Case Study: Canvas-013

Module 1: Metadata Table

Field Name	Technical Specifications & Value
Artwork ID	Canvas-013
Perceptual Impression	Uphill and Downhill Slopes
Basic Structure	Stepped Terraced Alignment
Syntax Classification	3D Relief Emphasized
Thread Specification	DMC Cotton Floss No.25 (4 strands folded, double-strand tension)
Color Scheme	Forest Green (#ef4444 marker), Off-White (#0284c7 marker)
Stitching Direction	Dual-track staggered layout, progressing diagonally from Top-Left to Bottom-Right

Module 2: Starting & Vector Operations

1. Array Layout & Starting Logic

The pattern employs a stepped, interlocking layout based on “3×3” and “2×2” grid units, organized into two intertwined geometric phases:

• Phase ① (Short Diagonal Stitches & Vertical Steps / Red Marker): Executes 1-unit diagonal stitches (135°) across a 3×3 grid zone (4 stitches horizontally), followed by vertical alignment (2 stitches) to establish the terraced border.
• Phase ② (Long Diagonal Stitches / Blue Marker): Executes 2-unit long diagonal stitches (135°) across the adjacent 2×2 grid zone, interlocking tightly into the steps established by Phase ①.

2. Precise Coordinates and Vector Operations

Defined on a standard 1-unit grid system (Unit = 40px):

• Phase ① (Stitches 1 – 12, Red Short Diagonals):
  • Horizontal Row (S1-S4):
    • S1: Start (180, 60) -> End (140, 100), Vector V = (-40, 40), Length L = 40 × √2 ≈ 56.57px, Angle θ = 135°
    • S2: Start (220, 60) -> End (180, 100), Vector V = (-40, 40)
    • S3: Start (260, 60) -> End (220, 100), Vector V = (-40, 40)
    • S4: Start (300, 60) -> End (260, 100), Vector V = (-40, 40)
  • Vertical Column (S5-S6):
    • S5: Start (300, 100) -> End (260, 140), Δx = -40, Δy = +40
    • S6: Start (300, 140) -> End (260, 180), Δx = -40, Δy = +40
• Phase ② (Stitches 13 – 24, Blue Long Diagonals):
  • Horizontal Row (S7-S10):
    • S7: Start (140, 100) -> End (60, 180), Vector V = (-80, 80), Length L = 80 × √2 ≈ 113.14px, Angle θ = 135°
    • S8: Start (180, 100) -> End (100, 180), Vector V = (-80, 80)
    • S9: Start (220, 100) -> End (140, 180), Vector V = (-80, 80)
    • S10: Start (260, 100) -> End (180, 180), Vector V = (-80, 80)
  • Vertical Column (S11-S12):
    • S11: Start (260, 140) -> End (180, 220), Vector V = (-80, 80)
    • S12: Start (260, 180) -> End (180, 260), Vector V = (-80, 80)

3. Group Translation Vector Matrix

The pattern propagates diagonally across the canvas by repeating the 24-stitch base unit:

• Offset Group 1 (Stitches 25 – 48): Translation Vector T1 = (+120, +120)
• Offset Group 2 (Stitches 49 – 72): Translation Vector T2 = (+240, +240)

Module 3: Structural Mechanics & Topology

1. Structural Backbone & Tensile Equilibrium

• Dual Shearing Tension Balance: Canvas-013 combines short-span (56.57px) and long-span (113.14px) diagonal threads aligned precisely at 135°. The uniform angle focuses fabric tension along the top-right to bottom-left axis.
• Stepped Stress Dispersion: The 90° directional shifts between horizontal and vertical stitch rows distribute surface tension across multiple grid points, preventing cloth puckering over extended stitched areas.

2. 3D Relief Mechanism & Tactile Depth

• Elevation Differential: Phase ② long stitches span twice the distance of Phase ① short stitches. The 4-strand folded thread creates physical volume as parallel lines bunch together, rising above the canvas surface.
• Shadow Terracing: The transition between 3×3 and 2×2 blocks produces a distinct stair-step relief. Light striking the angled threads highlights the terraced texture, conveying the perceptual impression of “uphill and downhill slopes.”

Module 4: Vector API & Interactive SVG Code

1. SVG Geometric Parameters and Rendering Specifications

• ViewBox specification：0 0 720 600
• Grid system: The base uses a 40px × 40px pattern grid with grid point radius r = 1.5px.
• Line specifications:
  • Red short slanted needle：stroke: #ef4444, stroke-width: 3.8, stroke-dasharray: 56.57
  • Blue long slanted needle：stroke: #0284c7, stroke-width: 3.8, stroke-dasharray: 113.14
• Animation control: Based on the Sequential Delay mechanism, the baseline interval for each step is 480ms, and the stroke-dashoffset is reduced to achieve a realistic embroidery line drawing effect.

2. HTML/SVG card code that can be directly rendered

Module 5: Visual Gallery

Front View (Physical)	Back View (Physical)	Design Diagram (Manuscript)
Figure 1: Front view showing the terraced 3D relief created by off-white and forest green threads.	Figure 2: Back view illustrating thread paths and tension nodes.	Figure 3: Original design manuscript detailing stitch sequences 1-72 and grid coordinates.

Module 6: Algorithm Extensions & Variant Syntax

1. Coverage Calculation

• Grid Cell Area: A_cell = 40px × 40px = 1600 px²
• Total Thread Length per Base Unit (24 Stitches):
  • Phase ① (6 stitches): 6 × 56.57px = 339.42px
  • Phase ② (6 stitches): 6 × 113.14px = 678.84px
  • Total Length L_total = 1018.26px
• Physical Coverage Ratio: With folded 4-strand DMC thread (effective width w ≈ 1.8px), the stitched coverage over a 6×6 grid unit (57,600 px²) yields a baseline coverage of ~31.8%, expanding to over 85% high-density coverage when fully layered.

2. Procedural Parameter Matrix

const Canvas013_Parameters = {
  unitSize: 40,               // Base grid size in pixels
  stepSequence: [3, 2],       // Stepped cycle: 3x3 block followed by 2x2 block
  phase1Length: 1.0,          // Phase 1 stitch length factor (sqrt(2)*40)
  phase2Length: 2.0,          // Phase 2 stitch length factor (2*sqrt(2)*40)
  strokeAngle: 135,           // Stitch direction angle in degrees
  repeatVector: { x: 3, y: 3 },// Diagonal offset vector for unit replication
  colors: {
    phase1: "#ef4444",        // Marker color for short diagonal stitches
    phase2: "#0284c7"         // Marker color for long diagonal stitches
  }
};