Case Study: Canvas-019

Yunbroidery Stitch Algorithm Syntax Card

Canvas-019 Research Case: Grid Climbing Pattern Embroidery Algorithm

Module 1. Metadata Table

Property	Content
Artwork ID	Canvas-019
Perceptual Image	Grid Climbing / Ladders (爬格子)
Basic Structure	Stepped structure composed of 4 diagonal lines horizontally and vertically
Syntax Type	Structural Support Stitch
Thread Specification	DMC No. 25, 3 strands folded (6 strands total)
Color Scheme	Dark Green (Tertiary/Base), Medium Green (Secondary/Mid), Light Green (Primary/Top)
Stitching Direction	Top-left diagonally towards bottom-center
Starting Logic	3 x 3 grid, 45-degree diagonal lines arranged in alternating horizontal and vertical steps

Module 2. Starting & Vector Operations

The embroidery algorithm for Canvas-019 employs a Stepped Staircase arrangement, alternating between horizontal and vertical diagonal lines to achieve a 3D “grid climbing” visual effect.

Phase 1: Base 3×3 Stepped Module Sequence

1. Grid Placement: Utilizes a 20x20px grid system. The base module consists of 6 parallel line segments of equal length (L = 40 × √2 ≈ 56.57 px) angled at -45°.
2. Polar Vector: Each stitch vector is defined as Vector V = (Δx, Δy) = (-40, +40), vector magnitude |V| = 56.57 px, inclination angle θ = 135° (or -45° to horizontal axis).
3. Intra-module Shift:
   • Horizontal Extension (Stitches 1-4): Vector shift ΔS_h = (+20, 0).
   • Vertical Extension Downwards (Stitches 5-6): Vector shift ΔS_v = (0, +20).

Phase 2: Group Transformations & Offset Matrix

The full pattern consists of 3 distinct color groups (Blue Group/Dark Green, Yellow Group/Medium Green, Red Group/Light Green), totaling 54 stitches (108 geometry nodes):

1. Primary Group (Group 1 – Blue/Dark Green):
   • Contains 3 base modules (Stitches 1-6, 7-12, 13-18).
   • Module displacement within the group ΔG1 = (+60, +60).
2. Secondary Group (Group 2 – Yellow/Medium Green):
   • Parallel shift from Group 1 (Stitches 19-36).
   • Offset vector ΔG2 = Group 1 + (-40, +40).
3. Tertiary Group (Group 3 – Red/Light Green):
   • Shifted further from Group 1 (Stitches 37-54).
   • Offset vector ΔG3 = Group 1 + (-80, +80).

Module 3. Structural Mechanics & Topology

1.Structural Spine

Canvas-019 constructs a continuous diagonal structural spine across the fabric surface through fixed-angle (-45°) tension lines. Arranged in a stepped 3×3 grid sequence, the intersection points form interlocking nodes that lock the fabric structure in place.

2.Tension Balance

1. Unidirectional Force Vector: All stitches follow a -45° vector direction, concentrating tension along the (x – y) axis.
2. Stepped Force Dissipation: By alternating shifts via ΔS_h (+20, 0) and ΔS_v (0, +20), the pull force is distributed across warp and weft threads evenly, preventing single-direction fabric puckering along diagonal axes.

3.Stress Dissipation Mechanism

1. Thread Volume Cushioning: Using 6 strands of embroidery thread (3 strands folded), the physical volume fills grid cavities and absorbs tension shocks during stitching.
2. Multi-layer Support Network: Three color groups overlap along the vertical axis, creating a three-layer mechanical support net that enhances structural stability.

Module 4. Vector API & Animated Showcase Data

1.Vector Geometry Parameters

• ViewBox: 0 0 310 330
• Grid System: 20px × 20px main grid with centroid node markers
• Dasharray Unit: Fixed at 56.57
• Animation Mechanism: CSS-only stroke-dashoffset and animation-delay orchestration rendering 54 sequential stitches.

2.Interactive SVG Animation Card (Pure HTML/CSS)

Module 5. Visual Gallery

Front View	Back View	Draft / Path Diagram
Front Pattern: 3D interlocking ladder grid texture	Back Pattern: Neat parallel horizontal and diagonal cross-lines	Draft Diagram: Precise grid coordinates and sequence markers

Module 6. Algorithm Extensions & Variant Syntax

Physical Coverage Rate

This pattern uses diagonal lines of length L = 56.57 px on a 20px grid.

• Unit Density: D = (Stitch count × Thread width) / Total Area = (54 × 1.2mm) / Area
• Coverage Estimation: With 6-strand thread (~1.2mm width), the overlapping color blocks produce a 30%-40% open mesh coverage, allowing the underlying fabric texture to remain visible.

Transformation Matrix

The embroidery pattern can be transformed via a 2D matrix: [ x' ] = [ cos(θ) -sin(θ) ] [ x ] + [ dx ] [ y' ] [ sin(θ) cos(θ) ] [ y ] [ dy ]

• 45° Tilt Variant: Setting θ = 45° transforms the stepped matrix into orthogonal alignments.
• Mirror Variant: Applying x-axis reflection matrix [ -1, 0; 0, 1 ] generates inverted ladder structures.

Procedural Expansion Parameter Table

const Canvas019_Parameters_EN = {
  unitSize: { x: 3, y: 3 },      // Base unit grid size (3x3)
  gridSpacing: 20,                // Grid spacing (px)
  stitchLength: 56.57,            // Individual stitch length (px)
  stepSequence: ["H", "H", "H", "H", "V", "V"], // 4 Horizontal, 2 Vertical step sequence
  colorGroupShift: {
    group1: { x: 0, y: 0 },
    group2: { x: -40, y: 40 },
    group3: { x: -80, y: 80 }
  },
  threadGauge: "DMC 25 # 6-strands"
};