Case Study: Canvas-020

Yunbroidery Stitch Algorithm Syntax Card

Field Name	Description
Work ID	Canvas-020
Perceptual Image	Brick Stairs (Exhibiting progressive elevation and stacked masonry brick texture)
Basic Structure	Combination of ╱ diagonals and diagonal horizontal-slanted rectangles
Thread Specification	DMC No. 25 Embroidery Floss
Color Palette	Dark Green, Medium Green, Light Green, Gold Metallic Thread
Stitching Direction	Dual-unit layout: Central diagonal vertical-slanted stitches first, followed by upper/lower 4×5 rectangles with 2.3.4.4.3.2 grid diagonal fills
Syntax Type	Diagonal Fill Type / Volume Support

Phase ① (Core Base): Initiate from the first 8×7 grid unit (Region 1). Execute central diagonal vertical-slanted stitches (stitches 1–14) first, followed by horizontal-slanted stitches (stitches 15–26).
Phase ② (Region Replication & Array Translation):
- Region 2 (Stitches 27–52): Replicate Region 1 (stitches 1–26), apply vector translation Δx = +2 grids, Δy = +4 grids. Re-number sequence to 27–52.
- Region 3 (Stitches 53–78): Replicate Region 2 with Δx = +2 grids, Δy = +4 grids. Re-number sequence to 53–78 and adjust color palette.

Vertical Diagonals (Stitches 1–14):
- Vector Direction: Top-Right to Bottom-Left (Top-Right (x+1, y) → Bottom-Left (x, y+1)).
- Vector Angle: -135° (or +225°).
- Length Specification: Single stitch length spans approximately √2 to 2√2 grid units.
Horizontal Diagonals (Stitches 15–26):
- Vector Direction: Top-Left to Bottom-Right (Top-Left (x, y) → Bottom-Right (x+1, y+1)).
- Vector Angle: -45° (or +315°).
- Length Specification: Vector displacement (+1, +1), single stitch length = √2 units.

Dual-Axis Cross Spine: Interlocking array formed by -135° Top-Right-to-Bottom-Left diagonals and -45° Top-Left-to-Bottom-Right diagonals, establishing a stable structural grid.
Stepped Topology: Progressing via translation vector Δx = +2, Δy = +4, building a masonry staircase-like visual spine that evenly transmits structural tension along diagonal directions.

Orthogonal Force Cancellation: Pull force vectors from Top-Right–Bottom-Left stitches intersect at 90° with Top-Left–Bottom-Right stitches, effectively canceling out single-direction fabric distortion.
Layered Stress Dispersion: By utilizing a progressive 2.3.4.4.3.2 stitch length layout within the 4×5 rectangular units, stress concentration is distributed across multiple canvas grid holes, preventing fabric distortion.

ViewBox: 0 0 500 650
Grid System: Base unit = 20px
Coordinates & Palette Mapping:
- Region 1 (1–26): Stitches 1–14 in Dark Blue #1b4f72; Stitches 15–26 in Red #cb4335.
- Region 2 (27–52): Stitches 27–40 in Medium Blue #2874a6; Stitches 41–52 in Emerald Green #27ae60.
- Region 3 (53–78): Stitches 53–78 in Yellow/Gold #f1c40f or #d4ac0d.

1-78 stitches (full pattern of zones 1-3) – includes pause function

⏸ Pause animation ↻ Replay

Front View (Physical)	Back View (Structure)	Manuscript Path Diagram
Fig 1: Front Physical Rendering Displays 3D brick staircase texture created with shades of green and gold threads.	Fig 2: Back Structural Detail Shows stable orthogonal backing lines and clean parallel stitch paths.	Fig 3: Original Manuscript Notes Accurately outlines sequence 1–78 and array translation parameters.

Single Stitch Coverage Width: Using DMC No. 25 floss (2 or 3 strands), single stitch visual coverage width ranges from 0.8 mm to 1.2 mm.
Unit Area Density: Within 8×7 and 4×5 matrix combinations, diagonal overlap rate reaches 85% – 95%, hiding fabric base to create a dense brick-like texture.

stepSequence: [2, 3, 4, 4, 3, 2] (Defines stitch count per row within trapezoidal units).
unitSpacing: Δx = 2, Δy = 4 (Translation distance for 8×7 brick modules).
gapRatio: 0.0 (Seamless joining to ensure continuous brick volume).
colorMatrix:
- Region_1: [Blue_Dark, Red_Accent]
- Region_2: [Blue_Medium, Green_Primary]
- Region_3: [Yellow_Gold, Green_Accent]