Case Study: Canvas-003

Computational Embroidery Syntax Card

Module 1: Metadata Table

Property	Specifications & Details
Archive ID	Canvas-003
Perceptual Image	Full surface coverage, strong vertical directionality, green base accented with flickering metallic gold thread
Basic Structure	$3 \times 2$ grid elongated diagonal stitch (Elongated Gobelin Stitch)
Thread Spec	DMC Stranded Cotton / No. 25, 4 strands folded; local metallic gold thread overlay/interweaving
Color Palette	Green series (Magic 3407/5, 8, 12, 17, 23 color blend), Metallic Gold Thread
Composition Vector	Progresses from top-left to top-right in vertical column fills; Row 1 completes top-left to top-right, followed by Row 2

Module 2: Starting Logic & Vector Operations

• Starting Rules:
  • Starting point is strictly set at the top-left corner of the canvas, executing $3\times 2$ diagonal stitches with green thread.
  • Front Side (Odd Paths 1, 3, 5, 7…): Exit: $(x, y+3)$ $\rightarrow$ Enter: $(x+2, y)$, forming a steep $3\times 2$ diagonal stitch $\slash$.
  • Back Side (Even Paths 2, 4, 6…): Enter: $(x+2, y)$ $\rightarrow$ Transit to the next exit point $(x, y+4)$ or adjacent grid on the back.
  • Gold Accents: Metallic gold thread is overlaid along the left margin and specific nodes during or after the green base stitching to add textural richness and luxury.
• Polar Coordinate Vectors & Angle Operations (Syntax Type: Line Organization / Steep Vertical Vector Array):
  • Front Diagonal Vector A: Angle $\approx 56.3^\circ \sim 63^\circ$, physical length $\approx 12.1\text{ mm}$ (Vertically stretched diagonal across a $3\text{ vertical} \times 2\text{ horizontal}$ grid).
  • Back Transition Vector B: Horizontal and slight diagonal shifts locking the vertical weave layout.
  • Terminal Gap Ratio Offset: Default $15\%$ end-point shrink to ensure long diagonal stitches stay parallel without overlapping or crowding.

Module 3: Structural Mechanics & Topology

• Core Topological Node Network:
  • Formed by a unidirectional parallel diagonal array over a $3 \times 2$ rectangular grid.
  • Metallic gold thread acts as a secondary topological overlayer, anchored at specific left-edge and internal nodes.
• Structural Mechanics Analysis:
  • Vertical Dominant Tension: The $3\text{-grid}$ vertical span provides strong vertical tension, making the canvas structural integrity extremely firm along the warp.
  • Gold Thread Rigidity: Metallic thread is stiffer than cotton; interweaving it with soft DMC cotton thread increases edge structural stability and light reflection.

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

Canvas-003 Computational Embroidery: Elongated Stitch & Gold Accent Animation

SVG Vector Geometry Parameters:

• ViewBox: 0 0 400 400
• Grid Cell Standard: $3\text{ vertical units} \times 2\text{ horizontal units} = 60 \times 40\text{ px}$
• Stitch Path (3×2 Elongated Diagonal): Start (40, 100) -> End (80, 40) | Angle: $\approx 56.3^\circ$ | Color: #5a8253
• Gold Accent Overlay: Start (40, 100) -> End (80, 40) | Color: #d4af37 | Weight: 2px

Module 5: Visual Gallery

• Front Physical Sample (CP_003.jpg): Dense green elongated diagonal stitches form an orderly vertical texture, with bright metallic gold accents along the left side and specific interior spots, creating a rich line organization.
• Back Physical Sample (CV_003B.jpg): Shows longer vertical and diagonal jumps on the back, with metallic gold threads weaving along the left margin, revealing continuous stitching paths.
• Hand-Drawn Draft Algorithm (CV_003H.jpg): Drafted on 2024/01/12, documenting the $63^\circ$ angle and $12.1\text{ mm}$ stitch length, using odd numbers 1, 3, 5, 7 (front-right) and even numbers 2, 4, 6 (front-left) to map path sequence and color distribution.

Module 6: Algorithm Extensions & Variant Syntax

• Thread Physics & Fabric Coverage:
  • Mesh Specification: 18-count Mono Canvas.
  • Coverage Optimization: The $3 \times 2$ elongated diagonal span is relatively long; DMC 4-strand folded thread provides dense coverage to prevent canvas exposure.
• Stitch Variant Matrix:
  • Gobelin Stitch Variants: Height-to-width ratios can be adjusted to $2\times 2$, $4\times 2$, or $5\times 2$ to vary the vertical elongation effect.
• Procedural Parameters:
  • gapRatio (Terminal Gap Offset): Default set to $0.15$. Keeps parallel elongated stitches tightly aligned while preserving a subtle hand-embroidered gap ratio.