fix(examples): rebuild triangulate-tangents buckler as a machined shield

README.md

@@ -917,7 +917,7 @@ those post-limit weights onto the arm as a colour attribute.
 </tr>
 <tr>
 <td width="46%" valign="middle">
-<a href="examples/triangulate-tangents/"><img src="examples/triangulate-tangents/preview.webp" alt="Triangulate and tangents: a machined steel buckler on a dark cradle - brushed grooves circulating the boss with an anisotropic sweep - proving the mikktspace tangent field a normal map depends on" /></a>
+<a href="examples/triangulate-tangents/"><img src="examples/triangulate-tangents/preview.webp" alt="Triangulate and tangents: a machined steel buckler on a walnut stand - pointed brass boss, domed face cut with concentric lathe grooves, riveted brass rim - proving the mikktspace tangent field a normal map depends on" /></a>
 </td>
 <td valign="middle">
 

docs/VISUAL-STYLE.md

@@ -94,8 +94,10 @@ the default stage.
   describe — and the falsification pass is satisfied by naming why no visual
   difference exists. Precedents: `vertex-weight-limit` (the prune preserves
   the pose by design, so the 4-influence cap is numeric) and
-  `triangulate-tangents` (the ring sweep is UV/bump-driven, so a
-  tangent-field break does not move pixels). This is for contracts that
+  `triangulate-tangents` (the lathe grooves are a bump read off UV v and
+  the anisotropic streak follows the renderer's own UV-map tangent, so a
+  break in the `calc_tangents()` loop data the check reads does not move
+  pixels). This is for contracts that
   genuinely cannot be seen, not for scenes that were not designed hard
   enough: where a visual witness is possible, it is required.
 - Presentation may be staged; evidence may not. When the witnessed artifact

docs/gallery/index.html

@@ -651,7 +651,7 @@ <h2><a href="vertex-weight-limit/">vertex-weight-limit</a></h2>
       </article>
       <article class="card" data-tags="mesh uv">
         <a class="card-media" href="triangulate-tangents/" tabindex="-1" aria-hidden="true">
-          <img src="assets/triangulate-tangents-hero.webp" alt="A round silver buckler leaning back on a low stand, its face brushed in circular grooves with an anisotropic highlight." loading="lazy" decoding="async" />
+          <img src="assets/triangulate-tangents-hero.webp" alt="A steel buckler on a walnut stand, turned three-quarter: pointed brass boss, domed face cut with two bands of concentric lathe grooves, brass rim ringed with steel rivets." loading="lazy" decoding="async" />
         </a>
         <div class="card-body">
           <h2><a href="triangulate-tangents/">triangulate-tangents</a></h2>

examples/gallery.json

@@ -380,7 +380,7 @@
       "name": "triangulate-tangents",
       "dir": "examples/triangulate-tangents",
       "teaches": "A machined buckler verifying the tangent-space contract a game engine's normal mapping depends on. Deterministic triangulation, unit orthogonal tangent frames, and the edge/UV-delta formula matching mikktspace within welding tolerance.",
-      "alt": "A round silver buckler leaning back on a low stand, its face brushed in circular grooves with an anisotropic highlight.",
+      "alt": "A steel buckler on a walnut stand, turned three-quarter: pointed brass boss, domed face cut with two bands of concentric lathe grooves, brass rim ringed with steel rivets.",
       "witnessesFix": "calc_tangents aborts on any ngon; planar UVs on a cylindrical wall collapse tangents onto normals; a MeshUVLoopLayer handle held across calc_tangents dangles on 4.5 (471 phantom flips, silent exit 0) while the mikktspace math is byte-identical on both versions.",
       "hero": "docs/gallery/assets/triangulate-tangents-hero.webp",
       "preview": "examples/triangulate-tangents/preview.webp",

examples/triangulate-tangents/README.md

@@ -1,7 +1,8 @@
 # Triangulate + Tangents
 
-A runnable example that builds a machined buckler — lathed dome with polar
-UVs, unwrapped rim and underside strips, a fanned back cap — and verifies
+A runnable example that builds a machined buckler — one closed lathe mesh:
+turned boss, flange, domed face and rolled rim with polar UVs, unwrapped rim
+and underside strips, fanned back and apex caps — and verifies
 the tangent-space contract a game engine's normal mapping depends on,
 following [`mesh-editing-and-bmesh`](../../skills/mesh-editing-and-bmesh/SKILL.md).
 
@@ -14,47 +15,58 @@ the exported normal maps are baked against.
 hazards around it.
 
