Case Study: Canvas-010

Computational Embroidery Grammar Card

Module 1: Metadata Table

Attribute / Parameter	Specification Details
Catalog Number	Canvas-010
Perceptual Image	Interlocking Color Blocks & Technique Perception (Utilizing dual colors of light green and light yellow to distinguish techniques of different directions and structures, showcasing the rhythmic elegance of interwoven diagonal slashes)
Basic Structure	Rhythmic Array of Diagonal Slashes (A diagonal slash unit with a 1-2-3-2-1 progressive sequence)
Grammar Type	Diagonal Slash Type
Thread Specification	DMC / No. 25 thread, 4 strands folded
Color	Light Green (#529471), Light Yellow (#D4C475)
Direction & Entry	Central Green Slash: Stitched in staggered diagonal directions (top-right to bottom-left, and bottom-left to top-right)
Sequence Path	Needle Nos. 1–10 form a progressive diagonal slash length array → Needle Nos. 11–22 progress with staggered 1-unit diagonal slashes
Unit Connection	Seamless tight sequence (unitSpacing = 0)

Module 2: Starting & Vector Operations

• Geometric Deduction & Coordinate Verification (20px Grid, endpoints locked to grid intersections): Grid Reference Points: x, y ∈ {30, 50, 70, 90, 110, 130, 150…}

Phase 1 (Progressive Long Diagonal Slash Block, Needle Nos. 1 to 10, Vector Angle = -135°):

1. Needle 1 (1-unit diagonal slash): Top-Right (70, 30) → Bottom-Left (50, 50)
2. Needle 2 (2-unit diagonal slash): Top-Right (90, 30) → Bottom-Left (50, 70)
3. Needle 3 (3-unit diagonal slash): Top-Right (110, 30) → Bottom-Left (50, 90)
4. Needle 4 (2-unit diagonal slash): Top-Right (110, 50) → Bottom-Left (70, 90)
5. Needle 5 (1-unit diagonal slash): Top-Right (110, 70) → Bottom-Left (90, 90)

Phase 2 (1-Unit Diagonal Slash Block, Needle Nos. 11 to 22, Staggered Vector Angles -135° & +45°):

1. Needle 11 (-135°): Top-Right (130, 30) → Bottom-Left (110, 50)
2. Needle 12 (-135°): Top-Right (150, 30) → Bottom-Left (130, 50)
3. Needle 13 (+45°): Bottom-Left (110, 70) → Top-Right (130, 50)
4. Needle 14 (+45°): Bottom-Left (150, 50) → Top-Right (130, 70)
5. Needle 15 (-135°, geometric correction point): Top-Right (150, 70) → Bottom-Left (130, 90)
6. Needle 16 (-135°): Top-Right (130, 70) → Bottom-Left (110, 90)

Polar Coordinates Vector & Angle Operations:

• Direction Vector:
  • -135° Vector (Top-Right to Bottom-Left): Δx : Δy = -1 : +1 (Y-axis increases downwards in screen coordinate system).
  • +45° Vector (Bottom-Left to Top-Right): Δx : Δy = +1 : -1.
• Vector Polar Length (Calculated on 20px grid):
  • 1-unit diagonal slash: √(20² + 20²) × 1 = √800 px ≈ 28.28 px (Approx. 3.0 mm physical length)
  • 2-unit diagonal slash: √(20² + 20²) × 2 = √3200 px ≈ 56.57 px (Approx. 6.1 mm physical length)
  • 3-unit diagonal slash: √(20² + 20²) × 3 = √7200 px ≈ 84.85 px (Approx. 12.1 mm physical length)

Module 3: Structural Mechanics & Topology

Core Topological Node Network:

• Continuous Diagonal Grid Structure: Phase 1 follows a 1-2-3-2-1 stepped progressive diagonal movement, combined with Phase 2’s staggered 1-unit diagonal slashes, creating high-density block and mesh patterns.
• Zero-Gap Interweaving: Endpoints of adjacent needles (such as the intersection of 11→12 and 13→14 at coordinate (130, 50)) coincide on the same grid node, forming a seamless, tight-knit texture.

Structural Mechanics Analysis:

• Diagonal Tension Balance: Unidirectional diagonal stitches tend to warp the canvas; counter-directional tension (+45° vs. -135°) in Phase 2 effectively cancels out deformation stresses across the fabric.
• Tension Distribution: Longer stitches bear the primary structural tension, while shorter stitches evenly distribute pull forces to surrounding mesh grid holes.

Module 4: Vector API & P5.js Dynamic Data

Complete data specifications can be directly integrated into Vector SVG API and P5.js canvas environments, providing structured parameter arrays for real-time vector rendering and mechanical simulations.

Module 5: Visual Gallery

Module 6: Algorithm Extensions & Variant Syntax

• Procedural Parameters:
  • unitSpacing: 0.0 (Seamless connection between consecutive units).
  • gapRatio: 0.0 (Zero endpoint offset).
  • meshSize: 20px grid size.
• Variant Syntax Matrix:
  • Checkerboard Alternation: Alternating yellow/green blocks with orthogonal directionality.