Case Study: Canvas-016 Algorithmic Analysis of Multi-layered Diagonal Brick Stitch

Module 1: Metadata Table

Metadata Item	Archival Record Details
Work ID	Canvas-016
Visual Perception	Staggered multi-tone green geometric composition, delivering a tactile, layered brick-stacking effect with flowing visual rhythm.
Structural Mechanics	Multi-layered Diagonal Rectangle Fill Structure.
Pattern Syntax	Brick Pattern Syntax.
Thread Specification	DMC / Stranded Cotton No. 25, 4 strands folded.
Color Palette	Dark Green, Medium Green, Light Green (Mapped to Dark Blue, Sky Blue, Red, and Pink in SVG Animation).
Stitch Direction	Repeated 4 x 3 grid rectangular arrays with a vector inclination of -45° (equivalent to 135° pathing), advancing from lower-left to upper-right with multi-layer vertical translation.

Module 2: Starting & Vector Operations

1. Geometric Base & Coordinate System

The work utilizes a standard 20px grid system. The starting logic and operations are divided into Phase 1 (Stitches 1–40) and Phase 2 (Stitches 41–80).

• Vector Angle: θ = -45° (or 135° directional pathing), length L1 = 20 × √2 ≈ 28.28 px (single diagonal unit), L2 = 40 × √2 ≈ 56.57 px (double diagonal unit).
• Basic Unit: Formed by 4 primary diagonal stitches (Red/Dark Blue) and 1 short corner-filling stitch (Pink/Sky Blue), comprising a 3-column × 2-row rectangular block.

2. Phase 1: Upper Layer Base Unit & Horizontal Array Replication (Stitches 1–40)

• Stitches 1–8 (Base Unit 0):
  • Stitch 1 (Pts 1-2): P1(290, 30) → P2(310, 50), Δx = +20, Δy = +20
  • Stitch 2 (Pts 3-4): P3(270, 30) → P4(310, 70), Δx = +40, Δy = +40
  • Stitch 3 (Pts 5-6): P5(250, 30) → P6(290, 70), Δx = +40, Δy = +40
  • Stitch 4 (Pts 8-7): P8(250, 50) → P7(270, 70), Δx = +20, Δy = +20 (Reverse corner entry)
• Replication Offset Vector: Δx_step = -40 px (Shift left by 2 grid units).
  • Repeated across 4 iterations (Replication 1 to 4), generating stitches 9–16, 17–24, 25–32, and 33–40.

3. Phase 2: Lower Layer Vertical Translation & Color Switching (Stitches 41–80)

• Vertical Translation Offset Vector: Δx = 0 px, Δy = +40 px (Shift down by 2 grid units).
• Coordinate Algorithm: For any stitch i ∈ [41, 80], its geometric coordinates mirror stitch j = i – 40 from Phase 1 according to:P_i = P_(i-40) + (0, 40)
• Color Switching Matrix:
  • Primary Stitches: Red is substituted with Dark Blue / Dark Green.
  • Specified Corner/Edge Stitches (47-48, 55-56, 63-64, 71-72, 79-80): Pink is substituted with Sky Blue / Light Green, creating high visual contrast and interlocking brick texture.

Module 3: Structural Mechanics & Topology

1. Structural Backbone & Topology

Canvas-016 relies on a “Double-layered Interlocking Sawtooth Topology”.

• Node Density: Each rectangular module contains 5 principal diagonal axes with a node overlap rate of 66.7%, locking tension firmly into the grid intersections.
• Path Topology: The front surface forms continuous -45° diagonal gliding lines, while the back displays neat vertical short spans (span ≤ 20px), maximizing thread efficiency and keeping fabric smooth.

2. Tension Equilibrium & Stress Distribution

• Vector Pull Balance:
  • Diagonal Tension Vector: F_long = T × (cos(-45°), sin(-45°)) = T × (√2/2, -√2/2)
  • Uniform -45° stitching can induce diagonal shearing on woven fabric. Canvas-016 neutralizes this by alternating long/short stitches (2-unit and 1-unit spans) and shifting Phase 2 vertically by 2 units, creating a stepped stress-buffering zone.
• Surface Coverage & Distortion Suppression:
  • The 4-strand folded DMC cotton thread provides significant physical bulk (damping effect). Lateral contact pressure between adjacent threads offsets diagonal fabric pulling, ensuring a flat, distortion-free outcome.

Module 4: SVG Vector Syntax & Visual Data (Vector API)

SVG Parameter Breakdown:

• ViewBox: 0 0 340 160 (Wide-aspect dual-region display canvas).
• Grid System: 20px square grid; Y-axis spans 20px to 140px, X-axis spans 0px to 340px.
• Animation Controls: Pure CSS stroke-dasharray: 80 & stroke-dashoffset: 80. Single stitch duration = 0.36s, with sequential step delays of +0.24s.
• Key Coordinates & Colors:
  • Region 1 (Stitches 1–40): Starts at P1(290, 30), ends at P40(30, 70). Colors: #e11d48 (Red) & #ec4899 (Pink).
  • Region 2 (Stitches 41–80): Starts at P41(290, 70), ends at P80(30, 110). Colors: #1e3a8a (Dark Blue) & #38bdf8 (Sky Blue).

Module 5: Visual Gallery

Category	File Tag	Description
Front View	CP_016_4.jpg	Demonstrates 4-strand DMC thread filling the fabric with rich diagonal brick layering in dark, medium, and light green tones.
Back View	CV_016B_4.jpg	Highlights highly disciplined vertical and short diagonal back-stitches (span ≤ 20px), exhibiting clean execution and low material waste.
Design Draft	CV_016H_4.jpg	Documents exact grid alignment, -45° (135°) vector angles, stitch lengths (5.1mm and 10.1mm), and structural coordinate assignments.
Step Breakdown	CV_016Hab_4.jpg	Details Phase 1 (1–40) to Phase 2 (41–80) array replication and color matrix transformation rules.

Module 6: Algorithm Extensions & Variant Syntax

1. Physical Coverage Density

• Physical Dimensions: Base grid unit = 2 mm × 2 mm. Rectangular module (4 × 3 grid) area = 8 mm × 6 mm = 48 mm².
• Coverage Calculation:
  • Each 4×3 module contains 4 full diagonals (~10.1 mm) and 1 short diagonal (~5.1 mm).
  • Total thread length L_total = 4 × 10.1 + 5.1 = 45.5 mm.
  • 4-strand thread diameter d ≈ 0.6 mm, yielding an effective area A_thread = 45.5 × 0.6 = 27.3 mm².
  • Single-layer physical coverage C_density ≈ (27.3 / 48) × 100% ≈ 56.88%. With Phase 2 vertical overlap, local fabric coverage reaches 100% complete density.

2. Variant Matrix & Procedural Parameters

• Step Sequence (stepSequence): [1, 2, 3, 4, 5, 6, 7, 8] core subset repeated via translation matrix T_x = -40px.
• Unit Spacing (unitSpacing): ΔX = 40 px (Horizontal step), ΔY = 40 px (Vertical offset).
• Gap Ratio (gapRatio): 0.0 (Seamless brick topology).
• Transformation Matrix:M_brick = [ cos(-45°) -sin(-45°) Δx ][ sin(-45°) cos(-45°) Δy ][ 0 0 1 ]”””