Isometric Ops

---
name: isometric-ops
description: "Create, refine, compose, and export isometric/dimetric assets for web and games: projection math, SVG/CSS/three.js generation, pixel-art and Blender workflows, engine tilemaps, ControlNet AI generation, and the iso-studio composer. Triggers on: isometric, dimetric, tileset, y-sort."
license: MIT
allowed-tools: "Read Write Bash"
metadata:
  author: claude-mods
  related-skills: "genart-ops, threejs-ops, color-ops, frontend-design, playwright-ops"
---

# Isometric Operations

Create, refine, compose, and export isometric illustrative assets for websites and
games — end to end. This skill covers the exact projection math, the vector/CSS/SVG and
three.js generation routes, the pixel-art and Blender pre-render pipelines, engine
tilemap integration, the AI-generation-with-structure-control workflow, asset sourcing
with licence discipline, and the companion **iso-studio** scene composer (a standalone
app that grew out of this skill). Every constant is
derived and machine-checked; every workflow is runnable; every claim is sourced in its
reference file.

> **Boundary — what this skill does NOT own.** General three.js / creative-coding
> scaffolding lives in [`genart-ops`](../genart-ops/SKILL.md); app- and game-scale
> three.js (GLTF pipeline, react-three-fiber, `InstancedMesh`) lives in the `threejs-ops`
> skill. Colour science and perceptual (OKLCH) ramp construction live in
> [`color-ops`](../color-ops/SKILL.md). `isometric-ops` owns **only the isometric delta**
> — it cross-links those siblings, it never restates them. Detail lives in the reference
> files below: this router points, it does not duplicate.

---

## 1. The projection decision — always step zero

Choose the projection **before** you draw, generate, or model anything. This is not a
deferrable stylistic preference: it fixes the grid math, the tile aspect ratio, the
camera rig, and the anti-aliasing strategy for the entire pipeline downstream. Changing
it later means re-cutting every asset.

| Job | Projection | Ground-axis angle | Tile / face rule | Where |
|---|---|---|---|---|
| Web / vector illustration, diagrams, icons, hero art | **True isometric** | **30°** (all three axes 120° apart) | all axes foreshorten equally; smooth vector edges ignore pixel stepping | [`projection-math.md`](references/projection-math.md) §1, [`svg-vector-generation.md`](references/svg-vector-generation.md), [`css-isometric.md`](references/css-isometric.md) |
| Game tiles, tilemaps, sprite worlds, most "isometric" games | **2:1 dimetric** (commonly called isometric in games) | **26.565°** = arctan(1/2) | integer 2px:1px steps tessellate; `tileW = 2·tileH` | [`projection-math.md`](references/projection-math.md) §2, [`coordinates-depth.md`](references/coordinates-depth.md), [`engine-integration.md`](references/engine-integration.md) |
| Hand-placed / library pixel-art primitives (cubes, bricks, slopes) | **Pixel-neat 1:2** | **22.6°** (obelisk.js pixel-dot pattern) | 1:2 pixel dot stepping avoids staircasing at primitive-drawing level | [`projection-math.md`](references/projection-math.md) §7, [`pixel-art-workflow.md`](references/pixel-art-workflow.md) |

**The failure mode this prevents.** Nearly every "isometric" game is actually
**dimetric** (only two of the three axis separations are equal: ≈116.565°, 116.565°,
126.870°). The trap: an artist draws a "30° isometric" tile, the engine places it on a
2:1 (26.565°) diamond grid, and **the tile edges do not meet their neighbours**. Small at
one tile, catastrophic across a 50×50 map. The fix is not a nudge tool — it is deciding,
up front, that game tiles are **2:1 dimetric at 26.565°** and writing that number into
the [tile spec](references/tile-spec.md) so every asset is cut to the same grid.

**Terminology discipline (applies everywhere).** On first use per document write
**"2:1 dimetric (commonly called isometric in games)"**, then "2:1 dimetric" thereafter.
Never call the 2:1 game projection "isometric" unqualified. Distinguish **"isometric
drawing"** (100% scale) from **"isometric projection"** (81.65% = √(2/3) scale) whenever
the distinction affects a measurement.

