fix(examples): re-review of the 20 judged-fine examples; seat the gear, buckler and crystal (#247)

* fix(examples): seat the triangulate-tangents buckler on the floor

The display stand hung 0.49 m above the floor with nothing under it, and
nothing held the buckler's 20-degree backward lean. The stand now rests on
the floor, the rim's lowest evaluated vertex bites 1 cm into its top, and a
kickstand strut runs from the buckler's back (found by a local-space ray) to
the floor. The camera and aim ride with the derived lift. Render path only;
exit codes are unchanged on 4.5.11, 5.1.2 and 5.2.1.

Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>
Signed-off-by: TMHSDigital <154358121+TMHSDigital@users.noreply.github.com>

* fix(examples): lean the bmesh-gear on a display wedge

The gear leaned 46 degrees back with nothing behind it, and its lowest tooth
was sunk 4.5 cm into the floor. The gear is now seated from its lowest
evaluated vertex (3 mm bite) and carried by a matte inclined wedge whose
slope lies in the back-cap plane. The camera rides with the seat height.
bmesh-gear is a pinned calibration reference: luma 0.305 -> 0.302, stage
0.237 -> 0.236, warmth +0.370 -> +0.374, saturation 0.195 -> 0.195.
Render path only; exit codes are unchanged on all three binaries.

Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>
Signed-off-by: TMHSDigital <154358121+TMHSDigital@users.noreply.github.com>

* fix(examples): build gp-lineart-contour's crystal as a bipyramid, and mount it

build_crystal duplicated an open cone and flipped it over the original. The
two crossed into an hourglass with open hexagonal ends and an inner spike,
which the old gallery alt described as an hourglass-shaped solid. It is now
the hexagonal bipyramid the docstring intended. The crystal also hovered
0.13 m above the floor; a two-tier hex mount, built after the check from the
lowest evaluated vertex, now holds its lower tip. The still dollies along the
check camera's bearing so the mount stays in frame.

The corrected mesh changes the measured Line Art counts from 10 strokes /
34 points to 2 / 12, identical on 4.5.11, 5.1.2 and 5.2.1. The gates are
lower bounds (>=1, >=4) and are unchanged, as are every assertion and exit
code (default 0, --no-contour 4, --output 0).

Shared gallery.json and gallery index updates for all three examples ride here.

Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>
Signed-off-by: TMHSDigital <154358121+TMHSDigital@users.noreply.github.com>

---------

Signed-off-by: TMHSDigital <154358121+TMHSDigital@users.noreply.github.com>
Co-authored-by: Claude Opus 5.5 (1M context) <noreply@anthropic.com>

