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# Technical Specification: Grid Snapping System (Grid Snapping Specification)
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This document defines the graphical user interface design and coordinate/signal processing algorithms required to build a synchronized grid snapping feature across both the Web Frontend and the Dockerized Python Desktop Backend.
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---
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## 1. Toolbar UI Design Upgrade
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The toolbar layout has been expanded to double its physical vertical height. This increase in interactive space allows for larger navigation buttons and the integration of a dedicated Snap controller.
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```text
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+───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────+
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| [Pro Toolbar - Height: 64px] |
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| +──────────+ +──────────+ +──────────+ +──────────+ +───────────────────────────────────────────────────────────────+ |
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| | Cut | | Copy | | Paste | | Snap: | | Transport Monitor | |
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| | [Ctrl+X]| | [Ctrl+C]| | [Ctrl+V]| | [1/4 ▼] | | [Tempo: 120 BPM] [Time Signature: 4/4] [Bar:Beat 1.3.00] | |
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| +──────────+ +──────────+ +──────────+ +──────────+ +───────────────────────────────────────────────────────────────+ |
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+───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────+
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```
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### 1.1. Snap Dropdown Configuration
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* **Placement:** Located immediately following the *Paste* button on the primary toolbar row.
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* **UI Syntax:** `Snap: <Dropdown_Widget>`
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* **Dropdown Option Matrix:**
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* `free`: Disables snapping; allows unrestricted pixel-by-pixel dragging.
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* `1`: Snaps to the beginning of each complete measure (Whole Bar / 1/1).
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* `1/2`: Divides the bar into 2 subdivisions (Half Note).
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* `1/4`: Divides the bar into 4 subdivisions (Quarter Note / 1 Beat).
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* `1/8`: Divides the bar into 8 subdivisions (Eighth Note).
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* `1/16`: Divides the bar into 16 subdivisions (Sixteenth Note).
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* `1/32`: Divides the bar into 32 subdivisions (Thirty-second Note).
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---
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## 2. DSP Grid Math: Grid Subdivision & Time Interval Calculations
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To calculate the absolute temporal duration between individual grid lanes, the time metrics must be derived dynamically from the project's master tempo.
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Let:
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* $B$ be the project tempo (Beats Per Minute, e.g., $120\text{ BPM}$).
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* $T_{\text{beat}}$ be the duration of a single beat (seconds).
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* $T_{\text{bar}}$ be the duration of a full measure/bar (seconds)—assuming a standard $4/4$ time signature (4 beats per bar).
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The foundational constants are established as follows:
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$$T_{\text{beat}} = \frac{60}{B} \quad (\text{seconds})$$
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$$T_{\text{bar}} = 4 \times T_{\text{beat}} = \frac{240}{B} \quad (\text{seconds})$$
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*Example:* At a tempo of $120\text{ BPM}$, a single $1\text{ Bar}$ measure spans exactly $2.0\text{ seconds}$.
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### 2.1. Determining Grid Time Interval Modifiers ($\Delta t$)
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Based on the user's active choice inside the snap dropdown selection ($S \in \{\text{free}, 1, 1/2, 1/4, 1/8, 1/16, 1/32\}$), the exact grid time step $\Delta t$ (seconds) is mapped as follows:
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$$\Delta t = \begin{cases} 0 & S = \text{free} \\ T_{\text{bar}} & S = 1 \\ \frac{T_{\text{bar}}}{2} & S = 1/2 \\ \frac{T_{\text{bar}}}{4} = T_{\text{beat}} & S = 1/4 \\ \frac{T_{\text{bar}}}{8} & S = 1/8 \\ \frac{T_{\text{bar}}}{16} & S = 1/16 \\ \frac{T_{\text{bar}}}{32} & S = 1/32 \end{cases}$$
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---
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## 3. Snapping Coordinate Calculation
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When a user executes a drag-and-drop event on an audio clip, or updates a timeline marker position, the system continuously converts raw cursor values into aligned coordinates.
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```text
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Grid Line 1 (k * dt) Grid Line 2 ((k+1) * dt)
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│ │
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├───────────────○─────────────┤
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▲
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│ [ Cursor dragging action ]
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Raw Time (t_raw)
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│
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▼ [ Apply Snap round() function ]
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────────────────┼─────────────►
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Snapped Time (t_snapped)
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```
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### 3.1. Pixel to Snap-Time Translation Workflow
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1. Intercept the actual client-side horizontal cursor position $X_{\text{raw}}$ (pixels).
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2. Convert it into a raw timeline duration metric $t_{\text{raw}}$ (seconds) utilizing the current scaling zoom factor $Z$ (pixels/second):
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$$t_{\text{raw}} = \frac{X_{\text{raw}}}{Z}$$
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3. Apply the rounding constraint formula to lock the raw timestamp to the absolute nearest grid marker:
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$$t_{\text{snapped}} = \begin{cases} t_{\text{raw}} & S = \text{free} \\ \text{round}\left( \frac{t_{\text{raw}}}{\Delta t} \right) \times \Delta t & S \neq \text{free} \end{cases}$$
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4. Map the snapped timeline index $t_{\text{snapped}}$ back to the layout canvas system coordinates to paint the element at its snapped visual boundary:
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$$X_{\text{snapped}} = t_{\text{snapped}} \times Z$$
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---
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## 4. Python Porting Blueprint
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When translating this architectural logic into a desktop Python core environment using frameworks like PyQt6, the snapping evaluations are tied directly into the tracking loop inside the `mouseMoveEvent` handler.
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```python
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# [PYTHON PORTING BLUEPRINT] - Integrating the Snap algorithm into Python UI layer
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import numpy as np
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class AudioSnapEngine:
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def __init__(self, bpm: float = 120.0):
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self.bpm = bpm
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def calculate_grid_step(self, snap_option: str) -> float:
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"""
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Calculates the grid's target duration step (seconds) based on Tempo and Snap selection.
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"""
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if snap_option == "free":
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return 0.0
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# 1 Bar in a standard 4/4 signature equals 240 / BPM seconds
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t_bar = 240.0 / self.bpm
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fraction_map = {
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"1": 1.0,
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"1/2": 2.0,
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"1/4": 4.0,
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"1/8": 8.0,
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"1/16": 16.0,
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"1/32": 32.0
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}
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division = fraction_map.get(snap_option, 4.0)
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return float(t_bar / division)
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def snap_time(self, raw_time_seconds: float, snap_option: str) -> float:
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"""
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Hard-clamps a raw timestamp to the nearest grid milestone. Prevents negative index overflows.
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"""
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dt = self.calculate_grid_step(snap_option)
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if dt == 0.0:
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return max(0.0, raw_time_seconds)
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# Find the nearest integer index k of the target grid lane: raw_time / dt
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k = round(raw_time_seconds / dt)
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snapped_time = k * dt
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return max(0.0, snapped_time)
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```
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---
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## 5. Visual Grid Alignment
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To maintain an intuitive environment for multi-channel editing, whenever a snapping constraint value other than `free` is engaged:
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* The rendering engine overlays thin, low-contrast vertical grid lines (`rgba(255, 255, 255, 0.05)`) over the background profile of every active Waveform Lane.
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* These marker lines are projected onto every timeline axis point that satisfies a whole multiple increment of $\Delta t$.
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* Displaying these alignment indicators ensures that users can visually anticipate bounding snapping positions before releasing their mouse track buttons.
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