Case Study: Canvas-018

Yunbroidery Stitch Algorithm Syntax Card

Module 1: Metadata Table

Parameter	Specification
Archive ID	Canvas-018
Perceptual Image	Good Friends
Basic Structure	2-3-3-2 unit grid forming a 3×4 rectangular mirror-symmetric matrix
Syntax Type	Mirror Symmetry
Thread Spec	DMC No. 5 / No. 25 3-ply folded
Color Scheme	Emerald Green, Bright Yellow
Stitch Direction	Green: Top-Left to Bottom-Right (-45°) / Yellow: Bottom-Right to Top-Left (135°)

Module 2: Starting & Vector Operations

1. Starting Logic & Phase Sequence

• Phase ①: Dual-Color Diagonal Cross Array Constructed on a 2-3-3-2 grid sequence, red/blue (green/yellow) vector stitches are placed alternately. Green stitches (-45°) descend from top-left to bottom-right, while yellow stitches (135°) traverse diagonally, forming a balanced tension grid.
• Phase ②: Regional Duplication & Matrix Extension
  • Region 1 (Base Shape, Stitches 1–16): Defines the core mirror-symmetric block.
  • Region 2 (Stitches 17–32): Shifted along the X-axis by Δx = +4 grid units (+80px).
  • Region 3 (Stitches 33–48): Shifted further along X-axis by Δx = +4 grid units (+80px).
  • Regions 4–6 (Stitches 49–96): Translated down the Y-axis by Δy = +3 grid units (+60px) to achieve a full 3×2 grid layout.

2. Vector Coordinates & Translation Calculations

• Grid Unit Scale: 1 grid unit = 20 px. Single stitch vector defined as V = (Δx, Δy).
• Base Vectors & Inclinational Angles:
  • Forward Stitch (e.g., Stitch 1): P1(30, 30) -> P2(50, 50), Vector V = (20, 20), Length L = 28.28 px, Angle θ = -45°.
  • Long Diagonal Stitch (e.g., Stitch 3): P1(90, 30) -> P2(50, 70), Vector V = (-40, 40), Length L = 56.57 px, Angle θ = 135°.
• Regional Shift Matrix: R(i, j) = Base_Shape + (i * 80px, j * 60px), where i ∈ {0, 1, 2} and j ∈ {0, 1}.

Module 3: Structural Mechanics & Topology

1. Structural Backbone & Intersections

Canvas-018 operates as a Bi-directional Diagonal Lattice.

• Topological Nodes: Intersection nodes at grid points (e.g., (50, 50), (50, 70)) sustain multiple thread penetrations, creating a robust multi-connected topological network.
• Variable Length Superposition: The 2-3-3-2 stepping pattern mixes long stitches (56.57 px) that act as primary tension beams with short stitches (28.28 px) that lock boundaries and distribute localized stress.

2. Tension Equilibrium & Stress Distribution

• Vectorial Counter-Balance: Opposing -45° and +135° stitch directions ensure that net force ΣF ≈ 0 across the canvas plane, effectively suppressing fabric distortion and warping.
• Stress Decomposition: Tension forces resolve into orthogonal components F_x = 0.707 F and F_y = 0.707 F. Equal and opposite component vectors across mirrored regions eliminate shear stress concentration.

Module 4: Vector API & Interactive Dynamic Renderer

1. Rendered Dynamic Embroidery Card

2. Vector Parameters Table

• ViewBox: -10 -10 320 180
• Grid Resolution: Base unit 20 px × 20 px, structured across 6 spatial translation blocks.
• Color Schemes: Primary Red/Green (#ef4444), Secondary Blue/Yellow (#3b82f6).
• Animation Delay Matrix: Duration = 0.6s per stitch, step interval = 0.4s. Total sequence runtime = 19.4s (96 steps).

Module 5: Visual Gallery

Front View	Back View	Manuscript Grid
Fig 1. Front Embroidery Displaying emerald green & bright yellow mirror-symmetric tension matrix.	Fig 2. Back Structure Clean back-stitching routes and knot distribution logic.	Fig 3. Original Manuscript Precision coordinate mapping for Regions 1–3 (Stitches 1–48).

Module 6: Algorithm Extensions & Variant Syntax

1. Coverage Calculation

• Unit Grid Area: 20 px × 20 px = 400 px²
• Physical Line Width: 3.5 px (approx. 1.2 mm thread density)
• Surface Coverage Ratio: Achieves 87.5% surface fill rate within dual-color overlap zones due to dense cross-hatching.

2. Procedural Configuration

const Canvas018_Config = {
  unitSize: 20,
  stepSequence: [2, 3, 3, 2],
  colors: { primary: '#ef4444', secondary: '#3b82f6' },
  gridDimensions: { columns: 3, rows: 2 },
  translationVector: { dx: 80, dy: 60 }
};

3. Variant Matrix

• Transposed Mirroring: Inverting vector angles to (+45°, -135°) yields an inverted chevron pattern.
• Scale Invariance: Scaling sequence to [3, 4, 4, 3] preserves structural integrity across larger spatial canvas formats.