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<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8" />
<meta name="viewport" content="width=device-width, initial-scale=1" />
<title>armature-bend — Examples — Blender Developer Tools</title>
<meta name="description" content="Rigging end to end in the data API — edit_bones chain construction, name-bound vertex groups with smoothstep blend zones, posing, and depsgraph evaluation — bending a tapered tube through rest, half, and full curl." />
<link rel="canonical" href="https://tmhsdigital.github.io/Blender-Developer-Tools/gallery/armature-bend/" />
<link rel="icon" href="../../assets/favicon.svg" type="image/svg+xml" />
<meta name="theme-color" content="#1a1b1e" />
<meta name="color-scheme" content="dark" />
<meta property="og:type" content="website" />
<meta property="og:title" content="armature-bend — Examples — Blender Developer Tools" />
<meta property="og:description" content="Rigging end to end in the data API — edit_bones chain construction, name-bound vertex groups with smoothstep blend zones, posing, and depsgraph evaluation — bending a tapered tube through rest, half, and full curl." />
<meta property="og:url" content="https://tmhsdigital.github.io/Blender-Developer-Tools/gallery/armature-bend/" />
<meta property="og:image" content="https://tmhsdigital.github.io/Blender-Developer-Tools/gallery/assets/armature-bend-hero.webp" />
<meta property="og:image:width" content="1280" />
<meta property="og:image:height" content="720" />
<meta property="og:image:alt" content="armature-bend: the example's own headless render" />
<meta property="og:site_name" content="Blender Developer Tools" />
<meta name="twitter:card" content="summary_large_image" />
<meta name="twitter:title" content="armature-bend — Examples — Blender Developer Tools" />
<meta name="twitter:description" content="Rigging end to end in the data API — edit_bones chain construction, name-bound vertex groups with smoothstep blend zones, posing, and depsgraph evaluation — bending a tapered tube through rest, half, and full curl." />
<meta name="twitter:image" content="https://tmhsdigital.github.io/Blender-Developer-Tools/gallery/assets/armature-bend-hero.webp" />
<meta name="twitter:image:alt" content="armature-bend: the example's own headless render" />
<style>
/* fonts are deployed by the landing build (docs/fonts/) */
@font-face { font-family: 'Barlow Condensed'; font-weight: 600; font-display: swap;
src: url('../../fonts/barlow-condensed-600.woff2') format('woff2'); }
@font-face { font-family: 'Inter'; font-weight: 400; font-display: swap;
src: url('../../fonts/inter-regular.woff2') format('woff2'); }
@font-face { font-family: 'Inter'; font-weight: 500; font-display: swap;
src: url('../../fonts/inter-medium.woff2') format('woff2'); }
@font-face { font-family: 'JetBrains Mono'; font-weight: 400; font-display: swap;
src: url('../../fonts/jetbrains-mono-regular.woff2') format('woff2'); }
/* Blender-viewport system, shared with the landing page. Dark only. */
:root {
color-scheme: dark;
--bg: #1a1b1e; --surface: #222327; --surface-2: #2a2b30; --bg2: #131417;
--border: #3a3b40; --text: #e8e9eb; --text-dim: #9698a0;
--select: #ff8c19; --ok: #6dc96d;
--radius: 4px; --radius-lg: 6px; --maxw: 1080px;
--font-display: 'Barlow Condensed', 'Arial Narrow', sans-serif;
--font-sans: 'Inter', -apple-system, BlinkMacSystemFont, 'Segoe UI', Helvetica, Arial, sans-serif;
--font-mono: 'JetBrains Mono', ui-monospace, 'SF Mono', Menlo, Consolas, monospace;
--code-k: #ff7b72; --code-s: #a5d6ff; --code-c: #9698a0; --code-n: #79c0ff;
}
* { box-sizing: border-box; margin: 0; padding: 0; }
html { scroll-behavior: smooth; }
body { font-family: var(--font-sans); background: var(--bg); color: var(--text);
line-height: 1.6; min-height: 100vh; -webkit-font-smoothing: antialiased; }
a { color: var(--select); text-decoration: none; }
a:hover { text-decoration: underline; }
:focus-visible { outline: 2px solid var(--select); outline-offset: 2px; border-radius: 3px; }
::selection { background: color-mix(in srgb, var(--select) 40%, transparent); }
.skip { position: absolute; left: -999px; top: 0; background: var(--select); color: #1a1b1e;
padding: 0.5rem 1rem; border-radius: var(--radius); z-index: 10; font-weight: 500; }
.skip:focus { left: 0.5rem; top: 0.5rem; }
.hud { font-family: var(--font-mono); font-size: 0.6875rem; letter-spacing: 0.04em;
color: var(--text-dim); text-transform: uppercase; }
.topbar { position: sticky; top: 0; z-index: 5; display: flex; align-items: center;
justify-content: space-between; gap: 1rem; padding: 0 1.25rem; height: 46px;
background: color-mix(in srgb, var(--surface) 92%, transparent);
backdrop-filter: blur(10px); border-bottom: 1px solid var(--border); }
.topbar .back { color: var(--text-dim); font-size: 0.8125rem; font-weight: 500; }
.topbar .back:hover { color: var(--select); text-decoration: none; }
.topbar-right { display: flex; align-items: center; gap: 0.85rem; }
.topbar-right .ghlink { color: var(--text-dim); font-size: 0.8125rem; font-weight: 500; }
.topbar-right .ghlink:hover { color: var(--select); text-decoration: none; }
header.hero { max-width: var(--maxw); margin: 0 auto; padding: 2.75rem 1.25rem 1.25rem; }
header.hero h1 { font-family: var(--font-display); font-weight: 600; text-transform: uppercase;
font-size: clamp(2.2rem, 5vw, 3.4rem); letter-spacing: 0.005em; line-height: 0.98; }