### Canonical constants (the authority table)

Machine-emitted by [`iso-math.py constants`](scripts/iso-math.py); full derivations and
ground-truth checks in [`projection-math.md`](references/projection-math.md).

| Symbol | Exact form | Value | Appears as |
|---|---|---|---|
| Cube tilt ("magic angle") | `arctan(1/√2) = arcsin(1/√3)` | **35.264°** | 3D iso rotation |
| Foreshortening (projection scale) | `cos(35.264°) = √(2/3)` | **81.65%** (0.81650) | true-projection edge scale |
| Isometric **drawing** scale | full-scale convention | **100%** | vector iso (edges read at 100%) |
| True ground angle | definition | **30°** | vector iso axes |
| SSR / top-plane squash | `cos(30°)` | **86.602%** (0.86603) | Illustrator scale, 2D plane matrices |
| Figma height / circle→ellipse | `tan(30°)` | **57.735%** (0.57735) | Figma hack, ellipse minor axis |
| CSS back-tip | `arctan(√2) = 90° − 35.264°` | **54.7356°** | CSS `rotateX` |
| CSS un-foreshorten | `√(3/2) = 1/cos(35.264°)` | **1.22474** | CSS `scale3d` |
| Dimetric ground angle | `arctan(1/2)` | **26.565°** | game tiles |
| Dimetric screen slope | `tileH/tileW` (2:1) | **0.5** | tile-space `+x` = `(+tileW/2, +tileH/2)` |

> Two Blender ortho-camera rigs, both must appear wherever rigs are discussed: **2:1
> dimetric = RotX 60°, RotY 0°, RotZ 45°** (cube top 2× wide as tall, `sin 30° = 0.5`);
> **true isometric = RotX 54.736°, RotY 0°, RotZ 45°** (all three faces equal). Most
> tutorials use 60/0/45 and mislabel it "isometric" — it is dimetric. See
> [`blender-prerender.md`](references/blender-prerender.md) §1.

---

## 2. Task router — six routes

Each route is a numbered mini-workflow. Follow the links for the exact numbers, code, and
gotchas — the steps here are the spine, the references are the flesh.

### Route A — Illustrate for the web (vector / CSS / SVG)

For diagrams, icons, hero art, marketing scenes → **true isometric (30°)**.

1. **Decide** true iso (§1). Pin the light direction and palette up front
   ([`style-guide.md`](references/style-guide.md)).
2. **Pick the medium.** Live DOM elements you want selectable / accessible / SEO-visible →
   CSS. Static shapes and icon sets → SVG. See the decision tables in
   [`css-isometric.md`](references/css-isometric.md) and
   [`svg-vector-generation.md`](references/svg-vector-generation.md).
3. **CSS route.** 3D: `transform-style: preserve-3d` on the container, per-face children,
   then the outer stack `rotateX(54.7356deg) rotateZ(-45deg) scale3d(1.22474,…)` — the
   scale goes on the container **only** (or faces double-scale). 2D affine for flat cards:
   the `rotate(-30deg) skewX(30deg) scaleY(0.866)` recipe family, derived per plane in
   [`css-isometric.md`](references/css-isometric.md).
4. **SVG route.** Reach for [`@elchininet/isometric`](references/svg-vector-generation.md)
   (SVG-native, planes/paths) or hand-roll diamond/cube/prism paths using the plane
   `matrix()` recipes (Top `matrix(0.86603, 0.5, 0.86603, -0.5, 0, 0)`, etc.). Grab a
   ready grid from [`assets/grids/`](assets/grids/) or emit one with
   `iso-math.py grid-svg`.
5. **Optimise & export.** Simplify paths in-tool → export → SVGO/SVGOMG → raster
   derivatives, **in that order** ([`svg-vector-generation.md`](references/svg-vector-generation.md) §7).
6. **Verify visually.** For map-heavy web work, headless-screenshot checks belong to
   [`playwright-ops`](../playwright-ops/SKILL.md); tie the render back to the
   [style checklist](references/style-guide.md).

### Route B — Build a game tileset (spec → generate → validate → pack → engine)

For tilemaps and sprite worlds → **2:1 dimetric (26.565°)**. This is the discipline route;
skipping the spec is how sets drift.

