s and 10.5 s. During those jobs, median `ui.inspect` round trips were 20.5 ms
and 8.3 ms; the slowest were 33.7 ms and 28.6 ms. This fixes the window freeze, not the
remaining cost of cold geometry evaluation.

Recent thumbnails are 240 × 150 PNG files in `SolidCraft/thumbnails` under the platform
cache directory (`LOCALAPPDATA` on Windows). Their keys include the source path, file size
and modification time. Open and Save render from the model already in memory. Cached
recents decode the PNG without reading or rebuilding a document, and run before cold
recents and sample thumbnails. Missing or invalid pictures fall back to a background rebuild.
No thumbnail or base64 image is added to the design JSON. A regression test verifies the
source bytes remain unchanged, a cached picture works even without a parseable source
file, and changing the source invalidates the cache.

`solidcraft-cli bench-open` also accepts STEP/IGES. For exchange files its `parse` phase
includes constructing and checking the imported B-rep, not merely decoding STEP syntax.

The live test loaded both cached recent cards in 21 ms and inserted the 2 MB lightweight
Pi STEP (27 bodies) into the case in 279 ms; undo restored the original two bodies. The
full 77 MB board STEP (2689 solid definitions, 45,689 faces) still had not completed after
300 s. Its window continued handling inspection and Cancel, and cancelling preserved the
case. Complex STEP construction remains an outstanding kernel performance problem.

# Sketch solver and drags (2026-10-11)

Unknowns the constraints pin down one after another from the constants (each one's own rows
of full, well-conditioned rank, reading nothing but constants and unknowns pinned before it)
are eliminated exactly: values the constructive seed placed and whose constraints hold there
stay constants while Levenberg–Marquardt solves the rest, and the rank analysis (degrees of
freedom, determined geometry) runs on the remainder only. A component tied to no constant takes
one point as a constant first (its translation). All the held solves of one live drag frame
share a 1M decomposition work budget (about 16 ms; a solve's own, 20M, is about 0.3 s), and a
drag's steps are a quarter of the smallest held size instead of an eighth, except once a seed
ran out of budget: the rest of that drag goes in eighths, as before, and continuation keeps
the branch the seed no longer places.

`cargo run --release -p solidcraft-sketch --example solve_bench`, macOS arm64, load average
45–75 (best of 5):

| Grid (origin corner fixed, rows horizontal, columns vertical, every edge a distance) | Start | Before | After |
|---|---|---:|---:|
| 10 × 10 | at solution | 0.36 ms | 0.21 ms |
| 10 × 10 | ±1 mm | 0.34 ms | 0.21 ms |
| 15 × 15 | at solution | 1.41 ms | 0.41 ms |
| 15 × 15 | ±1 mm | 1.39 ms | 0.40 ms |
| 20 × 20 | at solution | 4.06 ms | 0.72 ms |
| 20 × 20 | ±1 mm | 4.44 ms | 0.73 ms |

The seed constructs every grid point, so LM gets no variable (a test counts them). Before, the
time was the dense rank analysis of the whole grid. A 100-rectangle strip with nothing fixed,
solved whole from a moved corner, still costs 20–27 ms: nothing is constructed there and LM
iterates on every point with dense normal equations (a sparse solve would be the next step).

Drag frames, `sketch.drag` + `world_state()` per frame (60 frames of 0.5 mm, best of 5; the
"before" column is one run of the same bench on the previous code):

| Sketch | Points | Scripted ms/frame before → after | Live ms/frame before → after | `drag_end` ms before → after |
|---|---:|---:|---:|---:|
| 100 rectangles | 401 | 2.77 → 2.37 | 1.13 → 1.02 | 1.44 → 1.37 |
| 100 rectangles, rolled back under an extrude | 401 | 2.49 → 2.33 | 1.13 → 0.97 | 1.42 → 1.28 |
| 100-rectangle connected strip | 401 | 100.9 → 2.32 | 1.32 → 1.20 | 53.6 → 1.41 |
| 100-rectangle strip, rolled back under an extrude | 401 | 203.8 → 2.23 | 1.31 → 1.18 | 54.0 → 1.42 |
| rigid truss of 40 triangles, pinned at one end, dragged at the other | 42 | — → 6.8 | — → 6.3 | — → 0.59 |

The strip floats (nothing fixed), so its full solves (scripted frames, `drag_end`) ran the
dense rank analysis on 800 variables; with one corner taken as a constant all of it is
eliminated. A live frame's held solve was already cheap: the seed places the strip and LM
returns at once. Of a live strip frame, the seed reads the constraints in about 0.15 ms, so a
per-gesture cache of that reading is not worth its invalidation (its signs depend on the
reference positions, which change every step).