header.hero p { color: var(--text-dim); max-width: 62ch; margin-top: 0.7rem; font-size: 1rem; }
/* ---- index: sticky controls (search, density toggle, tag chips) ---- */
.controls { position: sticky; top: 46px; z-index: 4;
background: color-mix(in srgb, var(--bg) 94%, transparent);
backdrop-filter: blur(10px); -webkit-backdrop-filter: blur(10px);
border-bottom: 1px solid var(--border); }
.controls-inner { max-width: var(--maxw); margin: 0 auto; padding: 0.55rem 1.25rem 0.6rem;
display: flex; flex-direction: column; gap: 0.5rem; }
.controls-row { display: flex; align-items: center; gap: 0.6rem; flex-wrap: wrap; }
.searchwrap { position: relative; flex: 1 1 240px; min-width: 150px; }
.searchwrap input { width: 100%; background: var(--surface-2); border: 1px solid var(--border);
color: var(--text); border-radius: var(--radius); padding: 0.34rem 1.9rem 0.34rem 0.7rem;
font-family: var(--font-sans); font-size: 0.85rem; line-height: 1.4; }
.searchwrap input:focus { border-color: var(--select); outline: none; }
.searchwrap input::placeholder { color: var(--text-dim); }
.searchwrap input::-webkit-search-cancel-button { -webkit-appearance: none; appearance: none; }
.q-clear { position: absolute; right: 0.2rem; top: 50%; transform: translateY(-50%);
background: none; border: none; color: var(--text-dim); font-size: 1.05rem; line-height: 1;
cursor: pointer; padding: 0.25rem 0.45rem; border-radius: 3px; }
.q-clear:hover { color: var(--select); }
.count { font-family: var(--font-mono); font-size: 0.68rem; letter-spacing: 0.04em;
text-transform: uppercase; color: var(--text-dim); white-space: nowrap; }
.density { display: flex; border: 1px solid var(--border); border-radius: var(--radius);
overflow: hidden; }
.density-btn { background: var(--surface-2); border: none; color: var(--text-dim); cursor: pointer;
font-family: var(--font-mono); font-size: 0.68rem; letter-spacing: 0.04em;
text-transform: uppercase; padding: 0.36rem 0.7rem; transition: color 0.15s, background 0.15s; }
.density-btn + .density-btn { border-left: 1px solid var(--border); }
.density-btn:hover { color: var(--select); }
.density-btn.active { background: var(--select); color: #1a1b1e; }
.tags-toggle { display: none; background: var(--surface-2); border: 1px solid var(--border);
color: var(--text-dim); border-radius: 3px; padding: 0.3rem 0.7rem; cursor: pointer;
font-family: var(--font-mono); font-size: 0.7rem; letter-spacing: 0.04em; text-transform: uppercase; }
.tags-toggle:hover, .tags-toggle.has-active { color: var(--select); border-color: var(--select); }
/* Tag chips wrap by default (no-JS safe). With JS the row becomes a scroll
strip on wide viewports and collapses behind the Tags toggle on narrow
ones, so the sticky bar never eats the mobile viewport. */
.chips { display: flex; flex-wrap: wrap; gap: 0.4rem; }
html.js .chips { flex-wrap: nowrap; overflow-x: auto; padding-bottom: 0.25rem;
scrollbar-width: thin; scrollbar-color: var(--border) transparent; }
html.js .chips::-webkit-scrollbar { height: 5px; }
html.js .chips::-webkit-scrollbar-thumb { background: var(--border); border-radius: 3px; }
.chip { background: var(--surface-2); border: 1px solid var(--border); color: var(--text-dim);
border-radius: 3px; padding: 0.22rem 0.7rem; font-size: 0.72rem; font-weight: 400;
font-family: var(--font-mono); cursor: pointer; white-space: nowrap; flex: 0 0 auto;
transition: color 0.15s, border-color 0.15s; }
.chip:hover { color: var(--select); border-color: var(--select); }
.chip.active { color: #1a1b1e; background: var(--select); border-color: var(--select); }
@media (max-width: 719px) {
html.js .tags-toggle { display: inline-block; }
html.js .chips { display: none; }
html.js .chips.open { display: flex; flex-wrap: wrap; overflow-y: auto; max-height: 40vh; }
}
/* Compact density: hero + name + one-line teaser. The description and
WITNESSES text stay in the DOM (searchable, screen-reader reachable,
present with JS disabled when the class is never applied) but are
visually collapsed. Applied only by JS via the density-compact class. */
html.density-compact .grid { gap: 1rem; }
html.density-compact .card-body { padding: 0.65rem 0.9rem 0.7rem; }
html.density-compact .card-body h2 { font-size: 0.88rem; margin-bottom: 0.15rem; }
html.density-compact .teaches { font-size: 0.8rem; color: var(--text-dim); margin-bottom: 0;
white-space: nowrap; overflow: hidden; text-overflow: ellipsis; }
html.density-compact .witnesses { position: absolute; width: 1px; height: 1px; margin: -1px;
padding: 0; overflow: hidden; clip: rect(0 0 0 0); clip-path: inset(50%); white-space: nowrap; }
html.density-compact .card-link { display: none; }
.noresults { color: var(--text-dim); text-align: center; padding: 3rem 1rem; font-size: 0.95rem; }
.noresults .chip { margin-left: 0.6rem; }
.to-top { position: fixed; right: 1.25rem; bottom: 1.25rem; z-index: 6; cursor: pointer;
background: var(--surface-2); border: 1px solid var(--border); color: var(--text-dim);
border-radius: var(--radius); padding: 0.45rem 0.75rem;
font-family: var(--font-mono); font-size: 0.7rem; letter-spacing: 0.04em;
text-transform: uppercase; opacity: 0; visibility: hidden;
transition: opacity 0.2s, visibility 0.2s, color 0.15s, border-color 0.15s; }
.to-top.show { opacity: 1; visibility: visible; }
.to-top:hover { color: var(--select); border-color: var(--select); }
main { max-width: var(--maxw); margin: 0 auto; padding: 1rem 1.25rem 2rem; }
.grid { display: grid; grid-template-columns: 1fr; gap: 1.5rem; align-items: stretch; }
