nishi code wiki / research / ruler-craft
Ruler-craft: descriptive geometry to modern metrology, applied to precision realism
Published · lineage: forks off digital twinning (the precision bars) and serves the marble-doctrine pointing machine directly · question: what measurement CRAFT — classical and modern — lets a few rulers triangulate truth we cannot see directly?
Freshness declared. Search budget exhausted this session: verified to the author's May-2026 horizon plus the corpus; the May→July 2026 tail is UNVERIFIED and flagged inline where it most likely moved (feed-forward reconstruction, metric monocular depth). Re-verify + archive pass queued.
The finding, and it indicts our current instrument. The mason's and draftsman's discipline — Monge's descriptive geometry (1799) — exists precisely because one projection cannot determine a solid: two orthogonal views can. Our pointing machine measures ONE frontal view, which means nose projection, chin projection, brow projection and cheek fullness are not merely imprecise — they are UNOBSERVABLE to it. Every depth judgement we have made about the face was inference, not measurement. The classical fix costs nothing: render a deterministic PROFILE alongside the frontal and measure both. That single change converts our largest blind spot into a numbered axis.
1. The classical ladder (each rung is a ruler used creatively, not a finer ruler)
| craft | the trick | what it buys us |
|---|---|---|
| Descriptive geometry (Monge; the stonecutter's tradition) | Two orthogonal projections + transfer lines determine every point of a solid; true lengths recovered by rotation into a plane | DEPTH becomes measurable. Front + profile of the same frozen pose = the full 3D landmark set. Nose/chin/brow projection, the rhinoplasty angles (nasolabial, nasofrontal, Goode ratio) are PROFILE quantities — unmeasurable frontally, trivial in profile. |
| Projective invariants (cross-ratio, harmonic range) | The cross-ratio of four collinear points survives ANY perspective projection — unknown camera, unknown distance | Ratios comparable between OUR camera and THEIR video camera without matching either. The corpus's unknown-optics problem partially dissolves. |
| Single-view metrology (vanishing points, ground-plane + vertical VP; forensic-grade) | Three orthogonal vanishing points recover camera internals; heights and plane distances become metric from ONE photo | Absolute scale from casual imagery when a horizon or any vertical/rectilinear structure is in frame — the SCALE ANCHOR problem the twin brief flagged. |
| Geodetic network adjustment (triangulation/trilateration, least squares, error ellipses) | Never trust one measurement: take MANY redundant ones and let the network adjustment beat the error down as √n; every point ends with an error ELLIPSE, not a guess | Our 16 landmarks admit 120 pairwise distances — we currently use ~10 hand-picked measures. Redundancy + adjustment is free precision and gives per-point confidence honestly. |
| Procrustes / GPA (statistical shape analysis, Kendall shape space) | Superimpose two shapes by optimal translation+rotation+scale; the RESIDUALS are the shape difference | Kills our anchor bias. IPD-anchoring on two points forces all error elsewhere; Procrustes distributes it optimally, so a residual means shape, not anchor choice. |
| EDMA (Euclidean Distance Matrix Analysis) | Compare the full inter-landmark DISTANCE matrix — coordinate-free, invariant to rotation/translation/reflection, no superimposition choice at all | Removes the “which anchor / which alignment?” argument permanently. Form-difference matrix names exactly which distances differ and by how much. |
| Thin-plate splines (D'Arcy Thompson's deformation grids, made computable) | Warp one shape onto the other; decompose the transformation into AFFINE (global stretch) plus non-affine PRINCIPAL WARPS ordered by spatial scale (bending energy) | The marble order as mathematics. Affine component = pass-1 mass. Large-scale warps = pass-2 secondary form. Small warps = relief. The decomposition literally emits the cut list in carve order. |
| Visual hull / shape-from-silhouette | Each silhouette is a hard geometric BOUND on the solid; N views intersect to a tight envelope | Cheap and robust: our render emits exact silhouettes, segmentation gives theirs. Bounds beat estimates — a hull violation is a certain error, not a probable one. |
2. The modern rungs (2023–2026) that change the corpus economics
| line | status | relevance |
|---|---|---|
