Case Study: Canvas-014

Yunbroidery Stitch Algorithm Syntax Card

Module 1: Archives Metadata Table

Property	Value Specification
ID	Canvas-014
Perception	Twisting / Fluid Motion
Structure	Underground Pipe Network
Syntax Type	Pipe Type
Thread Specs	DMC Floss / Size 25, 4 strands folded
Color Palette	Green (#22c55e), Light Yellow (#d97706), Silver/Blue (#0284c7), Red (#ef4444)
Stitch Direction	Divided into two main routes: ① Stepping from top-right center line to bottom-left; ② Auxiliary pipe layout.

Module 2: Starting & Vector Operations Algorithm

1. Starting Logic & Vector Angles

• Origin: Begins from the top-right diagonal line \ , following the strict grid-counting rule (in physical grid counting, the 3rd grid of the vertical line and the 3rd grid of the balance line share the exact same vertex node).
• Vector Angles:
  • Short Diagonal Stitches (Yellow/Red): θ = 135°, vector length L ≈ 5.1 mm (single grid diagonal).
  • Long Pipe Span Stitches (Blue/Green): θ = 45°, vector length L ≈ 15.1 mm (extended span).

2. Phase Sequence & Shift Operations

• Phase ①: Primary Unit 1 (Stitches 1–40)
  • Start Coordinate: (410, 10)
  • Yellow Segment (Stitches 1–10): Vertical downward 5 stitches along 135° (Δx = -40, Δy = +40), nodes 1 to 10.
  • Blue Segment (Stitches 11–20): Horizontal span 5 stitches along 45° (Δx = +120, Δy = +120), nodes 11 to 20.
  • Red Segment (Stitches 21–30): Turning horizontal 5 stitches along 135° (Δx = -40, Δy = +40), nodes 21 to 30.
  • Green Segment (Stitches 31–40): Vertical span 5 stitches along 45° (Δx = +120, Δy = +120), nodes 31 to 40.
• Phase ②: Spatial Shift Operations
  • Unit 2 (Stitches 41–80): Shifted from Unit 1 by vector v₁ = (-200, +200) (5 units left, 5 units down).
  • Unit 3 (Stitches 81–120): Shifted from Unit 2 by vector v₂ = (-200, +200) (5 units left, 5 units down).

Module 3: Structural Mechanics & Topology

1. Structural Spine & Elbow Nodes

• Zigzag Spine (Z-Spine): The short yellow and red stitches form rigid 90° corner boundaries, acting like elbow joints in a pipe system.
• Shared Grid Nodes: The shared grid points in count-stitching create localized high-density tension zones that lock the fabric’s warp and weft threads.

2. Tension Equilibrium & Stress Dispersion

• Orthogonal Tension Cancellation: The 135° short compression stitches (Yellow/Red) and 45° long tension stitches (Blue/Green) create orthogonal force vectors.
• Deformation Suppression: High tension from the long span stitches (15.1 mm) is anchored by the short end stitches (5.1 mm), preventing fabric twisting or warping while creating a dynamic 3D tubular effect.

Module 4: Vector API & Dynamic Display Data

1. SVG Geometric Parameters

• ViewBox: -200 0 760 800
• Grid System: 20 × 20 unit base grid.
• Animation Parameters:
  • Short Stitches (Yellow/Red): stroke-dasharray: 60, stroke-dashoffset: 60
  • Long Stitches (Blue/Green): stroke-dasharray: 180, stroke-dashoffset: 180
  • Sequential Delay: 0.06 s per stitch.

2. Renderable HTML/SVG Code Card

Module 5: Visual Gallery & Comparison

Front View	Back View	Design Manuscript
Image Code: CP_014_4.jpg	Image Code: CV_014B_4.jpg	Image Code: CV_014H_4.jpg

Module 6: Algorithm Extensions & Variant Syntax

1. Physical Coverage

• Equation: Coverage = (N × L × W) / A_total
• Evaluation: High-density parallel laying of long-span pipe threads combined with 4-strand folded thread expansion yields a physical thread coverage rate of 88%–92%, rendering a distinctive relief-like pipe structure.

2. Procedural Extension Parameters & Matrix Data