.card { background: var(--surface); border: 1px solid var(--border); border-radius: var(--radius-lg);
overflow: hidden; display: flex; flex-direction: column;
outline: 2px solid transparent; outline-offset: -1px;
transition: outline-color 0.12s ease, border-color 0.12s ease; }
.card:hover { border-color: var(--select); outline-color: var(--select); }
.card.hidden { display: none; }
.card-media { display: block; background: var(--bg2); line-height: 0; }
.card-media img { display: block; width: 100%; aspect-ratio: 16 / 9; object-fit: cover; }
.card-body { padding: 1.15rem 1.4rem 1.45rem; display: flex; flex-direction: column; flex: 1 1 auto; }
.card-body h2 { font-family: var(--font-mono); font-size: 1rem; font-weight: 400; margin-bottom: 0.5rem; }
.card-body h2 a { color: var(--text); }
.card-body h2 a:hover { color: var(--select); text-decoration: none; }
.teaches { color: var(--text); margin-bottom: 0.7rem; font-size: 0.92rem; }
.witnesses { color: var(--text-dim); font-size: 0.85rem; margin-bottom: 1rem; }
.tag { display: inline-block; font-family: var(--font-mono); font-size: 0.62rem; text-transform: uppercase;
letter-spacing: 0.06em; color: var(--select); border: 1px solid color-mix(in srgb, var(--select) 55%, transparent);
border-radius: 3px; padding: 0.08rem 0.5rem; margin-right: 0.4rem; vertical-align: 1px; }
.card-link { font-weight: 600; font-size: 0.95rem; margin-top: auto; }
/* ---- detail page ---- */
.detail-hero { border: 1px solid var(--border); border-radius: var(--radius-lg); overflow: hidden;
background: var(--bg2); padding: 0; display: block; width: 100%; cursor: zoom-in; line-height: 0; }
.detail-hero img { display: block; width: 100%; aspect-ratio: 16 / 9; object-fit: cover; }
.zoom-hint { color: var(--text-dim); font-size: 0.78rem; margin-top: 0.4rem; }
.sr-only { position: absolute; width: 1px; height: 1px; overflow: hidden; clip: rect(0 0 0 0);
white-space: nowrap; }
.callout { border: 1px solid color-mix(in srgb, var(--select) 45%, var(--border));
border-left: 3px solid var(--select); border-radius: var(--radius);
background: color-mix(in srgb, var(--select) 7%, var(--surface));
padding: 0.85rem 1.1rem; margin: 1.5rem 0; font-size: 0.95rem; }
.runline { display: flex; align-items: stretch; gap: 0.5rem; margin: 1.5rem 0; }
.runline pre { flex: 1 1 auto; background: var(--surface-2); border: 1px solid var(--border);
border-radius: var(--radius); padding: 0.7rem 0.9rem; overflow-x: auto;
font-family: var(--font-mono); font-size: 0.83rem; line-height: 1.5; }
.copy-btn { flex: 0 0 auto; background: var(--surface-2); border: 1px solid var(--border);
color: var(--text-dim); border-radius: var(--radius); padding: 0 0.85rem; cursor: pointer;
font-family: var(--font-sans); font-size: 0.82rem; font-weight: 500; transition: color 0.15s, border-color 0.15s; }
.copy-btn:hover { color: var(--select); border-color: var(--select); }
.detail-section { margin-top: 2.25rem; }
.detail-section > h2 { font-family: var(--font-display); font-weight: 600; text-transform: uppercase;
font-size: 1.45rem; letter-spacing: 0.005em; padding-bottom: 0.5rem;
border-bottom: 1px solid var(--border); margin-bottom: 1rem; }
.md h1, .md h2, .md h3 { letter-spacing: -0.01em; margin: 1.4rem 0 0.6rem; line-height: 1.25; }
.md h1 { font-size: 1.35rem; } .md h2 { font-size: 1.15rem; } .md h3 { font-size: 1rem; }
.md p { margin: 0.7rem 0; }
.md ul, .md ol { margin: 0.7rem 0 0.7rem 1.4rem; }
.md li { margin: 0.3rem 0; }
.md .table-wrap { overflow-x: auto; margin: 0.9rem 0; }
.md table { border-collapse: collapse; font-size: 0.86rem; min-width: 100%; }
.md th, .md td { text-align: left; vertical-align: top; padding: 0.4rem 0.75rem 0.4rem 0;
border-bottom: 1px solid var(--border); }
.md th { color: var(--text-dim); font-weight: 600; white-space: nowrap; }
.md code { background: var(--surface-2); border: 1px solid var(--border); padding: 0.08rem 0.35rem;
border-radius: 4px; font-family: var(--font-mono); font-size: 0.84em; }
.md pre { background: var(--surface-2); border: 1px solid var(--border); border-radius: var(--radius);
padding: 0.85rem 1rem; overflow-x: auto; margin: 0.9rem 0; }
.md pre code { background: none; border: none; padding: 0; font-size: 0.83rem; line-height: 1.55; }
.src pre { background: var(--surface-2); border: 1px solid var(--border); border-radius: var(--radius);
padding: 1rem 1.1rem; overflow-x: auto; font-family: var(--font-mono);
font-size: 0.82rem; line-height: 1.55; }
.src .k { color: var(--code-k); } .src .s { color: var(--code-s); }
.src .c { color: var(--code-c); font-style: italic; } .src .n { color: var(--code-n); }
.src-meta { display: flex; justify-content: space-between; align-items: baseline; gap: 1rem;
flex-wrap: wrap; margin-bottom: 0.6rem; color: var(--text-dim); font-size: 0.85rem; }
.src-meta code { font-family: var(--font-mono); font-size: 0.82rem; }
.lightbox { border: 0; margin: 0; padding: 2rem; width: 100%; height: 100%; max-width: none;
max-height: none; background: rgba(0,0,0,0.85); cursor: zoom-out; }
.lightbox[open] { display: flex; align-items: center; justify-content: center; }
.lightbox::backdrop { background: transparent; }
.lightbox img { max-width: 100%; max-height: 100%; border-radius: var(--radius); }
.lightbox-close { position: absolute; top: 0.9rem; right: 0.9rem; background: var(--surface-2);
color: var(--text); border: 1px solid var(--border); border-radius: var(--radius);