Author: TMHSDigital

docs/gallery/assets/bmesh-gear-hero.webp

@@ -16,13 +16,13 @@
   <meta property="og:image" content="https://tmhsdigital.github.io/Blender-Developer-Tools/gallery/assets/bmesh-gear-hero.webp" />
   <meta property="og:image:width" content="1280" />
   <meta property="og:image:height" content="720" />
-  <meta property="og:image:alt" content="A gold fourteen-tooth gear lying at an angle, its face covered in concentric grooves." />
+  <meta property="og:image:alt" content="A gold fourteen-tooth gear leaning back on a dark display wedge, its face covered in concentric grooves." />
   <meta property="og:site_name" content="Blender Developer Tools" />
   <meta name="twitter:card" content="summary_large_image" />
   <meta name="twitter:title" content="bmesh-gear — Examples — Blender Developer Tools" />
   <meta name="twitter:description" content="A 14-tooth gear built entirely with bmesh — profile ring, face, extrude — with bm.free() in a try/finally, exactly as the ownership contract demands." />
   <meta name="twitter:image" content="https://tmhsdigital.github.io/Blender-Developer-Tools/gallery/assets/bmesh-gear-hero.webp" />
-  <meta name="twitter:image:alt" content="A gold fourteen-tooth gear lying at an angle, its face covered in concentric grooves." />
+  <meta name="twitter:image:alt" content="A gold fourteen-tooth gear leaning back on a dark display wedge, its face covered in concentric grooves." />
   <style>
     /* fonts are deployed by the landing build (docs/fonts/) */
     @font-face { font-family: 'Barlow Condensed'; font-weight: 600; font-display: swap;
@@ -268,8 +268,8 @@ <h1>bmesh-gear</h1>
     <p>A 14-tooth gear built entirely with bmesh — profile ring, face, extrude — with bm.free() in a try/finally, exactly as the ownership contract demands.</p>
   </header>
   <main id="main">
-    <button class="detail-hero" id="heroZoom" type="button" aria-label="View full size: A gold fourteen-tooth gear lying at an angle, its face covered in concentric grooves.">
-      <img src="../assets/bmesh-gear-hero.webp" alt="A gold fourteen-tooth gear lying at an angle, its face covered in concentric grooves." width="1280" height="720" />
+    <button class="detail-hero" id="heroZoom" type="button" aria-label="View full size: A gold fourteen-tooth gear leaning back on a dark display wedge, its face covered in concentric grooves.">
+      <img src="../assets/bmesh-gear-hero.webp" alt="A gold fourteen-tooth gear leaning back on a dark display wedge, its face covered in concentric grooves." width="1280" height="720" />
     </button>
     <p class="zoom-hint">Rendered headless by the example itself — click to zoom.</p>
     <div class="callout"><span class="tag">witnesses</span> Parametric bmesh topology is exactly predictable: verts, edges, and faces match their closed forms, and every edge borders exactly two faces (watertight).</div>
@@ -280,6 +280,7 @@ <h1>bmesh-gear</h1>
     <section class="detail-section md">
 <p>A runnable example that builds a 14-tooth gear entirely with bmesh — profile ring, face, <code>extrude_face_region</code>, translate — following the ownership contract from <a href="https://github.com/TMHSDigital/Blender-Developer-Tools/tree/main/skills/mesh-editing-and-bmesh/SKILL.md"><code>mesh-editing-and-bmesh</code></a> and the <a href="https://github.com/TMHSDigital/Blender-Developer-Tools/tree/main/rules/always-free-bmesh.mdc"><code>always-free-bmesh</code></a> rule: every <code>bmesh.new()</code> is paired with <code>bm.free()</code> in a <code>try</code>/<code>finally</code>.</p>
 <p><strong>What it witnesses:</strong> parametric bmesh construction has exactly predictable topology. The check asserts the closed-form counts — verts = 2 × (4 × teeth), faces = sides + 2 caps, edges = 3 × profile — and that the result is watertight (every edge borders exactly two faces). If an op leaks geometry or a face fails to close, the math catches it.</p>
+<p>The still leans the gear back on a matte inclined display wedge. Both contacts are derived from the posed mesh: the lowest back-cap vertex sits 3 mm into the floor, and the wedge&#x27;s slope lies in the back-cap plane, so the lean is carried rather than held in the air.</p>
 <h2>Run</h2>
 <pre><code># Cheap correctness check (no render) — the CI check:
 blender --background --python bmesh_gear.py --
@@ -322,6 +323,7 @@ <h2>Source</h2>
     blender --background --python bmesh_gear.py -- --output g.png  # + render
 &quot;&quot;&quot;</span>
 <span class="k">import</span> bpy, bmesh, sys, os, math, argparse
+<span class="k">from</span> mathutils <span class="k">import</span> Vector
 
 TEETH = <span class="n">14</span>
 R_ROOT = <span class="n">1.0</span>
@@ -330,6 +332,11 @@ <h2>Source</h2>
 <span class="c"># fraction of a tooth period spent at the tip vs the root</span>
 TOOTH_DUTY = <span class="n">0.45</span>
 
+<span class="c"># render staging only (not part of the check)</span>
+STAGE_BITE = <span class="n">0.003</span>    <span class="c"># contact depth into the floor and into the gear&#x27;s back</span>
+WEDGE_SLOPE = <span class="n">1.55</span>    <span class="c"># display wedge slope length, up the gear&#x27;s back face</span>
+WEDGE_WIDTH = <span class="n">1.8</span>     <span class="c"># display wedge width across the gear</span>
+
 
