Case Study: Canvas-006

Embroidery Computational Syntax Card

Module 1: Metadata Table

Property / Item	Metadata & Specification Content
Archive ID	Canvas-006
Perceptual Impression	Stepped slant-slope extension, rhythmic alternating long-short lengths, featuring a strong 3D linear flow and dynamic sloped geometric texture
Basic Structure	Alternating 1-unit short diagonals and 2-unit long diagonals, arrayed and shifted towards the lower-right direction
Thread Specification	DMC / Size 25 Stranded Cotton, 4 strands folded
Color Palette	Alternating Olive Green and Dark Green (Dual-color toggle highlighting step-layering)
Composition Direction	Progressing from upper-left to lower-right; short and long stitches executed sequentially in arrayed extensions

Module 2: Starting & Vector Operations

• Starting Rules:
  • Base Group 1-2 (Short Stitch): Starts at lower-left $(30, 90)$, ends at upper-right $(50, 70)$, forming a 1-unit diagonal short stitch.
  • Base Group 3-4 (Long Stitch): Starts at lower-left $(30, 110)$, ends at upper-right $(70, 70)$, forming a 2-unit diagonal long stitch.
  • Lower-Right Array Step: After completing each set (short + long), the starting coordinates offset towards the lower-right by $(\Delta x = +20, \Delta y = +20)$.
• Polar Coordinate Vector & Angle Operations (Syntax Type: Stepped Slope Array):
  • Short Stitch Vector (1-2): Angle $45^\circ$, vector displacement $(\Delta x = 20, \Delta y = -20)$, spanning 1 grid unit.
  • Long Stitch Vector (3-4): Angle $45^\circ$, vector displacement $(\Delta x = 40, \Delta y = -40)$, spanning 2 grid units.
  • Gap Offset: Default $0.5$ unit (endpoints aligned precisely to grid intersection centers +0.5), ensuring high precision.

Module 3: Structural Mechanics & Topology

• Core Topological Node Network:
  • Composed of alternating short-long diagonal topology with endpoints snapped precisely to grid intersection centers $(+0.5)$.
  • Forms a stable diagonal tension network through progressive dual-layer stacking.
• Structural Mechanics Analysis:
  • Short/Long Stitch Stress Balance: Long stitches provide diagonal tension across longer spans, while short stitches lock local geometric nodes to prevent thread floating or loosening.
  • Stepped Progressive Tension: Equal-distance progression at a $45^\circ$ angle spreads tension evenly across the canvas, preventing fabric distortion caused by diagonal stitching.

Module 4: Vector API & Data

Canvas-006 Computational Embroidery: Alternating Long-Short Diagonal Slope Array

SVG Vector Geometric Parameters:

• ViewBox: 0 0 240 240
• Grid Cell Standard: Grid unit = 20px, endpoints aligned at grid center +0.5
• Stitch 1-2 (Short Diagonal): Start $(30, 90) \rightarrow$ End $(50, 70)$ | Length: 1 unit ($\sqrt{2}$)
• Stitch 3-4 (Long Diagonal): Start $(30, 110) \rightarrow$ End $(70, 70)$ | Length: 2 units ($2\sqrt{2}$)
• Array Offset Vector: Step $(\Delta x = +20, \Delta y = +20)$ | Repeated 4 times (Total 5 groups / 10 stitches / 20 points)

Module 5: Visual Gallery

Module 6: Algorithm Extensions & Variant Syntax

• Thread Physics & Coverage:
  • Mesh Size: 18-count Mono Canvas.
  • Coverage & Layering: Alternating dual colors (Dark Green and Light Green) create dynamic flow and pronounced 3D stepped texture.
• Stitch Variant Matrix:
  • Density Expansion Variant: Adjusting the short-to-long span ratio (e.g., 1 unit to 3 units) converts the pattern into a high-steepness slope variant.
• Procedural Parameters:
  • gapRatio: Default $0.0$, locking endpoints strictly to grid intersection centers +0.5 to exhibit procedural computational embroidery geometry.