font: 500 0.8rem var(--font-sans); padding: 0.4rem 0.75rem; cursor: pointer; }
.lightbox-close:hover { border-color: var(--select); color: var(--select); }
footer { border-top: 1px solid var(--border); background: var(--surface); margin-top: 2rem; }
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<header class="hero">
<h1>armature-bend</h1>
<p>Rigging end to end in the data API — edit_bones chain construction, name-bound vertex groups with smoothstep blend zones, posing, and depsgraph evaluation — bending a tapered tube through rest, half, and full curl.</p>
</header>
<main id="main">
<button class="detail-hero" id="heroZoom" type="button" aria-label="Zoom armature-bend render">
<img src="../assets/armature-bend-hero.webp" alt="armature-bend render" 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> edit_bones exists only in edit mode (empty in object mode), vertex groups bind to bones strictly by name, and the armature modifier is exactly linear blend skinning: every evaluated vertex must equal Σ wᵢ·(pose_bone.matrix @ bone.matrix_local.inverted()) @ rest, root ring pinned, tip deflected — a straight tube fails.</div>
<div class="runline">
<pre id="runCmd">blender --background --python examples/armature-bend/armature_bend.py --</pre>
<button class="copy-btn" id="copyRun" type="button">Copy</button>
</div>
<section class="detail-section md">
<p>A runnable example that rigs a tapered, segmented tube with a four-bone armature chain — <code>edit_bones</code> construction, name-bound vertex groups with smoothstep blend zones, a posed curl — and checks the depsgraph-evaluated result against closed-form linear blend skinning, following <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 <a href="https://github.com/TMHSDigital/Blender-Developer-Tools/tree/main/skills/depsgraph-and-evaluated-data/SKILL.md"><code>depsgraph-and-evaluated-data</code></a>.</p>
<p><strong>What it witnesses:</strong> the three contracts AI-generated rigging code most often gets wrong.</p>
<ol><li><code>edit_bones</code> only exists in edit mode — the collection is asserted empty in object mode and holding the full chain (heads/tails at closed-form positions) inside <code>mode_set(mode='EDIT')</code>. Outside edit mode, reads silently return nothing.</li><li>Vertex groups bind to bones <strong>by name</strong>; a typo deforms nothing without erroring. Every group here is named after its bone and the deform proves the binding.</li><li>The armature modifier is exactly linear blend skinning: for <em>every</em> vertex, <code>evaluated == Σ wᵢ · (pose_bone.matrix @ bone.matrix_local.inverted()) @ rest</code>. The check re-implements LBS from the pose matrices and compares the whole evaluated mesh (max error ~5e-7). The root ring must stay pinned and the tip must deflect — a straight tube is a failure.</li></ol>
<p>The armature API is identical on Blender 4.5 LTS and 5.1 — no version gate needed. One portability hazard is baked in as a comment: interleaving <code>color_attributes</code> writes with <code>VertexGroup.add()</code> dangles the attribute reference when the deform layer is allocated (hard crash on 4.5, silent luck on 5.1), so the script finishes all weight writes before creating the color attribute.</p>
<p>The render shows rest → half curl → full curl left to right, with per-bone weight bands visualized through a <code>BoneTint</code> color attribute — the smooth color blends at the joints are the same weights the LBS check asserts.</p>
<h2>Run</h2>
<pre><code># Cheap correctness check (no render) — the CI check:
blender --background --python armature_bend.py --
# Falsifier: rest pose. Must exit non-zero (tip deflection).
blender --background --python armature_bend.py -- --zero-curl
# Also render a still (EEVEE on a GPU host; use --engine cycles on GPU-less hosts):
blender --background --python armature_bend.py -- --output bend.png
blender --background --python armature_bend.py -- --output bend.png --engine cycles</code></pre>
<h2>Exit codes</h2>
<p>Per-script sequential checks. <code>9</code> is a valid check code; there is no rule against it.</p>
<div class="table-wrap"><table><thead><tr><th scope="col">Code</th><th scope="col">Meaning</th></tr></thead><tbody><tr><td>0</td><td>Success</td></tr><tr><td>1</td><td>Uncaught exception (FATAL wrapper)</td></tr><tr><td>2</td><td>argparse / usage</td></tr><tr><td>3</td><td><code>edit_bones</code> populated in object mode</td></tr><tr><td>4</td><td>Edit-mode bone chain off closed form</td></tr><tr><td>5</td><td>Evaluated vertex count changed</td></tr><tr><td>6</td><td>Evaluated mesh off closed-form LBS</td></tr><tr><td>7</td><td>Root ring moved</td></tr><tr><td>8</td><td>Tip did not deflect (<code>--zero-curl</code> lands here)</td></tr><tr><td>9</td><td><code>--output</code> produced no file</td></tr></tbody></table></div>
<p>The <code>blender-smoke</code> workflow runs the check on Blender 5.2 LTS and 4.5 LTS (5.1 on the weekly cron, the <code>needs-5.1</code> PR label, or manual dispatch). Smoke does not pass <code>--output</code> or <code>--zero-curl</code>.</p>
</section>
<section class="detail-section src">
<h2>Source</h2>
<div class="src-meta">
<code>examples/armature-bend/armature_bend.py</code>
<a href="https://github.com/TMHSDigital/Blender-Developer-Tools/tree/main/examples/armature-bend/armature_bend.py">View on GitHub →</a>
</div>
<pre><span class="s">"""An armature bending a weighted tube, checked against closed-form skinning.