1. **Write the spec first.** Copy the fill-in template from
   [`tile-spec.md`](references/tile-spec.md) and pin: projection + exact angle, tile W×H
   (`W = 2H`), unit elevation (px per z-step), anchor **at the feet**, footprint grammar
   (1×1, 2×1, 2×2…), transparent margin/bleed, palette tokens, one light direction, output
   format, `name_direction_variant.png` naming, and scale grammar (one human = N tiles).
2. **Generate** the tiles — draw them ([`pixel-art-workflow.md`](references/pixel-art-workflow.md)),
   pre-render from 3D (Route D), or AI-generate (Route C). Every asset obeys the spec's
   numbers.
3. **Validate** each tile against the spec:
   `uv run scripts/tile-validate.py --tile-w 64 --tile-h 32 tiles/*.png` — flags dimension
   drift, alpha halos, edge-bleed, off-centre anchor, palette overflow (exit 10 on any
   violation). Every spec line maps to a check
   ([`tile-spec.md`](references/tile-spec.md) "How the spec feeds tile-validate.py").
4. **Pack** into an atlas:
   `uv run scripts/sheet-pack.py tiles/ --trim --padding 2 --pot` → one sheet PNG + a JSON
   atlas. An atlas turns N texture binds into 1 — the single biggest win for tile-heavy
   scenes ([`coordinates-depth.md`](references/coordinates-depth.md) §11).
5. **Integrate** into the engine — Godot 4 `TileMapLayer` (Shape=Isometric, Layout=Diamond
   Down, Y-Sort on, origin at feet), Unity orthographic checklist, or Phaser/PixiJS manual
   cart↔iso. Atlas anchor/pivot mapping is spelled out in
   [`engine-integration.md`](references/engine-integration.md).
6. **The runtime math** — tile↔screen, picking, and the `(x+y, z, layer, zBias)` depth
   sort with anchor-at-feet — lives in [`coordinates-depth.md`](references/coordinates-depth.md)
   and is mirrored by `iso-math.py to-screen` / `to-tile` (round-trip verified).

### Route C — AI pipeline (generate → control → refine → vectorize)

Model by output type, scaffolded prompts, ControlNet structure control, refine, vectorize, licence check: [task-routes.md](references/task-routes.md).

### Route D — Pre-render from 3D (Blender / three.js)

Ortho rig per projection, bake N-direction sprites (Blender or three.js), re-enter Route B at validate: [task-routes.md](references/task-routes.md).

### Route E — Compose a scene (iso-studio)

Snap-grid staging, automatic depth sort, PNG/scene-JSON export, blockout to ControlNet in the standalone app: [iso-studio.md](references/iso-studio.md).

### Route F — Source existing assets (licences)

CC0 first, then marketplaces; verify plan, licence and **AI-training clause** before delivery: [task-routes.md](references/task-routes.md).

---

## 3. Scripts

All scripts follow the [Skill Resource Protocol](../../docs/SKILL-RESOURCE-PROTOCOL.md):
stdout = data only, semantic exit codes, `--help` with EXAMPLES, `--json` envelopes.
Pure-stdlib scripts run with `python`; Pillow scripts use PEP 723 inline metadata via
`uv run` (on this Windows machine avoid the Store `python3` stub — it exits 49).

| Script | What it does | Launch |
|---|---|---|
| [`iso-math.py`](scripts/iso-math.py) | Canonical constants, tile↔screen transforms, SVG grids, CSS/SVG/Illustrator/Figma transform recipes | `python scripts/iso-math.py constants --projection true --json` · `… to-screen 3 2 --tile-w 64 --tile-h 32` · `… grid-svg --projection dimetric21 --tile-w 64 --extent 8 > grid.svg` · `… transforms --target css-3d` |
| [`tile-validate.py`](scripts/tile-validate.py) | QA gate for (especially AI) tiles: dimension, alpha-halo, edge-bleed, anchor, palette checks; exit 10 on violation | `uv run scripts/tile-validate.py --tile-w 64 --tile-h 32 tiles/*.png` |
| [`sheet-pack.py`](scripts/sheet-pack.py) | Pack a tiles directory into a spritesheet PNG + JSON atlas; `--trim --padding N --pot`, deterministic order | `uv run scripts/sheet-pack.py tiles/ --trim --padding 2 --pot` |
| [`check-iso-facts.py`](scripts/check-iso-facts.py) | §7 staleness verifier: `--offline` asserts constants + reference citations; `--live` npm-checks named packages (exit 7 advisory / 10 drift) | `python scripts/check-iso-facts.py --offline` |

## 4. Assets

| Asset | What it is | Use |
|---|---|---|
| [`prompt-library.md`](assets/prompt-library.md) | Ready-to-paste prompt scaffolds by target tool (city block, room cutaway, floating island, warehouse, control room, dashboard, sprite tileset, icon) + universal negative block + Midjourney/Firefly/Recraft/Flux cheatsheets | Route C, step 2 |
| [`palettes/three-tone-presets.json`](assets/palettes/three-tone-presets.json) | 8 three-tone presets (`kenney-prototype-grey`, `pastel-dollhouse`, `industrial-muted`, `cyberpunk-teal-violet`, `blueprint`, `earthy-game`, `mono-ink`, `brand-neutral`); top-lightest verified by WCAG luminance | Route A/B, [`style-guide.md`](references/style-guide.md) |
| [`grids/`](assets/grids/) | Pre-generated `true-iso-{32,64,128}.svg` and `dimetric-2to1-{32,64,128}.svg` (line slope 0.5 dimetric / tan30° true iso) | Route A, backdrops |
| [`blender-iso-rig.py`](assets/blender-iso-rig.py) | Headless Blender ortho-rig + N-direction sprite baker + optional depth/normal passes | Route D, step 2 |
| **iso-studio** (external) | The zero-dependency scene composer — standalone repo at github.com/0xDarkMatter/iso-studio, owns `scene-schema.json` + the asset library; pointer: [`iso-studio.md`](references/iso-studio.md) | Route E, §5 |

