Case Study: Canvas-004

Computational Embroidery Syntax Card

Module 1: Metadata Table

Property	Specifications & Details
Archive ID	Canvas-004
Perceptual Image	Embedded/intertwined accents, extreme padded 3D relief texture, dense green vertical weave with metallic gold thread vertical bands
Basic Structure	$4 \times 2$ grid steep diagonal stitch (Vertical half-span interleaved grid fill)
Thread Spec	DMC Stranded Cotton / No. 25, 4 strands folded; local metallic gold thread intertwining
Color Palette	Green series (Magic 3407/12, 18, 21 color blend), Metallic Gold Thread
Composition Vector	Progresses from top-left to top-right; after completing Row 1, Row 2 starts at Grid 3 and enters at Grid 4, vertically interlocking across parallel columns

Module 2: Starting Logic & Vector Operations

• Starting Rules:
  • Starting point is strictly set at the top-left corner of the canvas, executing $4\times 2$ diagonal stitches $\slash$ with green thread.
  • Row 1 Execution: Exit: $(x, y+4)$ $\rightarrow$ Enter: $(x+2, y)$, forming a steep $72^\circ$ diagonal stitch.
  • Row 2 Interlocking Execution: Starts at the 3rd vertical grid position $(x, y+2)$ of the previous row and enters at the 4th grid position, creating a $50\%$ vertical overlap for a dual-layer interlocked texture.
  • Metallic Gold Intertwining: Embedded along specific vertical axes within the thick green base layer, forming vertical chain-like golden accents.
• Polar Coordinate Vectors & Angle Operations (Syntax Type: Padded Thick Structure / Ultra-Steep Interleaved Vector Array):
  • Front Diagonal Vector A: Angle $72^\circ$ (annotated as $63^\circ \sim 72^\circ$ in hand-drawn drafts), physical length $\approx 12.1\text{ mm}$.
  • Vertical Interlocking Vector B: $\Delta y = 2\text{ grid units}$ (half-span vertical shift), achieving thread overlap for maximum structural thickness.
  • Terminal Gap Ratio Offset: Default $12\%$ end-point shrink to maintain stitch flow under high-density filling.

Module 3: Structural Mechanics & Topology

• Core Topological Node Network:
  • Formed by a vertically interleaved network across a $4 \times 2$ grid matrix.
  • Metallic gold thread forms an intertwined sandwich topology (Intertwined Vertical Bands) embedded within the dual-layer green thread matrix.
• Structural Mechanics Analysis:
  • Padded Thickness Enhancement: Because Row 2 inserts into the midpoint (Grid 3) of Row 1, the frontal thread density per unit area doubles, resulting in significant 3D relief, cushion, and tactile volume.
  • Vertical Dominant Tension: The $72^\circ$ steep vector exerts strong warp-wise tension, keeping the dense structure firm and preventing loose threads.

Module 4: Vector API & P5.js Dynamic Animation Data

Canvas-004 Computational Embroidery: Ultra-Steep Stitch & Padded Intertwining

SVG Vector Geometry Parameters:

• ViewBox: 0 0 400 400
• Grid Cell Standard: $4\text{ vertical units} \times 2\text{ horizontal units} = 80 \times 40\text{ px}$
• Stitch Path (4×2 Steep Diagonal): Start (40, 120) -> End (80, 40) | Angle: $72^\circ$ | Color: #4a7243
• Interleaved Offset Path: Start (40, 160) -> End (80, 80) | Shift: $\Delta y = 40\text{ px}$
• Gold Intertwined Overlay: Start (120, 120) -> End (160, 40) | Color: #d4af37 | Weight: 3px

Module 5: Visual Gallery

• Front Physical Sample (CP_004.jpg): Exhibits a dense green diagonal relief base with two vertical metallic gold chain lines embedded directly into the fabric surface, creating a plush, padded tactile quality.
• Back Physical Sample (CV_004B.jpg): Due to the heavy frontal overlaps, the back features a dense and substantial mesh of thread crossings, confirming high volumetric thread packing.
• Hand-Drawn Draft Algorithm (CV_004H.jpg): Completed on 2024/01/12, using three oval diagrams to detail diagonal stitch angles ($63^\circ \sim 72^\circ$), $12.1\text{ mm}$ length, and multi-color (Magic 3407/12, 18, 21) interlocked paths.

Module 6: Algorithm Extensions & Variant Syntax

• Thread Physics & Fabric Coverage:
  • Mesh Specification: 18-count Mono Canvas.
  • Stacking Density: The $4 \times 2$ half-span interleaving achieves $120\% – 150\%$ fabric coverage (dual-layer overlap), giving the surface a distinct padded feel.
• Stitch Variant Matrix:
  • Padded Gobelin Variant: Further reducing vertical shift increments (e.g., shifting by $1\text{ grid unit}$) creates an ultra-raised, leather-like padded texture.
• Procedural Parameters:
  • gapRatio (Terminal Gap Offset): Default set to $0.12$. Low gap ratios deliver a plush, carpet-like padded appearance.