Witnesses the three contracts AI-generated rigging code most often gets wrong:
1. `edit_bones` only exists in edit mode. Outside `mode_set(mode='EDIT')` the
collection is empty — reads silently return nothing, writes are lost. The
check asserts it is empty in object mode and holds the full chain in edit
mode, with heads/tails at their closed-form positions.
2. Vertex groups bind by *name*. The armature modifier matches group names to
bone names; a typo deforms nothing without erroring. Here every group name
is the bone name and the deform proves the binding.
3. The armature modifier is exactly linear blend skinning. For every vertex,
evaluated_position == sum_i( w_i * (pose_bone_i.matrix @
bone_i.matrix_local.inverted()) @ rest_position ). The check re-implements
LBS from the pose matrices and compares all vertices of the
depsgraph-evaluated mesh against it. A straight (undeformed) tube is a
failure: the tip must deflect while the root ring stays fixed.
The same API works unchanged on Blender 4.5 LTS and 5.1 — no version gate is
needed, which this example demonstrates by running identically on both.
``--zero-curl`` leaves every pose bone at rest and still asserts the tip
deflects. That is the falsifier (``--same-axis`` in export-preset-axis).
By default it runs only the correctness check (no render) — the CI smoke
check. Pass --output to also render a still:
blender --background --python armature_bend.py -- # check only
blender --background --python armature_bend.py -- --zero-curl # must fail
blender --background --python armature_bend.py -- --output b.png # + render
"""</span>
<span class="k">import</span> bpy, bmesh, sys, os, math, argparse
BONES = <span class="n">4</span>
BONE_LEN = <span class="n">1.0</span>
HEIGHT = BONES * BONE_LEN
SIDES = <span class="n">24</span>
RINGS = <span class="n">41</span> <span class="c"># vertex rings along the tube, tip cap included</span>
R_BASE = <span class="n">0.34</span>
R_TIP = <span class="n">0.16</span>
BLEND = <span class="n">0.3</span> <span class="c"># half-width of the weight blend zone at each joint</span>
CURL_DEG = <span class="n">34.0</span> <span class="c"># per-joint bend for the full pose</span>
LBS_TOL = <span class="n">5e-4</span> <span class="c"># float32 mesh coords vs double pose matrices</span>
<span class="c"># one tint per bone so the render shows the weight bands the check asserts</span>
PALETTE = [(<span class="n">0.02</span>, <span class="n">0.28</span>, <span class="n">0.38</span>), (<span class="n">0.0</span>, <span class="n">0.55</span>, <span class="n">0.55</span>), (<span class="n">0.95</span>, <span class="n">0.52</span>, <span class="n">0.12</span>), (<span class="n">0.85</span>, <span class="n">0.16</span>, <span class="n">0.18</span>)]
BONE_NAMES = [<span class="s">f"</span><span class="s">Seg_</span>{i}<span class="s">"</span> <span class="k">for</span> i <span class="k">in</span> range(BONES)]
<span class="k">def</span> bone_weights(t):
<span class="s">"""Normalized per-bone weights at parametric height t in [0, BONES]."""</span>
<span class="k">for</span> j <span class="k">in</span> range(<span class="n">1</span>, BONES): <span class="c"># smoothstep across each joint</span>
<span class="k">if</span> abs(t - j) <= BLEND:
a = (t - (j - BLEND)) / (<span class="n">2</span> * BLEND)
s = a * a * (<span class="n">3.0</span> - <span class="n">2.0</span> * a)
w = [<span class="n">0.0</span>] * BONES
w[j - <span class="n">1</span>], w[j] = <span class="n">1.0</span> - s, s
<span class="k">return</span> w
w = [<span class="n">0.0</span>] * BONES
w[min(BONES - <span class="n">1</span>, int(t))] = <span class="n">1.0</span>
<span class="k">return</span> w
<span class="k">def</span> build_tube():
me = bpy.data.meshes.new(<span class="s">"Tube"</span>)
bm = bmesh.new()
<span class="k">try</span>:
rings = []
<span class="k">for</span> k <span class="k">in</span> range(RINGS):
f = k / (RINGS - <span class="n">1</span>)
z, r = HEIGHT * f, R_BASE + (R_TIP - R_BASE) * f
rings.append([bm.verts.new((r * math.cos(a), r * math.sin(a), z))
<span class="k">for</span> a <span class="k">in</span> (<span class="n">2</span> * math.pi * s / SIDES <span class="k">for</span> s <span class="k">in</span> range(SIDES))])
<span class="k">for</span> k <span class="k">in</span> range(RINGS - <span class="n">1</span>):
<span class="k">for</span> s <span class="k">in</span> range(SIDES):
bm.faces.new((rings[k][s], rings[k][(s + <span class="n">1</span>) % SIDES],
rings[k + <span class="n">1</span>][(s + <span class="n">1</span>) % SIDES], rings[k + <span class="n">1</span>][s]))
bm.faces.new(list(reversed(rings[<span class="n">0</span>])))
bm.faces.new(rings[-<span class="n">1</span>])
bmesh.ops.recalc_face_normals(bm, faces=bm.faces)
bm.to_mesh(me)
<span class="k">finally</span>:
bm.free()
<span class="k">for</span> poly <span class="k">in</span> me.polygons:
poly.use_smooth = <span class="k">True</span>
obj = bpy.data.objects.new(<span class="s">"Tube"</span>, me)
bpy.context.collection.objects.link(obj)
<span class="k">return</span> obj
<span class="k">def</span> build_rig(curl_deg):
<span class="s">"""A weighted tube plus a posed 4-bone chain, both at the origin."""</span>
tube = build_tube()