## 5. iso-studio — the scene composer (standalone app)

Standalone zero-dependency app (github.com/0xDarkMatter/iso-studio), run with `node <iso-studio>/server.mjs`. Palettes, blockout mode, manual pointer: [iso-studio.md](references/iso-studio.md).

---

## 6. Gotcha index — the top 10 footguns

| # | Footgun | Fix | Reference |
|---|---|---|---|
| 1 | **Mislabelled dimetric** — calling 2:1 game tiles "isometric" and cutting them to a 30° grid; tiles don't tessellate | Game tiles are **2:1 dimetric at 26.565°**; write the exact angle into the tile spec | [`projection-math.md`](references/projection-math.md) §2/§4, [`tile-spec.md`](references/tile-spec.md) |
| 2 | **Skew without scale** — shearing a flat asset onto the iso axes but skipping the `cos(30°)=0.86603` vertical scale; right axes, wrong height, won't stack | Run the full **Scale → Shear → Rotate**; build on the iso plane, never skew-and-call-it-done | [`projection-math.md`](references/projection-math.md) §3.2/§3.3 |
| 3 | **Centre anchors break y-sort** — a tall sprite's centre is high on screen, so a centre-based sort draws it behind nearer objects | Anchor every sprite at its **visual feet** (ground contact); the sort key uses the tile it stands on | [`coordinates-depth.md`](references/coordinates-depth.md) §8 |
| 4 | **Elevation folded into the depth key** — using `x+y+z` makes a tall near object sort behind a short far one | `z` is a **tie-breaker after** `(x+y)`, never added into it: `(x+y, z, layer, zBias)` | [`coordinates-depth.md`](references/coordinates-depth.md) §5/§7 |
| 5 | **Unity near-clip clipping** — default near plane hides geometry behind the ortho camera on the XZ map | Push near clip to a large negative (−1000+); Stable Fit → Close Fit shadows; disable cascades | [`engine-integration.md`](references/engine-integration.md) §2 |
| 6 | **Ortho frustum not recomputed on resize** — the iso view stretches when the viewport changes | Recompute aspect-scaled left/right/top/bottom in the resize handler; update the projection matrix | [`threejs-orthographic.md`](references/threejs-orthographic.md) §3 |
| 7 | **AI halo edges** — semi-transparent fringe around AI-generated tiles that shows as a seam | Alpha-threshold / defringe; `tile-validate.py` flags halo % mechanically | [`ai-refinement.md`](references/ai-refinement.md) §3 |
| 8 | **Licence AI-training clause** — "commercial use OK" is not "dataset use OK"; DrawKit forbids AI training | Verify plan + licence + **AI-training clause** before client delivery | [`asset-sourcing.md`](references/asset-sourcing.md) |
| 9 | **Flux-dev LoRA licences** — Flux.1-dev derivatives are **non-commercial**; shipping them in a client project is a violation | Check each LoRA's licence flag; prefer permissively-licensed adapters for commercial work | [`ai-generation.md`](references/ai-generation.md) §2/§7 |
| 10 | **Staircasing & the >4× upscale trap** — 30° lines staircase in pixel art; pushing an upscaler past 4× invents perspective-breaking detail | Commit to 2:1 pixel-neat stepping; above 4× **regenerate at a higher base**, don't upscale | [`pixel-art-workflow.md`](references/pixel-art-workflow.md) §1, [`ai-refinement.md`](references/ai-refinement.md) §1 |

---

## Related skills

[`genart-ops`](../genart-ops/SKILL.md) (general three.js / creative coding) ·
`threejs-ops` (app/game-scale three.js: GLTF, r3f, `InstancedMesh`) ·
[`color-ops`](../color-ops/SKILL.md) (colour science, OKLCH ramps) ·
`frontend-design` (Claude-Code-bundled; production UI craft) ·
[`playwright-ops`](../playwright-ops/SKILL.md) (headless render verification).