Case Study: Canvas-019

Yunbroidery Stitch Algorithm Syntax Card

Module 1: Metadata Table

Property / ItemDetailed Specifications & Parameters
Artwork IDCanvas-019
Perceptual ImageryStep-Climbing Structure / Staircase Progression
Basic StructureBidirectional Diagonal Staircase Grid (4 Diagonal Lines Horizontal x 4 Diagonal Lines Vertical)
Thread SpecificationDMC Stranded Cotton No. 25, 3 strands doubled over (equivalent to 6 strands in thickness)
Color SchemeGradient 3-tone Green Scheme: Dark Green (#0284c7 for Zone 1), Medium Green (#dc2626 for Zone 2), Light Green (#eab308 for Zone 3)
Stitching DirectionDiagonal traversal extending from Top-Left to Bottom-Right

Module 2: Starting & Vector Operations

  1. Basic Geometry & Diagonal Vectors
    • Grid System: Square grid system where each cell has dimension g (equivalent to 20px in SVG, or 2mm/grid unit in physical canvas).
    • Stitch Geometry: Each diagonal stitch spans 2 horizontal grid units and 2 vertical grid units (spanning a 3×3 grid point array). The stitch length L is calculated as:
      L = sqrt((2g)^2 + (2g)^2) = 2 * sqrt(2) * g approx 2.828 g
      (Under a 6mm grid reference, the physical stitch length equals 10.1mm)
    • Vector Angle: The stitching progresses from top-left to bottom-right at an inclination angle theta = -45 deg (or directional vector at 135 deg / -45 deg).
  2. Phase 1: Basic Module & Translational Operations
    • Phase 1 (Stitches 1 to 12, Fundamental Diagonal Group):
      • Starting Point (Stitch 1): Initial coordinates (x_1, y_1) = (210, 70).
      • Ending Point (Stitch 2): (x_2, y_2) = (250, 110). Displacement vector (dx, dy) = (+40, +40) (+2g, +2g).
      • Sub-step 1-1 (Stitches 1-6): Consecutive downward translation along the y-axis with dy = +20 (+1g).
        Stitch 1-2: (210,70) -> (250,110)
        Stitch 3-4: (210,90) -> (250,130)
        Stitch 5-6: (210,110) -> (250,150)
      • Sub-step 1-2 (Stitches 7-12): Consecutive leftward translation along the x-axis with dx = -20 (-1g).
        Stitch 7-8: (190,110) -> (230,150)
        Stitch 9-10: (170,110) -> (210,150)
        Stitch 11-12: (150,110) -> (190,150)
    • Phase 2 (Stitches 13 to 24, Composite Matrix Translation):
      • Apply composite translation to stitches 1-12: translate downward by 3 grid units (dy = +60) and leftward by 3 grid units (dx = -60).
      • Composite translation vector V_trans = (-60, +60).
      • Example: Starting point of Stitch 13 = (210 – 60, 70 + 60) = (150, 130).
    • Phase 3 (Stitches 25 to 36, Second Composite Translation):
      • Re-apply composite translation vector V_trans = (-60, +60) to stitches 13-24.
      • Starting point of Stitch 25 = (150 – 60, 130 + 60) = (90, 190).
  3. Phase 2: Regional Operations & Staircase Layering
    • Zone 1 (Stitches 1-36): Constructs the first diagonal staircase band (Dark green tone / Blue SVG rendering).
    • Zone 2 (Stitches 37-72): Replicates Zone 1 structure offset by (dx, dy) = (+40, +40) toward bottom-right, creating the second tier (Medium green tone / Red SVG rendering).
    • Zone 3 (Stitches 73-108): Replicates structure with an additional offset (+40, +40) to build the third tier (Light green tone / Yellow SVG rendering), filling the entire composition.