<span class="c"># vertex groups named after the bones — the name IS the binding</span>
groups = [tube.vertex_groups.new(name=n) <span class="k">for</span> n <span class="k">in</span> BONE_NAMES]
<span class="k">for</span> idx, v <span class="k">in</span> enumerate(tube.data.vertices):
<span class="k">for</span> i, wi <span class="k">in</span> enumerate(bone_weights(v.co.z / BONE_LEN)):
<span class="k">if</span> wi > <span class="n">0.0</span>:
groups[i].add([idx], wi, <span class="s">'REPLACE'</span>)
<span class="c"># create the color attribute only AFTER all group writes: the first</span>
<span class="c"># VertexGroup.add() allocates the deform layer, which reallocates the</span>
<span class="c"># mesh's CustomData and dangles any attribute reference held across it</span>
<span class="c"># (crashes 4.5 LTS; 5.1 merely survives by luck)</span>
col = tube.data.color_attributes.new(<span class="s">"BoneTint"</span>, <span class="s">'FLOAT_COLOR'</span>, <span class="s">'POINT'</span>)
<span class="k">for</span> idx, v <span class="k">in</span> enumerate(tube.data.vertices):
w = bone_weights(v.co.z / BONE_LEN)
rgb = [sum(w[i] * PALETTE[i][c] <span class="k">for</span> i <span class="k">in</span> range(BONES)) <span class="k">for</span> c <span class="k">in</span> range(<span class="n">3</span>)]
col.data[idx].color = (*rgb, <span class="n">1.0</span>)
arm_data = bpy.data.armatures.new(<span class="s">"Chain"</span>)
arm = bpy.data.objects.new(<span class="s">"Chain"</span>, arm_data)
bpy.context.collection.objects.link(arm)
bpy.context.view_layer.objects.active = arm
<span class="c"># edit_bones is only populated between these two mode_set calls</span>
bpy.ops.object.mode_set(mode=<span class="s">'EDIT'</span>)
prev = <span class="k">None</span>
<span class="k">for</span> i, name <span class="k">in</span> enumerate(BONE_NAMES):
eb = arm_data.edit_bones.new(name)
eb.head = (<span class="n">0.0</span>, <span class="n">0.0</span>, i * BONE_LEN)
eb.tail = (<span class="n">0.0</span>, <span class="n">0.0</span>, (i + <span class="n">1</span>) * BONE_LEN)
<span class="k">if</span> prev <span class="k">is</span> <span class="k">not</span> <span class="k">None</span>:
eb.parent = prev
eb.use_connect = <span class="k">True</span>
prev = eb
bpy.ops.object.mode_set(mode=<span class="s">'OBJECT'</span>)
mod = tube.modifiers.new(<span class="s">"Armature"</span>, <span class="s">'ARMATURE'</span>)
mod.object = arm
mod.use_vertex_groups = <span class="k">True</span>
mod.use_bone_envelopes = <span class="k">False</span>
<span class="k">for</span> name <span class="k">in</span> BONE_NAMES[<span class="n">1</span>:]: <span class="c"># root stays upright</span>
pb = arm.pose.bones[name]
pb.rotation_mode = <span class="s">'XYZ'</span>
pb.rotation_euler.x = -math.radians(curl_deg)
<span class="k">return</span> tube, arm
<span class="k">def</span> check(tube, arm):
<span class="c"># contract 1: edit_bones is empty outside edit mode, full inside</span>
<span class="k">if</span> len(arm.data.edit_bones) != <span class="n">0</span>:
print(<span class="s">"ERROR: edit_bones populated in object mode"</span>, file=sys.stderr)
<span class="k">return</span> <span class="n">3</span>
bpy.context.view_layer.objects.active = arm
bpy.ops.object.mode_set(mode=<span class="s">'EDIT'</span>)
ebs = arm.data.edit_bones
ok = len(ebs) == BONES <span class="k">and</span> all(
(ebs[n].head - ebs[n].tail).length > <span class="n">0</span> <span class="k">and</span>
abs(ebs[n].head.z - i * BONE_LEN) < <span class="n">1e-6</span> <span class="k">and</span>
abs(ebs[n].tail.z - (i + <span class="n">1</span>) * BONE_LEN) < <span class="n">1e-6</span>
<span class="k">for</span> i, n <span class="k">in</span> enumerate(BONE_NAMES))
bpy.ops.object.mode_set(mode=<span class="s">'OBJECT'</span>)
<span class="k">if</span> <span class="k">not</span> ok:
print(<span class="s">"ERROR: edit-mode bone chain does not match its closed form"</span>, file=sys.stderr)
<span class="k">return</span> <span class="n">4</span>
deps = bpy.context.evaluated_depsgraph_get()
ob_eval = tube.evaluated_get(deps)
me_eval = ob_eval.to_mesh()
<span class="k">try</span>:
<span class="c"># contract 3: the armature modifier is exactly linear blend skinning</span>
mats = [arm.pose.bones[n].matrix @ arm.data.bones[n].matrix_local.inverted()
<span class="k">for</span> n <span class="k">in</span> BONE_NAMES]
rest = tube.data.vertices
<span class="k">if</span> len(me_eval.vertices) != len(rest):
print(<span class="s">"ERROR: evaluated mesh vertex count changed"</span>, file=sys.stderr)
<span class="k">return</span> <span class="n">5</span>
worst = <span class="n">0.0</span>
<span class="k">for</span> idx, v <span class="k">in</span> enumerate(rest):
w = bone_weights(v.co.z / BONE_LEN)
predicted = sum((wi * (m @ v.co) <span class="k">for</span> wi, m <span class="k">in</span> zip(w, mats) <span class="k">if</span> wi > <span class="n">0.0</span>),
start=v.co * <span class="n">0.0</span>)
worst = max(worst, (me_eval.vertices[idx].co - predicted).length)
<span class="k">if</span> worst > LBS_TOL:
print(<span class="s">f"</span><span class="s">ERROR: evaluated mesh deviates from closed-form LBS by </span>{worst:<span class="s">.6f</span>}<span class="s">"</span>,
