Case Study: Canvas-002

Computational Embroidery Syntax Card

Module 1: Metadata Table

Property	Specifications & Details
Archive ID	Canvas-002
Perceptual Image	Deformation-free tension control, smooth alternating dark/light green diagonal stripes, satin flat sheen
Basic Structure	2 grid units × 2 grid units grid diagonal stitch (Diagonal stepped stripe fill)
Thread Spec	DMC Stranded Cotton / No. 25, 4 strands folded
Color Palette	Dark Green (Magic 3407/8), Light Green (Magic 3407/13)
Composition Vector	Starts from the bottom-left corner, progressing diagonally; alternating rows of dark and light green

Module 2: Starting Logic & Vector Operations

• Starting Rules:
  • Embroiderers must strictly follow grid coordinates for stitching.
  • Front: 2 grid units × 2 grid units diagonal half-cross stitch (stitch out at (x, y+2) → stitch in at (x+2, y)).
  • Back: 180° horizontal line (stitch in at (x+2, y) → stitch out at (x, y) or jump across grid units).
  • Sequence: Front 2 grid units × 2 grid units diagonal stitch → back horizontal lock → repeat continuous diagonal weaving.
• Key Point: Single 2 grid units × 2 grid units diagonal half-cross stitch; hand-drawn draft feel comes from unjoined line ends, preserving approx. 18% gap space between endpoints.
• Polar Vectors & Angular Calculation (Syntax Type: Smooth Luster Line / Horizontal Tension Anchor Matrix):
  • Standard Diagonal Half-Stitch Vector A: Angle 45°, physical length 6.1 mm (Square 2 grid units × 2 grid units diagonal, √(2² + 2²) × 2.15 mm ≈ 6.08 mm).
  • Back Horizontal Anchor Vector B: Angle 180° (horizontally left/right), physical length 4.3 mm (2 grid units span).
  • Endpoint Gap Offset: Both vector ends shrink by 18% to maintain the visual gap between independent stitches seen in hand-drawn drafts.

Module 3: Structural Mechanics & Topology

• Core Topological Network:
  • Formed by square array nodes P_(i,j) = (2i, 2j) and Q_(i,j) = (2i+2, 2j+2), constructing an N × M parallel diagonal tension topology mesh.
  • Front diagonal stitches / (45°) and back horizontal stitches — (180°) alternate to form a closed, horizontally tightened structural grid with elastic support.
• Structural Analysis:
  • Front 45° Diagonal Shear Tension: Unidirectional shear stress is evenly distributed across the surface, creating an extremely smooth coverage and lustrous sheen.
  • Back 180° Horizontal Tensile Support: Unlike Canvas-001’s vertical lines on the back, Canvas-002 features 180° horizontal line segments on the back, effectively locking the transverse warp and weft grid to prevent diagonal warping when the fabric is pulled vertically.

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

Canvas-002 Computational Embroidery: Stitch-by-Stitch Animation

SVG Vector Geometry Parameters:

• ViewBox: 0 0 400 400
• Grid Cell Standard: 2 × 2 grid units = 40 × 40 px (with 18% Gap Ratio Offset)
• Stitch Path 1 (Row 1, Unit 1): Start (37.2, 62.8) -> End (62.8, 37.2) | Angle: 45° | Color: #3c6e47
• Stitch Path 2 (Row 1, Unit 2): Start (77.2, 62.8) -> End (102.8, 37.2) | Angle: 45° | Color: #3c6e47
• Stitch Path 3 (Row 1, Unit 3): Start (117.2, 62.8) -> End (142.8, 37.2) | Angle: 45° | Color: #3c6e47
• Stitch Path 4 (Row 2, Unit 1 [Reverse Direction]): Start (117.2, 102.8) -> End (142.8, 77.2) | Angle: 45° | Color: #2e5b37

Module 5: Visual Gallery

Module 6: Algorithm Extensions & Variant Syntax

• Thread Physics & Coverage:
  • Mesh Size: 18-count Mono Canvas (grid spacing ≈ 1.41 mm).
  • Thread Tension & Coverage Rate: DMC Size 25, 4 strands folded (actual 8 strands width), achieving a coverage rate of 95% – 98% under a 2 × 2 grid, presenting high density and a flat surface.
• Stitch Variant Matrix:
  • Full Cross Stitch Transition:
    • Layer 1 (Base Layer): Execute primary 2 × 2 diagonal half-cross stitch (45°, vector (2, -2)).
    • Layer 2 (Top Layer): Overlay 2 × 2 reverse diagonal stitch (135°, vector (-2, -2)).
  • Gobelin Stitch Extension:
    • Vertical Extension: Modify the 2 × 2 grid matrix to a 2 × 3 or 2 × 4 matrix, shifting vector angles from 45° to 56.3° or 63.4°, suitable for quick filling across different aspect ratios.
• Procedural Parameters:
  • gapRatio: Default set to 0.18 (adjustable range 0.10 – 0.25). Higher values emphasize the independent stitch appearance of hand-drawn drafts; set to 0 to return to industrial print connectivity.