Case Study: Canvas-005

Computational Embroidery Grammar Card

Module 1: Metadata Table

Property Item	Metadata & Specifications
Collection ID	Canvas-005
Perceptual Imagery	Rhythmic, stepped progressive structure, crisp interlacing green diagonal geometry with gold thread accents
Basic Structure	2-3-2 Axisymmetric Module (span 2 – span 3 – span 2), filling via dual-axis diagonal translation
Thread Specification	DMC / No. 25 strand, 4-ply folded, accented with parallel gold metallic thread
Color Palette	Green (Magic 3407 series), Accent Gold Thread
Composition Direction	Top-left to bottom-right diagonal progression; each unit translates 2 grid units (Δx = +40px, Δy = +40px)

Module 2: Starting & Vector Operations

• Starting Rule: Initial needle position is anchored at the top-left corner, executing the 2-3-2 green diagonal symmetrical group.
• Unit 1 Stitching Sequence (Stitches 1–6):
  • Stitches 1–2 (Span 2): Exit (70, 50) → Enter (50, 70), vector (-20, +20).
  • Stitches 3–4 (Span 3): Exit (90, 50) → Enter (50, 90), vector (-40, +40), serving as the central long axis.
  • Stitches 5–6 (Span 2): Exit (90, 70) → Enter (70, 90), vector (-20, +20).
• Multi-Unit Translation Pattern: Each subsequent unit translates along the diagonal vector (Δx = +40, Δy = +40).
  • Unit 2 (Stitches 7–12): Exit/enter coordinates shift upward by 2 grid units to seamlessly connect directly below Unit 1.
  • Unit 3 (Stitches 13–18): Exit (150, 130) → Enter (130, 150), extending the diagonal array.
• Vector & Angle Operations (Grammar Type: Axisymmetric / Stepped Array Translation):
  • Front Diagonal Vector: Maintains a -45° inclination angle, with endpoints precisely aligned to grid centroids (Centroid Align).
  • Unit Spacing Vector: (Δx, Δy) = (+40px, +40px) for gapless tiling.

Module 3: Structural Mechanics & Topology

• Core Topological Node Network:
  • Uses the span-3 long stitch (3-4) as the central geometric spine, flanked symmetrically by two span-2 short stitches (1-2 and 5-6) to form a triadic module.
  • The gold thread module runs parallel to the right side of the green unit, establishing a dual-track topology.
• Structural Tension Analysis:
  • Symmetrical Tension Balance: The structure distributes fabric tension evenly across diagonal axes, minimizing single-direction warping.
  • Stepped Interlocking Mechanics: Subsequent unit entry points hook into the lower grid of preceding units, achieving high geometric stability.

Module 4: Vector API (SVG & P5.js Dynamic Display)

SVG Vector Geometry Parameters:

• ViewBox: 0 0 280 280
• Grid Cell Standard: 20 × 20 px Grid System (Centroid Grid Offset)
• Unit 1 Path (1–6):
  • Stitch 1–2: Start (70, 50) -> End (50, 70) | Color: #5a8253
  • Stitch 3–4: Start (90, 50) -> End (50, 90) | Color: #5a8253
  • Stitch 5–6: Start (90, 70) -> End (70, 90) | Color: #5a8253
• Unit 2 Shifted Path (7–12):
  • Stitch 7–8: Start (110, 90) -> End (90, 110) | Color: #5a8253
• Gold Accent Path Overlay:
  • Gold 1: Start (110, 50) -> End (90, 70) | Color: #d4af37

Module 5: Visual Gallery

Module 6: Algorithm Extensions & Variant Syntax

• Thread Physics & Coverage:
  • Mesh Size: Optimized for 18-count Mono Canvas (20px grid spacing).
  • Geometric Density: Stepped stacking of the 2-3-2 module retains fabric breathability while producing crisp geometric lines.
• Stitch Variant Matrix:
  • Gold Accent Variant: Toggling the optional gold thread module transforms minimal green textures into luxurious dual-color metallic patterns.
• Procedural Parameters:
  • unitShift: Default set to 40px (2 grid units). Adjusting shift distance alters module overlap and tiling cadence.