file=sys.stderr)
<span class="k">return</span> <span class="n">6</span>
<span class="c"># root ring pinned, tip deflected — a straight tube is a failure</span>
base_move = max((me_eval.vertices[i].co - rest[i].co).length
<span class="k">for</span> i <span class="k">in</span> range(SIDES))
tip_move = (me_eval.vertices[len(rest) - <span class="n">1</span>].co - rest[len(rest) - <span class="n">1</span>].co).length
<span class="k">if</span> base_move > <span class="n">1e-5</span>:
print(<span class="s">f"</span><span class="s">ERROR: root ring moved </span>{base_move:<span class="s">.6f</span>}<span class="s"> (root bone is unposed)</span><span class="s">"</span>,
file=sys.stderr)
<span class="k">return</span> <span class="n">7</span>
<span class="k">if</span> tip_move < <span class="n">0.8</span>:
print(<span class="s">f"</span><span class="s">ERROR: tip only moved </span>{tip_move:<span class="s">.4f</span>}<span class="s"> — armature did not deform </span><span class="s">"</span>
<span class="s">"the tube"</span>, file=sys.stderr)
<span class="k">return</span> <span class="n">8</span>
<span class="k">finally</span>:
ob_eval.to_mesh_clear()
print(<span class="s">f"</span><span class="s">bones=</span>{BONES}<span class="s"> verts=</span>{len(tube.data.vertices)}<span class="s"> lbs_max_err=</span>{worst:<span class="s">.2e</span>}<span class="s"> </span><span class="s">"</span>
<span class="s">f"</span><span class="s">tip_deflection=</span>{tip_move:<span class="s">.3f</span>}<span class="s">"</span>)
<span class="k">return</span> <span class="n">0</span>
<span class="k">def</span> eevee_engine_id():
<span class="k">return</span> <span class="s">'BLENDER_EEVEE'</span> <span class="k">if</span> bpy.app.version >= (<span class="n">5</span>, <span class="n">0</span>, <span class="n">0</span>) <span class="k">else</span> <span class="s">'BLENDER_EEVEE_NEXT'</span>
<span class="k">def</span> render_still(rigs, path, engine):
scene = bpy.context.scene
mat = bpy.data.materials.new(<span class="s">"WeightBands"</span>)
mat.use_nodes = <span class="k">True</span>
nt = mat.node_tree
bsdf = nt.nodes[<span class="s">"Principled BSDF"</span>]
attr = nt.nodes.new(<span class="s">"ShaderNodeAttribute"</span>)
attr.attribute_name = <span class="s">"BoneTint"</span>
nt.links.new(attr.outputs[<span class="s">"Color"</span>], bsdf.inputs[<span class="s">"Base Color"</span>])
bsdf.inputs[<span class="s">"Roughness"</span>].default_value = <span class="n">0.32</span>
<span class="c"># rest -> half curl -> full curl, left to right; the rigs are rotated so</span>
<span class="c"># the curl sweeps across the picture plane instead of away from camera</span>
<span class="k">for</span> (tube, arm), x <span class="k">in</span> zip(rigs, (-<span class="n">3.1</span>, -<span class="n">0.6</span>, <span class="n">2.4</span>)):
<span class="k">for</span> ob <span class="k">in</span> (tube, arm):
ob.location.x = x
ob.rotation_euler.z = math.radians(<span class="n">90.0</span>)
tube.data.materials.append(mat)
floor_me = bpy.data.meshes.new(<span class="s">"Floor"</span>)
bm = bmesh.new()
<span class="k">try</span>:
bmesh.ops.create_grid(bm, x_segments=<span class="n">1</span>, y_segments=<span class="n">1</span>, size=<span class="n">30.0</span>)
bm.to_mesh(floor_me)
<span class="k">finally</span>:
bm.free()
fmat = bpy.data.materials.new(<span class="s">"Studio"</span>)
fmat.use_nodes = <span class="k">True</span>
fb = fmat.node_tree.nodes[<span class="s">"Principled BSDF"</span>]
fb.inputs[<span class="s">"Base Color"</span>].default_value = (<span class="n">0.03</span>, <span class="n">0.032</span>, <span class="n">0.037</span>, <span class="n">1.0</span>)
fb.inputs[<span class="s">"Roughness"</span>].default_value = <span class="n">0.7</span>
floor_me.materials.append(fmat)
floor = bpy.data.objects.new(<span class="s">"Floor"</span>, floor_me)
scene.collection.objects.link(floor)
wall = bpy.data.objects.new(<span class="s">"Wall"</span>, floor_me.copy())
wall.location = (<span class="n">0.0</span>, <span class="n">9.0</span>, <span class="n">0.0</span>)
wall.rotation_euler = (math.radians(<span class="n">90</span>), <span class="n">0.0</span>, <span class="n">0.0</span>)
scene.collection.objects.link(wall)
world = bpy.data.worlds.new(<span class="s">"World"</span>)
world.use_nodes = <span class="k">True</span>
world.node_tree.nodes[<span class="s">"Background"</span>].inputs[<span class="s">"Color"</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>)
scene.world = world
<span class="k">def</span> light(name, loc, energy, size, col, rot):
ld = bpy.data.lights.new(name, <span class="s">'AREA'</span>)
ld.energy = energy; ld.size = size; ld.color = col
ob = bpy.data.objects.new(name, ld)
ob.location = loc
ob.rotation_euler = tuple(math.radians(a) <span class="k">for</span> a <span class="k">in</span> rot)
scene.collection.objects.link(ob)
<span class="c"># a shaped warm key from the upper left, a faint cool fill so the shadow</span>
<span class="c"># side of each tube stays legible, a cool rim to lift the silhouettes off</span>
<span class="c"># the backdrop, and a warm wedge raking the back wall — the falloff pool</span>
<span class="c"># behind the subjects that the rest of the gallery stages against.</span>
