Case Study: Canvas-020

Yunbroidery Stitch Algorithm Syntax Card

Field Name	Description / Data
Case Number	Canvas-020 (Structural Category: Canvas-019)
Perceptual Image	Grid Climbing Step-Pattern
Basic Structure	Bidirectional Stepped Interlocking Matrix (4 diagonal units horizontally and vertically)
Thread Spec	DMC Cotton Embroidery Floss No.25, 3-strand folded (6-strand equivalent for high volumetric fill)
Color Scheme	Gradient Tri-color System: Deep Green (#0284c7 Cyan-Green), Medium Green (#e11d48 / #eab308 Warm Green), Light Green (#16a34a Emerald Green)
Embroidery Direction	Top-Left Diagonal to Center-Bottom Sequence
Syntax Type	Volumetric Structural Support

Horizontal Diagonal Stitch Length (S1): 3 units x 3 units, Inclination angle = -45° (or 135°), physical length approx. 18.1 mm (based on 1 unit = 6.0 mm).
Vertical Diagonal Stitch Length (S2): 1 unit x 1 unit, Inclination angle = 45°, physical length ranging from 6.1 mm to 12.1 mm.
Base Translation Vector (delta x, delta y):
- Block Replication Vector: (delta x, delta y) = (+60, +80) (Corresponding grid spacing: +3 units right, +4 units down).

Phase I (Main Diagonal Support Stitches – Blue lines, Stitches 1 to 14):
- Start Point P(1) = (150, 70), End Point Q(2) = (90, 130). Vector delta P = (-60, +60), Angle = -45°.
- Recursive Shift: Translate +20 units (+1 grid) vertically down per step for 5 consecutive stitches (Stitches 1-2, 3-4, 5-6, 7-8, 9-10).
- Transition Shift: Translate +20 units (+1 grid) horizontally right per step for 2 consecutive stitches (Stitches 11-12, 13-14).
Phase II (Interlocking Cross Stitches – Red/Yellow lines, Stitches 15 to 26):
- Start Point P(15) = (190, 70), End Point Q(16) = (210, 90). Vector delta P = (+20, +20), Angle = 45°.
- Stepped Variable-Length Fill: Length expands incrementally from 1 diagonal unit (6.1 mm) to 3 diagonal units (18.1 mm) and contracts back to 1 unit, establishing an interwoven structural lock.

Region 1 (Stitches 1 – 26): Base primary structural block (Blue / Red combination).
Region 2 (Stitches 27 – 52): Translated from Region 1 with vector offset (delta x = +60, delta y = +80), stitch indices offset +26, Phase II thread substituted with Yellow/Warm Green.
Region 3 (Stitches 53 – 78): Translated from Region 2 with vector offset (delta x = +60, delta y = +80), stitch indices offset +26, Phase II thread substituted with Emerald Green.

Structural Backbone & Topology:Canvas-020 features an Orthogonal-Diagonal Weave Topology. By cross-interlocking 135° primary stress lines with 45° secondary locking lines, a continuous stepped ladder backbone is constructed across the 2D grid matrix.

Node Distribution: Grid intersection points form a periodic 20 px x 20 px point matrix. Main diagonal stitches span 3 grid units to supply primary tensile strength.
Spatial Overlap Ratio: Phase I and Phase II stitch paths intersect at 90° angles on grid vertices, creating rigid mechanical locking nodes.

Fabric Deformation Control: Unidirectional diagonal stitching introduces significant shear strain at -45°, causing fabric puckering. Canvas-020 incorporates orthogonal 45° counter-directional stitches so that internal shear stress (tau_xy) and normal stresses (sigma_x, sigma_y) neutralize each other, achieving net-zero result force (F = 0) and maintaining total tension equilibrium.
Volumetric Support Index: The 6-strand thread weight provides rich physical volume. The cross-weaving technique causes threads to bulge slightly, forming a 3D tactile surface while substantially boosting surface compression resistance.

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

⏸ Pause animation ↻ Replay

ViewBox Domain: 60 40 300 360
Coordinate Grid System: Defined via SVG with a 20px x 20px dot lattice.
Animation Controls:
- Keyframe path rendering driven by stroke-dasharray: 150; stroke-dashoffset: 150;
- Single stitch draw duration set to 0.8s with cubic-bezier(0.4, 0, 0.2, 1) timing function.
- Sequential delay increment (0.6s per stitch) yielding a total runtime of 23.4s across 78 stitches.
Color & Coordinates Mapping:
- Region 1 (Blue/Red): Blue (x1=150~190, y1=70~150), Red (x1=150~190, y1=70~130).
- Region 2 (Blue/Yellow): Blue (x1=210~250, y1=150~230), Yellow (x1=210~250, y1=150~210).
- Region 3 (Blue/Green): Blue (x1=270~310, y1=230~310), Green (x1=270~330, y1=230~290).

Perspective	Image Filename	Structural Details & Key Highlights
Front View	CP_020_4.jpg	Highlights volumetric support and gradient tri-color aesthetic with 3D stepped texture.
Back View	CV_020B_4.jpg	Demonstrates tidy reverse stitching, tight parallel thread routing, and balanced tension.
Manuscript Plot	CV_020H_4.jpg	Original hand-drawn vector coordinates with marked angles (135° & 45°) and lengths (6.1mm, 12.1mm, 18.1mm).

Stitch Density: Layered using 6-strand thread (3-strand folded) over 20 px x 20 px (approx. 6mm x 6mm) grid units. Coverage C = (N * d * L) / A
- Where N = stitch count, d = thread diameter (~0.8 mm), L = mean stitch length (12.1 mm), A = block surface area.
- Measured physical coverage rate reaches 98.5%, completely concealing base fabric for dense volumetric support.

stepSequence: [7, 6, 7, 6] (Phase I 7 blue stitches + Phase II 6 red/yellow/green stitches)
unitSpacing: 20px (Base grid unit size)
gapRatio: 0.0 (Seamless tight interlocking)
offsetVector: { deltaX: +60, deltaY: +80 } (Stepped block shift vector)
fillAngleArray: [-45, 45, -45, 45] (Bidirectional crossing angle configuration)