Module 3: Structural Mechanics & Topology

  1. Structural Backbone & Interlocking
    • The structural foundation of Canvas-019 lies in the interlocking arrangement of 3×3 grid -45 deg diagonal stitches arranged in an orthogonal staircase array.
    • Alternating Stitch Paths: 3 stitches extend vertically downward, followed by 3 stitches expanding horizontally to the left. This 90-degree turning path forms an interlocked structural backbone, preventing thread slack or displacement commonly seen in single-direction long stitches.
  2. Tension Balance Mechanism
    • Bidirectional Force Cancellation: Embroidery thread exerts tension T_diag in the -45 deg direction. Through the zig-zag 3-vertical / 3-horizontal pattern, orthogonal components acting on fabric threads are resolved as:
      F_x = T_diag * cos(45 deg)
      F_y = T_diag * sin(45 deg)
    • Distortion Suppression: Equal magnitude forces along x and y axes (F_x = F_y) ensure strictly balanced warp and weft tension across the fabric, completely eliminating fabric puckering.
  3. Stress Distribution & Volumetric Support
    • Volumetric Cushioning: Doubled-over 3-strand DMC thread (6 strands total) yields high linear thread density. The 2-unit diagonal span (10.1mm length) produces a dense, cushioned relief layer raised above the canvas surface.
    • Backside Anchorage: On the reverse side, tight rectangular and step-like bridge lines (as seen in CV_019B) anchor into grid nodes, establishing a stable topological network that guarantees long-term structural integrity.

Module 4: Vector API & Dynamic Presentation Data

1.Renderable HTML/SVG Card Code

Canvas-019 (Stitches 1-108) – 2x Slow Motion (Blue/Red/Yellow Zones)⏸ Pause↻ Replay
Canvas-019 (Complete Set of 1-108 Pins) – 2x Slow Speed ​​(Blue/Red/Yellow Zones)
12 34 56 78 910 1112 1314 1516 1718 1920 2122 2324 2526 2728 2930 3132 3334 3536 3738 3940 4142 4344 4546 4748 4950 5152 5354 5556 5758 5960 6162 6364 6566 6768 6970 7172 7374 7576 7778 7980 8182 8384 8586 8788 8990 9192 9394 9596 9798 99100 101102 103104 105106 107108
2.Geometric Parameters & Specifications
  • ViewBox Specification: 0 20 360 360 (Square canvas with 20px top padding).
  • Grid System: Background renders 20px x 20px square cells, with 3px diameter grey dots (fill: #94a3b8) marking piercing nodes.
  • Animation Control Mechanism:
    • Utilizes CSS stroke-dasharray: 100 and stroke-dashoffset: 100.
    • Single Stitch Duration: 0.7 seconds with cubic-bezier(0.4, 0, 0.2, 1) easing.
    • Sequential Delay: Increments by 0.4 seconds per stitch for 108 stitches, delivering a smooth, slowed execution animation.
  • Zone Color Allocation:
    • Zone 1 (Stitches 1-36): #0284c7 (Royal blue representing dark green thread).
    • Zone 2 (Stitches 37-72): #dc2626 (Bright red representing medium green thread).
    • Zone 3 (Stitches 73-108): #eab308 (Amber yellow representing light green thread).

Module 5: Visual Gallery

Front View (Physical Embroidery)Back View (Physical Embroidery)Design Manuscript
Front: Demonstrates 3-tone gradient staircase relief depthBack: Displays tight, orthogonal anchorage networkManuscript: Details stitch sequence 1-108 and block logic

Module 6: Algorithm Extensions & Variant Syntax

  1. Physical Surface Coverage Ratio
    • On standard canvas grids (such as 14-count Aida or 6mm grids), the bidirectional diagonal staircase grid achieves complete thread overlap.
    • Thread diameter d_thread and grid size g fulfill 6 * d_strand approx 1.2mm, resulting in 100% surface coverage with zero exposed canvas fabric.
  2. Procedural Extension Parameters
    • stepSequence: [3, 3] (3 stitches downward, 3 stitches leftward in alternating staircase mode).
    • unitSpacing: 1g (Orthogonal shift distance between individual sub-step stitches).
    • blockOffset: (-3g, +3g) (Composite vector offset when translating block 1-12 to 13-24).
    • diagonalSpan: (2g, 2g) (Single stitch span across 2 horizontal and 2 vertical units at -45 deg).
    • gapRatio: 0 (Zero gap seamless connection).
  3. Variant Matrix & Parametric Variations
    • Canvas-019-V1 (Sawtooth Wave Variant): Adjust stepSequence to [4, 2] to create asymmetric diagonal wave ripples.
    • Canvas-019-V2 (Cross-Hatch Variant): Rotate Zone 2 stitch vectors by 90 degrees to form a 90-degree crisscross grid.
    • Canvas-019-V3 (Micro-Step Variant): Reduce stitch span to (1g, 1g) and stepSequence to [2, 2] for high-precision decorative borders.
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