Case Study: Canvas-002

Computational Embroidery Syntax Card

Property	Specifications & Details
Archive ID	Canvas-002
Perceptual Image	Deformation-free tension control, smooth alternating dark/light green diagonal stripes, satin flat sheen
Basic Structure	$2 \times 2$ grid diagonal stitch (Diagonal stepped stripe fill)
Thread Spec	DMC Stranded Cotton / No. 25, 4 strands folded
Color Palette	Dark Green (Magic 3407/8), Light Green (Magic 3407/13)
Composition Vector	Starts from the bottom-left corner, progressing diagonally; alternating rows of dark and light green

Starting Rules:
- Starting point is strictly set at the bottom-left corner of the canvas, initiating with dark green $2 \times 2$ diagonal stitches.
- Front Side: Exit: $(x, y+2)$ $\rightarrow$ Enter: $(x+2, y)$, forming a $45^\circ$ diagonal stitch $\slash$.
- Back Side: Enter: $(x+2, y)$ $\rightarrow$ Exit: $(x, y)$, forming a strictly horizontal back stitch of 2-grid length ($\Delta x = -2, \Delta y = 0$).
- Execution Order: Complete one diagonal row of dark green $\rightarrow$ Switch to light green for the next parallel row $\rightarrow$ Progressively fill the canvas diagonally.
Key Visual Property: Thread tension and spatial displacement regularity across the canvas. Maintaining proper tension is the cornerstone of keeping the embroidered structure flat and preventing fabric distortion. The terminal gap offset is maintained for the hand-drawn aesthetic.
Polar Coordinate Vectors & Angle Operations (Syntax Type: Satin Flat Sheen / Horizontal Tension Anchor Array):
- Front Diagonal Vector A: Angle $45^\circ$, physical length $6.1\text{ mm}$ (Diagonal of a $2 \times 2$ square unit).
- Back Horizontal Anchor Vector B: Angle $180^\circ$ (straight leftwards), physical length $4.3\text{ mm}$ ($2\text{-grid}$ span).
- Terminal Gap Ratio Offset: Default $18\%$ end-point shrink to preserve hand-drawn independent stitch visual gaps.

Core Topological Node Network:
- Formed by a dual-color alternating network over a diagonal stepped node array.
- Alternating front diagonal stitches $\slash$ ($45^\circ$) and back horizontal stitches $\text{—}$ ($180^\circ$) create a staggered translation topology.
Structural Mechanics Analysis:
- Back $180^\circ$ Horizontal Anchor Tension: Unlike Canvas-001’s vertical back stitches, Canvas-002 features entirely horizontal back stitches.
- Tension Balance & Anti-Deformation: The horizontal tension on the back offsets the $45^\circ$ diagonal shear stress on the front, locking the canvas weft threads. This eliminates lateral pulling or skewing, achieving a “distortion-free tension” with a smooth, glossy surface finish.

準備運針中…

ViewBox: 0 0 400 400
Grid Cell Standard: $2 \times 2\text{ grid units} = 40 \times 40\text{ px}$ (with $18\%$ Gap Ratio Offset)
Stitch Path 1 (Diagonal 1, Dark Green): Start (37.2, 342.8) -> End (62.8, 317.2) | Angle: $45^\circ$ | Color: #1b4d24
Stitch Path 2 (Diagonal 2, Light Green Step 1): Start (37.2, 302.8) -> End (62.8, 277.2) | Angle: $45^\circ$ | Color: #82a93b
Stitch Path 3 (Diagonal 2, Light Green Step 2): Start (77.2, 342.8) -> End (102.8, 317.2) | Angle: $45^\circ$ | Color: #82a93b

Thread Physics & Fabric Coverage:
- Mesh Specification: 18-count Mono Canvas.
- Thread Tension & Balance: DMC No. 25 thread (4 strands folded). Horizontal back stitches effectively bind the canvas weft threads, preventing diagonal skewing under high stitching tension.
Stitch Variant Matrix:
- Bi-Directional Texture Variant (Herringbone / Basketweave):
  - Rotating the diagonal stitch entry angle by $90^\circ$ in adjacent sub-domains transforms the pattern into a Herringbone or Basketweave pattern, providing rich visual sheen variations.
Procedural Parameters:
- gapRatio (Terminal Gap Offset): Default set to $0.18$. Preserves tiny gaps at diagonal line boundaries to maintain sharp definition between alternating green color bands.