Case Study: Canvas-007

Embroidery Computational Syntax Card

Module 1: Metadata Table

Property / Item	Metadata & Specification Content
Archive ID	Canvas-007
Perceptual Impression	Rhythmic 3-5-7-5-3 progressive long-short diagonal array with overlapping tracks, exhibiting repetitive flow and 3D stepped cadence
Basic Structure	Alternating $45^\circ$ diagonal stitches spanning 2-3-4-3-2 grid units, arrayed towards the lower-right while sharing a 3-unit diagonal track
Thread Specification	DMC / Size 5 Pearl Cotton (2 strands folded), Size 25 Stranded Cotton
Color Palette	Yellow and Green (Dual-color toggle creating flowing stepped layers)
Composition Direction	Progressing from upper-left to lower-right; starting at upper-right and ending at lower-left ($45^\circ$ diagonal stitches)

Module 2: Starting & Vector Operations

• Starting Rules:
  • Base Unit (Stitches 1-8):
    • Stitch 1-2 (Spans 2 units): Upper-Right $(70, 30) \rightarrow$ Lower-Left $(30, 70)$
    • Stitch 3-4 (Spans 3 units): Upper-Right $(90, 30) \rightarrow$ Lower-Left $(30, 90)$
    • Stitch 5-6 (Spans 4 units, peak stitch): Upper-Right $(110, 30) \rightarrow$ Lower-Left $(30, 110)$
    • Stitch 7-8 (Spans 3 units): Upper-Right $(110, 50) \rightarrow$ Lower-Left $(50, 110)$
  • Lower-Right Array Step (Stitches 9-18, sharing 3-unit track):
    • Stitch 9-10 (Spans 2 units, identical to 1-2 structure): Upper-Right $(110, 70) \rightarrow$ Lower-Left $(70, 110)$ [Shares diagonal track with preceding unit]
    • Each completed unit offsets towards the lower-right by $(\Delta x = +40, \Delta y = +40)$ for repetitive progression.
• Polar Coordinate Vector & Angle Operations (Syntax Type: Rhythmic Repetition Array):
  • Diagonal Vector: Angle $225^\circ$ (Upper-Right to Lower-Left), unit vector displacement $(\Delta x = -20, \Delta y = +20)$.
  • Stitch Span Lengths: 2 units ($\sqrt{800}$ px), 3 units ($\sqrt{1800}$ px), 4 units ($\sqrt{3200}$ px).
  • Gap Offset: Default $0.0$ (Endpoints aligned precisely to grid intersection centers +0.5).

Module 3: Structural Mechanics & Topology

• Core Topological Node Network:
  • Forms a central diamond tension core through interlaced 2-3-4-3-2 long and short diagonal stitches.
  • Interlocking adjacent units by overlapping across 3 shared diagonal grid units builds a seamless and durable topological network.
• Structural Mechanics Analysis:
  • Interlaced Stress Release: Peak long stitches (4 units) define the main visual diagonal, while flanking short stitches (2 and 3 units) anchor local nodes to prevent thread slackness.
  • Diagonal Overlap Stability: Dual-layer thread stacking on shared tracks enhances canvas solidity and wear resistance, preventing diagonal fabric distortion.

Module 4: Vector API & Data

Canvas-007 Computational Embroidery: 3-5-7-5-3 Rhythmic Diagonal Array

SVG Vector Geometric Parameters:

• ViewBox: 0 0 300 300
• Grid Cell Standard: Grid unit = 20px, endpoints aligned at grid center +0.5
• Base Pattern Span: 2-3-4-3-2 Units
• Vector Path Sequential:
  • Stitch 1-2: $(70,30) \rightarrow (30,70)$ | Length: 2 units
  • Stitch 3-4: $(90,30) \rightarrow (30,90)$ | Length: 3 units
  • Stitch 5-6: $(110,30) \rightarrow (30,110)$ | Length: 4 units
  • Stitch 7-8: $(110,50) \rightarrow (50,110)$ | Length: 3 units
  • Stitch 9-10: $(110,70) \rightarrow (70,110)$ | Length: 2 units (Overlapping track)

Module 5: Visual Gallery

Module 6: Algorithm Extensions & Variant Syntax

• Thread Physics & Coverage:
  • Mesh Size: 18-count Mono Canvas.
  • Coverage & Layering: Alternating yellow and green colors provide high coverage with a strong dynamic rhythm.
• Stitch Variant Matrix:
  • Rhythm Expansion Variant: Expanding the peak stitch to 5 units (forming a 2-3-4-5-4-3-2 array) increases the relief height and slope variance.
• Procedural Parameters:
  • gapRatio: Default $0.0$, locking endpoints strictly to grid intersection centers +0.5 to exhibit procedural computational embroidery geometry.