 - **Deterministic triangulation and the engine basis.** `calc_loop_triangles`
-  yields the closed-form count (two tris per quad + the cap fan, 720), and
-  every loop tangent is unit length (err 1.3e-07) and exactly orthogonal to
-  its loop normal (err 6.0e-08), with the bitangent exactly
+  yields the closed-form count (two tris per quad + the two cap fans, 4992),
+  and every loop tangent is unit length (err 1.3e-07) and exactly orthogonal
+  to its loop normal (err 9.9e-08), with the bitangent exactly
   `bitangent_sign * (normal x tangent)` (err 0.0). One ngon anywhere in the
-  mesh and `calc_tangents` **aborts the whole call** — the back cap is an
-  explicit fan for exactly that reason.
+  mesh and `calc_tangents` **aborts the whole call** — both caps are
+  explicit fans for exactly that reason.
 - **The tangent frame follows the UVs.** On smooth-field triangles the
   per-loop tangents match the independently derived edge/UV-delta formula
-  within mikktspace's vertex-welding tolerance (measured 2.3e-06, tol 0.15);
+  within mikktspace's vertex-welding tolerance (measured 3.3e-02, tol 0.15 —
+  the face is smooth-shaded with sharp edges at the machined breaks, so
+  mikktspace genuinely welds frames across shared vertices);
   a flipped frame inside a smooth field is never legal (0 measured). At UV
-  seams the frame orientation is implementation-defined — 42 seam flips, 9
-  at chart seams, identical on both versions — and planar UVs on a
+  seams the frame orientation is implementation-defined — 150 seam flips, 12
+  at chart seams, identical on all three versions — and planar UVs on a
   cylindrical wall are degenerate: they collapse the tangent onto the
   normal (dot 0.998, measured and fixed by unwrapping strips).
 - **The reference-lifetime hazard (the real divergence).** A
   `MeshUVLoopLayer` handle held across `calc_tangents()` dangles: on
   Blender 4.5 reads through it return tangent floats, not UVs — measured
   while authoring as a phantom **471 flipped frames and 385 phantom seam
-  positions, exit 0, a silent wrong answer**. On 5.1 the same stale read
-  survives by memory-layout luck. The mikktspace math itself is
-  byte-identical on 4.5.11 and 5.1.2; the apparent version divergence was
+  positions, exit 0, a silent wrong answer** (on the current buckler: 2829
+  phantom seam flips over 2497 phantom seam positions, still exit 0). On
+  5.1 and 5.2 the same stale read survives by memory-layout luck. The
+  mikktspace math itself is identical on 4.5.11, 5.1.2 and 5.2.1; the
+  apparent version divergence was
   entirely the corrupt handle. Never hold layer handles across
   CustomData-reallocating calls — re-fetch by name.
 
 **What each check catches on failure:** a remeshed asset breaking the
 triangulation count (probe: dropped profile ring, exit 3, 624 vs 720); a
 wrong tangent formula in the independent derivation (probe: swapped du/dv,
-exit 7, weld 1.459); and the stale-handle read (probe: no re-fetch — corrupt
-measurements on 4.5, correct values on 5.1 by luck).
+exit 7, weld 1.460); and the stale-handle read (probe: no re-fetch — corrupt
+measurements on 4.5, correct values on 5.1/5.2 by luck).
 
-**Version witness:** mikktspace output is identical on Blender 4.5.11 LTS
-and 5.1.2 (same weld deviations, same seam flips). The `calc_tangents(uvmap=)`
+**Version witness:** mikktspace output is identical on Blender 4.5.11 LTS,
+5.1.2 and 5.2.1 LTS (same weld deviation, same seam flips). The `calc_tangents(uvmap=)`
 signature is stable. The lifetime hazard above is the only behavioral split,
 and it corrupts measurements rather than raising.
 
-The render shows the buckler on its cradle: brushed grooves circulating the
-boss with the anisotropic sweep riding them — the circulating tangent field
-made visible. The staging is derived from the posed mesh: the stand rests on
-the floor, the rim's lowest vertex sits 1 cm into its top, and a kickstand
-strut runs from the buckler's back (found by a local-space ray) to the floor
-behind it.
+The render shows the buckler turned three-quarter on a walnut stand: a
+pointed brass boss on a riveted blued-steel flange, a turned-steel dome, and
+a brass rolled rim ringed with steel rivets. Materials are assigned per lathe
+ring. The dome's lathe grooves are a bump read straight off UV v (the
+radius), so they are exact circles, with no procedural distortion. Its
+anisotropic highlight follows the renderer's own UV-map tangent, so it
+fans out radially from the boss. This is a numeric-only contract
+(docs/VISUAL-STYLE.md): the renderer derives its tangents from the UVs, so a
+break in the `calc_tangents()` loop data the check reads does not move
+pixels. The staging is derived from the posed mesh: the stand rests on the
+floor, the rim's lowest vertex sits 1 cm into its top, and a kickstand strut
+runs from the buckler's back (found by a local-space ray) to the floor behind
+it, angled away from the camera.
 
 ## Run
 
@@ -73,7 +85,8 @@ blender --background --python triangulate_tangents.py -- --output buckler.png --
 ## Exit codes
 
 Per-script sequential checks. `9` is a valid check code; there is no rule
-against it. `10` is the shared framing helper.
+against it. `10` is the shared framing helper, `11` the shared asset-quality
+helper.
 
 | Code | Meaning |
 | --- | --- |
@@ -87,6 +100,7 @@ against it. `10` is the shared framing helper.
 | 7 | Tangents deviate from the edge/UV closed form |
 | 8 | Flipped tangent inside a clean triangle |
 | 10 | Gallery framing violation; also `--output` produced no file |
+| 11 | Asset-quality floor violation (`--output` only; shared helper) |
 
 The `blender-smoke` workflow runs the check on Blender 5.2 LTS and 4.5 LTS
 (5.1 on the weekly cron, the `needs-5.1` PR label, or manual dispatch).