| Feed-forward uncalibrated two-view reconstruction (DUSt3R 2024, MASt3R matching; successors through 2025) | RESEARCH, rapidly productising | Two photos of the same subject → a dense 3D pointmap with NO known camera parameters. This is the single most applicable new tool for our archive problem: any two frames become geometry. ⚠ most likely to have moved May→July 2026. |
| Metric monocular depth (Depth Anything V2, Metric3D/UniDepth class, 2024–25) | RESEARCH, strong | Absolute-scale depth priors from ONE frame — a second, independent scale anchor to cross-check the interpupillary prior. |
| Neural implicit surfaces + 3D Gaussian splatting reconstruction pipelines | RESEARCH → shipping tools | Multi-view video → mm-class surfaces; the practical route to T2/T3 twins from footage rather than scanners. |
| Dense 2D landmarking + segmentation as commodity (MediaPipe FaceLandmarker 468-point, in-browser) | SHIPPING | Already our detector leg. Its own anatomical prior is a known bias — measured this session at ~30% resistance to contradicting paint. |
| Bundle adjustment + self-calibration (COLMAP lineage) | SHIPPING, mature | The rigorous fallback: many frames, one consistent camera solution, residuals with covariances — the geodesy lesson applied to photographs. |
3. What we adopt, in order, and the exit for each
| # | adoption | cost | exit criterion |
|---|---|---|---|
| M1 | Orthogonal-pair measurement (Monge): a deterministic PROFILE view beside the frontal in the frozen ?anat mode; profile landmarks added to the table | one render lever + reference profile frames | nose/chin/brow PROJECTION reported in mm; the rhinoplasty angles measurable at last (nasolabial 105–115° target becomes checkable, not aspirational) |
| M2 | Full distance matrix + Procrustes/EDMA replacing 2-point anchoring and hand-picked measures | pure math on landmarks we already extract | every point carries an error ellipse; verdicts no longer depend on anchor choice; 120 distances instead of 10 measures |
| M3 | TPS decomposition of reference→ours; affine part reported separately from principal warps | standard morphometrics math | the cut list is EMITTED in carve order (affine → large warps → small warps) instead of chosen by me |
| M4 | Silhouette bound check per view | render already emits alpha; segmentation for the reference | any hull violation flagged as a CERTAIN geometric error — a floor no statistical fit can talk its way past |
| M5 | Two-view feed-forward reconstruction on corpus frames (DUSt3R-class) as the T2 twin path | a model + a GPU pass | reference geometry as a 3D pointmap, so our render is compared surface-to-surface, not landmark-to-landmark |
Why this ordering is the frugal one: M1–M4 are free precision — classical craft applied to data we already have, no new capture, no new models. M1 alone converts our largest measurement blind spot (depth) into numbers, and M3 makes the instrument, not the operator, decide which cut comes next. M5 is the only rung needing new machinery, and it is the one that eventually retires landmark comparison altogether.
4. The general law this brief exists to state
Precision comes from the CRAFT of measurement before it comes from finer instruments. The mason with a straightedge, a compass and two projection planes cut stone to tolerances that shame a careless machinist with a micrometer — because the method carried the accuracy: redundancy, transfer lines, orthogonal views, invariants that survive the unknown. Our climb obeys the same rule. Every domain in the ecosystem (graphics, geometry, physics, product surfaces) should be asked the same three questions: what quantity is unobservable to my current view? what redundant measurement would let me triangulate it? and what invariant survives the thing I cannot control?
UNVERIFIED / declared gaps
- May→July 2026 tail unverified (search budget). Most volatile: the feed-forward reconstruction line (DUSt3R successors), metric monocular depth leaders, and any new open shape-analysis tooling. Re-verify + citation archive queued.
- Single-view metrology needs structure in frame — a horizon, a vertical, a rectilinear object. Beach footage often lacks all three; the technique is conditional, not universal, and must report when it cannot apply.
- Procrustes vs EDMA is a live methodological debate in morphometrics (superimposition can smear localized change; distance-matrix methods lose spatial intuition). We adopt BOTH and require them to agree — disagreement is itself a finding.
- Detector prior bias is measured but not corrected: our landmarker resists paint that contradicts skull shading (~30% purchase per unit, this session). Until geometry drives the features, landmark verdicts carry that bias — stated, not hidden.