light(<span class="s">"Key"</span>, (-<span class="n">4.0</span>, -<span class="n">5.0</span>, <span class="n">6.0</span>), <span class="n">650.0</span>, <span class="n">4.5</span>, (<span class="n">1.0</span>, <span class="n">0.96</span>, <span class="n">0.9</span>), (<span class="n">48</span>, <span class="n">0</span>, -<span class="n">38</span>))
light(<span class="s">"Fill"</span>, (<span class="n">5.0</span>, -<span class="n">4.0</span>, <span class="n">3.0</span>), <span class="n">110.0</span>, <span class="n">9.0</span>, (<span class="n">0.75</span>, <span class="n">0.85</span>, <span class="n">1.0</span>), (<span class="n">62</span>, <span class="n">0</span>, <span class="n">50</span>))
light(<span class="s">"Rim"</span>, (<span class="n">0.5</span>, <span class="n">4.5</span>, <span class="n">5.0</span>), <span class="n">350.0</span>, <span class="n">4.0</span>, (<span class="n">0.6</span>, <span class="n">0.78</span>, <span class="n">1.0</span>), (-<span class="n">55</span>, <span class="n">0</span>, <span class="n">175</span>))
light(<span class="s">"Wedge"</span>, (<span class="n">2.5</span>, <span class="n">3.5</span>, <span class="n">4.2</span>), <span class="n">520.0</span>, <span class="n">6.0</span>, (<span class="n">1.0</span>, <span class="n">0.76</span>, <span class="n">0.5</span>), (-<span class="n">72</span>, <span class="n">0</span>, <span class="n">195</span>))
cam_data = bpy.data.cameras.new(<span class="s">"Cam"</span>)
cam_data.lens = <span class="n">45.0</span>
cam = bpy.data.objects.new(<span class="s">"Cam"</span>, cam_data)
cam.location = (-<span class="n">0.3</span>, -<span class="n">10.5</span>, <span class="n">2.4</span>)
cam.rotation_euler = (math.radians(<span class="n">87</span>), <span class="n">0.0</span>, <span class="n">0.0</span>)
scene.collection.objects.link(cam)
scene.camera = cam
scene.render.engine = <span class="s">'CYCLES'</span> <span class="k">if</span> engine == <span class="s">'cycles'</span> <span class="k">else</span> eevee_engine_id()
<span class="k">if</span> engine == <span class="s">'cycles'</span>:
scene.cycles.samples = <span class="n">32</span>
<span class="k">else</span>:
<span class="k">try</span>:
scene.eevee.taa_render_samples = <span class="n">64</span>
<span class="k">except</span> AttributeError:
<span class="k">pass</span>
scene.render.resolution_x = <span class="n">1280</span>
scene.render.resolution_y = <span class="n">720</span>
scene.render.image_settings.file_format = <span class="s">'PNG'</span>
scene.render.filepath = path
<span class="c"># AgX (the 4.x/5.x default) desaturates the BoneTint bands toward pastel,</span>
<span class="c"># hiding exactly the weight boundaries the LBS check asserts.</span>
scene.view_settings.view_transform = <span class="s">'Standard'</span>
bpy.ops.render.render(write_still=<span class="k">True</span>)
<span class="k">return</span> os.path.exists(path) <span class="k">and</span> os.path.getsize(path) > <span class="n">0</span>
<span class="k">def</span> main():
argv = sys.argv[sys.argv.index(<span class="s">"--"</span>) + <span class="n">1</span>:] <span class="k">if</span> <span class="s">"--"</span> <span class="k">in</span> sys.argv <span class="k">else</span> []
p = argparse.ArgumentParser()
p.add_argument(<span class="s">"--output"</span>, default=<span class="k">None</span>, help=<span class="s">"optional: render a still PNG here"</span>)
p.add_argument(<span class="s">"--engine"</span>, default=<span class="s">"eevee"</span>, choices=(<span class="s">"eevee"</span>, <span class="s">"cycles"</span>),
help=<span class="s">"render engine for --output (cycles for GPU-less hosts)"</span>)
p.add_argument(<span class="s">"--zero-curl"</span>, action=<span class="s">"store_true"</span>,
help=<span class="s">"leave pose bones at rest (must fail)"</span>)
args = p.parse_args(argv)
bpy.ops.wm.read_factory_settings(use_empty=<span class="k">True</span>)
curl = <span class="n">0.0</span> <span class="k">if</span> args.zero_curl <span class="k">else</span> CURL_DEG
tube, arm = build_rig(curl)
code = check(tube, arm)
<span class="k">if</span> code:
<span class="k">return</span> code
<span class="k">if</span> args.output:
rigs = [build_rig(<span class="n">0.0</span>), build_rig(CURL_DEG / <span class="n">2</span>), (tube, arm)]
<span class="k">if</span> <span class="k">not</span> render_still(rigs, os.path.abspath(args.output), args.engine):
print(<span class="s">"ERROR: render produced no file"</span>, file=sys.stderr)
<span class="k">return</span> <span class="n">9</span>
print(<span class="s">f"</span><span class="s">rendered still </span>{args.output}<span class="s">"</span>)
print(<span class="s">"armature-bend OK"</span>)
<span class="k">return</span> <span class="n">0</span>
<span class="k">if</span> __name__ == <span class="s">"__main__"</span>:
<span class="k">try</span>:
sys.exit(main())
<span class="k">except</span> Exception <span class="k">as</span> e:
<span class="k">import</span> traceback; traceback.print_exc(); print(<span class="s">f"</span><span class="s">FATAL: </span>{e}<span class="s">"</span>, file=sys.stderr); sys.exit(<span class="n">1</span>)
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