Case Study: Canvas-011

Embroidery Algorithm & Topological Analysis

Module 1: Metadata Table

ItemSpecification Details
Work IDCanvas-011
Perceptual ImageVerdant stepped rhythm, embellished with subtle silver luxury
Basic StructureDiagonal Line, Raindrop
Thread SpecificationDMC No. 25, 4 strands folded
Color SchemeGreen, Yellow, Silver Metallic
Embroidery DirectionSequential execution divided into Phase 1 and Phase 2
Syntax TypeFull Fill Type

Module 2: Starting Logic & Vector Operations

1. Fundamental Geometric Unit & Scalar Parameters

  • Grid System: Canvas grid system set at 10 x 10 pixels per unit square.
  • Single Stitch Vector:
    • Diagonal Main Stitch (Long Stitch): Geometric span Δx = -60, Δy = +60 (or Δx = -20, Δy = +20), inclination angle θ = -45°.
    • Raindrop Short Stitch: Geometric span Δx = -20, Δy = +20, length L = 20 × √2 ≈ 28.28 pixels, inclination angle θ = -45°.

2. Execution Phases & Sequence Logic

  • Phase 1 (Main Diagonal Backbone Array):
    • Starting Point: Point 1 (70, 10).
    • Stitch Sequence: Sequential diagonal lines arranged in a 2-3-4-3-2 grid pattern (Segments 1-2, 3-4, 5-6, 7-8, 9-10), forming the primary structural ridge.
  • Phase 2 (Raindrop Diagonal Combination Group):
    • Starting Point: Point 11 (90, 10).
    • Stitch Sequence: 2-grid diagonal lines paired with 3 rows × 6 raindrop short diagonal units (Segments 11-12 through 27-28).

3. Array Copy & Transformation Operators

  • Base Group (Segments 1-28): Comprises segments 1 through 28.
  • Translation Group 1 (Segments 29-56):
    • Translation Vector: T1 = (+120, 0) (Shift right by 6 grid units).
    • Coordinates & Color: Segments 29-38 start at (190, 10) with color modified to Light Blue; Segment 56 ends at (230, 70).
  • Translation Group 2 (Segments 57-84):
    • Translation Vector: T2 = (-60, +60) (Shift left by 3 grid units, shift down by 3 grid units).
    • Coordinates & Color: Cloned from segments 11-38. Segment 57 starts at (30, 70); Segment 84 ends at (110, 130).
  • Translation Group 3 (Segments 85-112):
    • Translation Vector: T3 = (+120, 0) (Shift right by 6 grid units).
    • Coordinates & Color: Cloned from segments 57-84. Segment 85 starts at (150, 70); Segments 103-112 modified to Blue; Segment 112 ends at (230, 130).

Module 3: Structural Mechanics & Topology

1. Structural Backbone & Geometric Guidance

Canvas-011 utilizes a one-dimensional continuous orientation (-45° inclination angle), with all stitches running parallel to the main diagonal. This uniform orientation ensures consistent light refraction, while the stepped staggered layout (2-3-4-3-2 grid and raindrop units) breaks visual monotony.

2. Tension Balance & Stress Dispersion

  • Axial Tension: The tension vector of individual stitches points uniformly toward 135° (bottom-left diagonal), with force magnitude F_stitch proportional to segment length.
  • Tension Equalization: By intertwining Phase 1 long diagonal stitches with Phase 2 short raindrop stitches, high-tension zones from long stitches are interrupted by dense anchor points of short stitches. This effectively prevents single-direction canvas distortion and puckering.
  • Physical Equilibrium: Adjacent translated units (Δx = +120, Δy = 0 and Δx = -60, Δy = +60) create an intersecting stress grid across the fabric, evenly distributing tension along the canvas warp and weft.

Module 4: Vector API & Dynamic Render Data

1. Interactive SVG Dynamic Card

Yunbroidery Canvas-011 Embroidery pattern animation
Yunbroidery Canvas-011 Embroidery pattern animation
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112

2. SVG Vector Geometry Parameters

  • ViewBox Definition: 0 0 250 150.
  • Grid System: Underlying 10 x 10 pixel grid for precise canvas coordinate mapping.
  • Color Palette Codes:
    • Blue: #1e88e5
    • Light Blue: #00acc1
    • Red: #e53935
    • Yellow: #fdd835
    • Green: #43a047

Module 5: Visual Gallery

Front ViewBack ViewDraft Chart
File ID: CP_011_4.jpgFile ID: CV_011B_4.jpgFile ID: CV_011H_4.jpg

Module 6: Algorithm Extensions & Variant Syntax

1. Physical Coverage Calculation

  • Stitch Density: Interlocking stitch overlap rate is approximately 88%.
  • Total Thread Consumption: Approximately 480 mm per base unit (calculated based on 4 strands folded).

2. Procedural Parameter Definitions

  • stepSequence = [2, 3, 4, 3, 2] (Spine span stepped sequence)
  • unitSpacing = 6 units (Horizontal X-axis translation distance)
  • shiftVector = (-3, +3) (Secondary array translation operator)
  • gapRatio = 0.15 (Raindrop stitch spacing ratio)
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