Summary

A new complex playground view (5th tool-rail button, the graph glyph) that warps the loaded image — a gallery picture, the bundled sample, or the generated grid/polar patterns — through a chosen complex function f(z), GeoGebra-style. Built from a shaping session (shaping/complex-playground-shaping.md).

Feature (feat(playground))

• 12 presets, one GLSL branch each in a WebGL2 uber-shader, mirrored on CPU for the no-WebGL2 fallback: identity, z², zⁿ, 1/z, Möbius k(z−z₀)/(z−z∞), Joukowski, exp, log, Escher zᵃ, sin, tan, sin(1/z). Each carries an analytic f' for mip-LOD anti-aliasing.
• Live, schema-generated controls (sliders / complex number-fields) + reset; the active formula renders live and updates as you tweak.
• Hand-drag adds a complex constant c to the formula, with a toggle for domain f(z+c) vs output f(z)+c; wheel zooms.
• Draggable on-canvas handles for a preset's zero/pole (Möbius), plus an origin cross and unit-circle overlay.
• Fill modes (tile / clamp / mirror) so out-of-image samples never go black.

It runs on its own complex frame (origin + scale), independent of the Droste doc.rect; it only borrows doc.image and the existing image-source paths (DropZone sample/patterns, Gallery).

New files: src/lib/render/playground/{presets.ts,shader.frag.glsl,gl.ts,cpu.ts}, src/lib/ui1/playground.svelte.ts, src/components/ui1/{PlaygroundStage,PlaygroundControls}.svelte, tests/render/playground-presets.test.ts. Wired into state.svelte.ts (ViewMode), ToolRail.svelte, UiVariant1.svelte, icons.ts.

Test Coverage

tests/render/playground-presets.test.ts — 22 tests covering preset f(z) values, the Möbius f' sign, uniform packing, and live-formula text in both pan modes. Suite: 22 → 44 tests total, all passing.

Coverage is on the pure preset library (the math). The Svelte components and GL/CPU renderers are verified by live browser QA below (the .svelte.ts state + GLSL can't run under node/vitest).

Pre-Landing Review

Inline checklist pass: no SQL/data/LLM trust-boundary surface; no secrets; resource cleanups present (dispose, cancelAnimationFrame, ResizeObserver.disconnect); reactivity reads inputs synchronously. One self-caught nit (Möbius f' sign, AA-only) fixed in commit 2.

Adversarial Review (Codex, cross-model)

Codex flagged 2 × P2 (no P1):

• Reset button stayed disabled on param-only edits → fixed (playgroundDirty() now includes param drift). Verified live.
• WebGL2 init failure left the stage blank → fixed (glInitFailed flips to the CPU path).

Verification (live, via headless browser)

No console errors across: Escher zᵃ (spiral), 1/z (inversion), Möbius (handles + correct formula), sin(1/z) (essential-singularity kaleidoscope), drag→c updating the formula, mirror fill, reset enabling after a param edit, dragging the Möbius zero. Mobile (390×844) layout verified — control strip wraps, tool rail becomes a bottom bar.

Plan Completion

All shaping slices V1–V5 landed (see shaping/complex-playground-shaping.md). Conformal coordinate grid was intentionally dropped (clutter vs. the image warp itself); origin cross + unit circle kept.

Notes

• This repo has no VERSION/CHANGELOG.md, so no version bump (consistent with prior PRs).
• README still says "Two views" and lists some deleted components — pre-existing staleness, left out of scope here.

Test plan

• npm run test — 44 passing
• npm run check — 0 errors
• npm run build — clean
• Live QA, desktop + mobile, no console errors

🤖 Generated with Claude Code

Staging: https://silvio-tententoon-complex-playground.pgs.sh/ — open the app, then click the 5th tool-rail button (graph glyph) to enter the complex playground.