# math_wave Color Strip Source — Implementation Plan

## Overview

A new CSS type that generates LED colors from configurable mathematical wave functions. Each LED position gets a wave value based on spatial position and time, mapped to a color via a gradient palette. Supports multiple superimposed wave layers, sync clocks, and bindable parameters.

## Requirements

- Waveform types: sine, triangle, sawtooth, square
- Parameters per wave layer: waveform, frequency, amplitude, phase, offset
- Global parameters: speed (bindable), gradient_id (color mapping)
- Wave superposition: list of wave layers combined additively
- Spatial dimension: wave value depends on LED position (0.0-1.0) + time
- Sync clock integration for time parameter
- Color mapping: combined wave output (0.0-1.0) mapped through a gradient

## Phase 1: Storage Model

**File: `server/src/wled_controller/storage/color_strip_source.py`**
- Add `MathWaveColorStripSource` dataclass after `GameEventColorStripSource`
- Fields:
  - `waves: list` — default `[{"waveform": "sine", "frequency": 1.0, "amplitude": 1.0, "phase": 0.0, "offset": 0.0}]`
  - `speed: BindableFloat` — default 1.0
  - `gradient_id: Optional[str]` — references Gradient entity
- Implement `to_dict`, `from_dict`, `create_from_kwargs`, `apply_update` (follow `CandlelightColorStripSource` pattern)
- Valid waveforms: `{"sine", "triangle", "sawtooth", "square"}`
- Add `"math_wave": MathWaveColorStripSource` to `_SOURCE_TYPE_MAP`

## Phase 2: Stream Implementation

**File: `server/src/wled_controller/core/processing/math_wave_stream.py`** (new)
- Class `MathWaveColorStripStream(ColorStripStream)` following `CandlelightColorStripStream` pattern
- Key methods: `__init__`, `_update_from_source`, `configure`, `start`, `stop`, `get_latest_colors`, `update_source`, `set_clock`, `set_gradient_store`
- Animation loop (`_animate_loop`):
  - Get `t` from clock (if set) or wall clock
  - For each LED at normalized position `p = i / (N-1)`:
    - Sum all wave layers: `sum += amplitude * waveform(2*pi*frequency*(p + speed*t) + phase) + offset`
    - Clamp result to [0.0, 1.0]
  - Map per-LED values to RGB via gradient LUT
- Waveform functions (vectorized with numpy):
  - `sine`: `0.5 + 0.5 * np.sin(x)`
  - `triangle`: `2.0 * np.abs(np.mod(x / (2*pi), 1.0) - 0.5)`
  - `sawtooth`: `np.mod(x / (2*pi), 1.0)`
  - `square`: `(np.sin(x) >= 0).astype(float)`
- Double-buffering pattern (same as candlelight)
- Use `self.resolve("speed", self._speed)` for bindable speed
- Gradient resolution via `set_gradient_store` pattern

## Phase 3: API Integration

**File: `server/src/wled_controller/api/schemas/color_strip_sources.py`**
- Add `MathWaveCSSResponse`, `MathWaveCSSCreate`, `MathWaveCSSUpdate`
- Add to `ColorStripSourceResponse`, `ColorStripSourceCreate`, `ColorStripSourceUpdate` unions

**File: `server/src/wled_controller/core/processing/color_strip_stream_manager.py`**
- Import `MathWaveColorStripStream`
- Add `"math_wave": MathWaveColorStripStream` to `_SIMPLE_STREAM_MAP`
- Existing `set_gradient_store` and `_inject_clock` injection handles it automatically

## Phase 4: Frontend

**File: `server/src/wled_controller/static/js/types.ts`**
- Add `'math_wave'` to `CSSSourceType` union

**File: `server/src/wled_controller/static/js/core/icons.ts`**
- Add `math_wave: _svg(P.activity)` to `_colorStripTypeIcons`

**File: `server/src/wled_controller/templates/modals/css-editor.html`**
- Add `<option value="math_wave">` to type select
- Add `<div id="css-editor-math-wave-section">` with:
  - Gradient picker (EntitySelect)
  - Speed (BindableScalarWidget)
  - Wave layers list (dynamic rows: waveform IconSelect, frequency/amplitude/phase/offset inputs, add/remove buttons)

**File: `server/src/wled_controller/static/js/features/color-strips.ts`**
- Add to `CSS_TYPE_KEYS`, `CSS_SECTION_MAP`, `CSS_TYPE_SETUP`, `NON_PICTURE_TYPES`
- Add to `clockTypes` array in `saveCSSEditor`
- Add type handler: `load(css)`, `reset()`, `getPayload(name)`
- Add card renderer showing wave count, gradient swatch, speed, clock badge
- Add wave layer management: `_renderMathWaveRow`, `addMathWaveLayer`, `removeMathWaveLayer`

**Files: `en.json`, `ru.json`, `zh.json`**
- Add i18n keys for type name, description, all field labels, waveform names

## Phase 5: Testing

**File: `server/tests/core/test_math_wave_stream.py`** (new)
- Test wave functions produce expected values at known inputs
- Test single wave spatial pattern
- Test wave superposition
- Test gradient color mapping
- Test clock integration
- Test `update_source` hot-update
- Test `configure` auto-sizing

**File: `server/tests/e2e/test_color_strip_flow.py`**
- Add `test_math_wave_crud` to lifecycle tests

**Storage model tests:**
- Test `from_dict` roundtrip
- Test `create_from_kwargs` with valid/invalid waveforms
- Test `apply_update`
- Test `_SOURCE_TYPE_MAP` dispatch

## Risks & Mitigations

- **Wave layer UI complexity** — Follow existing composite layers / game event mappings patterns
- **Performance with many layers** — Vectorize with numpy; cap max wave layers to 8
- **Gradient resolution** — Stream manager already injects `set_gradient_store` automatically