 <span class="k">def</span> gear_profile():
     <span class="s">&quot;&quot;&quot;Vertex ring for the gear silhouette: 4 verts per tooth (root-root-tip-tip).&quot;&quot;&quot;</span>
@@ -425,8 +432,53 @@ <h2>Source</h2>
     nt.links.new(rings.outputs[<span class="s">&quot;Fac&quot;</span>], rough.inputs[<span class="s">&quot;Value&quot;</span>])
     nt.links.new(rough.outputs[<span class="s">&quot;Result&quot;</span>], bsdf.inputs[<span class="s">&quot;Roughness&quot;</span>])
     obj.data.materials.append(mat)
-    obj.location = (<span class="n">0.0</span>, <span class="n">0.0</span>, <span class="n">0.85</span>)
+    <span class="c"># the gear leans back on an inclined display wedge. Both contacts are</span>
+    <span class="c"># derived from the posed mesh: the lowest back-cap vertex bites into</span>
+    <span class="c"># the floor, and the wedge&#x27;s slope lies in the back-cap plane, sunk into</span>
+    <span class="c"># the gear, so the lean is carried rather than hung in the air</span>
     obj.rotation_euler = (math.radians(<span class="n">46</span>), <span class="n">0.0</span>, math.radians(<span class="n">22</span>))
+    obj.location = (<span class="n">0.0</span>, <span class="n">0.0</span>, <span class="n">0.0</span>)
+    bpy.context.view_layer.update()
+    obj.location.z = -min((obj.matrix_world @ v.co).z <span class="k">for</span> v <span class="k">in</span> obj.data.vertices) - STAGE_BITE
+    bpy.context.view_layer.update()
+    mw = obj.matrix_world
+    rot = mw.to_3x3()
+    side = (rot @ Vector((<span class="n">1.0</span>, <span class="n">0.0</span>, <span class="n">0.0</span>))).normalized()
+    up = (rot @ Vector((<span class="n">0.0</span>, <span class="n">1.0</span>, <span class="n">0.0</span>))).normalized()
+    into = (rot @ Vector((<span class="n">0.0</span>, <span class="n">0.0</span>, <span class="n">1.0</span>))).normalized()
+    low = min((mw @ v.co <span class="k">for</span> v <span class="k">in</span> obj.data.vertices), key=<span class="k">lambda</span> p: p.z)
+    centre = mw @ Vector((<span class="n">0.0</span>, <span class="n">0.0</span>, <span class="n">0.0</span>))
+    foot = low + side * (centre - low).dot(side) + into * STAGE_BITE
+    top = foot + up * WEDGE_SLOPE
+    back = Vector((top.x, top.y, -STAGE_BITE))
+    front = Vector((foot.x, foot.y, -STAGE_BITE))
+    wedge_me = bpy.data.meshes.new(<span class="s">&quot;Wedge&quot;</span>)
+    bm = bmesh.new()
+    <span class="k">try</span>:
+        half = side * (WEDGE_WIDTH / <span class="n">2</span>)
+        ring = [[bm.verts.new(p + sgn * half) <span class="k">for</span> p <span class="k">in</span> (front, foot, top, back)]
+                <span class="k">for</span> sgn <span class="k">in</span> (-<span class="n">1.0</span>, <span class="n">1.0</span>)]
+        a, b = ring
+        bm.faces.new(a)
+        bm.faces.new(b[::-<span class="n">1</span>])
+        <span class="k">for</span> i <span class="k">in</span> range(<span class="n">4</span>):
+            j = (i + <span class="n">1</span>) % <span class="n">4</span>
+            bm.faces.new((a[i], a[j], b[j], b[i]))
+        bmesh.ops.recalc_face_normals(bm, faces=bm.faces)
+        bm.to_mesh(wedge_me)
+    <span class="k">finally</span>:
+        bm.free()
+    wmat = bpy.data.materials.new(<span class="s">&quot;DisplayStand&quot;</span>)
+    wmat.use_nodes = <span class="k">True</span>
+    wb = wmat.node_tree.nodes[<span class="s">&quot;Principled BSDF&quot;</span>]
+    <span class="c"># matte and dark: the slope faces the key square-on, and at the floor&#x27;s</span>
+    <span class="c"># finish its specular sheen alone (~45/255, measured) reads as paper</span>
+    wb.inputs[<span class="s">&quot;Base Color&quot;</span>].default_value = (<span class="n">0.02</span>, <span class="n">0.021</span>, <span class="n">0.025</span>, <span class="n">1.0</span>)
+    wb.inputs[<span class="s">&quot;Roughness&quot;</span>].default_value = <span class="n">0.9</span>
+    spec = wb.inputs.get(<span class="s">&quot;Specular IOR Level&quot;</span>) <span class="k">or</span> wb.inputs.get(<span class="s">&quot;Specular&quot;</span>)
+    spec.default_value = <span class="n">0.1</span>
+    wedge_me.materials.append(wmat)
+    scene.collection.objects.link(bpy.data.objects.new(<span class="s">&quot;Wedge&quot;</span>, wedge_me))
 
     floor_me = bpy.data.meshes.new(<span class="s">&quot;Floor&quot;</span>)
     bm = bmesh.new()
@@ -473,7 +525,9 @@ <h2>Source</h2>
     cam_data = bpy.data.cameras.new(<span class="s">&quot;Cam&quot;</span>)
     cam_data.lens = <span class="n">55.0</span>
     cam = bpy.data.objects.new(<span class="s">&quot;Cam&quot;</span>, cam_data)
-    cam.location = (<span class="n">0.0</span>, -<span class="n">7.6</span>, <span class="n">4.2</span>)
+    <span class="c"># the camera rides with the gear&#x27;s derived seat height (it was posed for</span>
+    <span class="c"># a gear hung at z=0.85), so the composition is unchanged</span>
+    cam.location = (<span class="n">0.0</span>, -<span class="n">7.6</span>, <span class="n">4.2</span> + obj.location.z - <span class="n">0.85</span>)
     cam.rotation_euler = (math.radians(<span class="n">66</span>), <span class="n">0.0</span>, <span class="n">0.0</span>)
     scene.collection.objects.link(cam)
     scene.camera = cam
@@ -531,7 +585,7 @@ <h2>Source</h2>
   </main>
   <dialog class="lightbox" id="lightbox" aria-label="Full-size render">
     <button class="lightbox-close" type="button" autofocus>Close</button>
-    <img src="../assets/bmesh-gear-hero.webp" alt="A gold fourteen-tooth gear lying at an angle, its face covered in concentric grooves." />
+    <img src="../assets/bmesh-gear-hero.webp" alt="A gold fourteen-tooth gear leaning back on a dark display wedge, its face covered in concentric grooves." />
   </dialog>
   <footer>
     <div class="statusbar">