Case Study: Canvas-017

Module 1: Metadata Table

ItemSpecification / Value
Case IDCanvas-017 DOCX
Perceptual ImageAscending / Uphill Movement DOCX
Basic StructureRectangle Diagonal Line Fill DOCX
Thread SpecificationDMC Embroidery Floss No. 25, 3 Strands Folded DOCX
Color SchemeDeep Green, Medium Green, Light Green DOCX
Stitch DirectionDiagonal sequence of 2.3.3.2 grid units starting from top-left, sharing 2 grid units, repeatedly filling with 3.3.2 diagonal grids DOCX
Syntax TypeContinuous / Sequential Syntax DOCX

Module 2: Starting & Vector Operations

1. Spatial Layout Logic (Phase ① & Phase ②)

  • Phase ① Basic Unit Construction:
    • Starting Coordinates: Begins at the top-left rectangular area, Centroid(x, y) = (80, 40). JPG+ 1
    • Rectangular Base Unit: Defines a rectangular space of 20 px width and 80 px height (1 grid wide, 4 grids high), bounded from (50, 30) to (110, 110).
    • First Unit Sequence (Stitches 1-6): Advances diagonally from top-left to bottom-right. Sequence: Stitch 1 (span of 2 grids), Stitch 2 (span of 3 grids), Stitch 3 (span of 3 grids), Stitch 4 (span of 2 grids), Stitch 5 (span of 3 grids), Stitch 6 (span of 3 grids).
  • Phase ② Sequential Array Expansion:
    • Shared Grid Continuation: Uses the last 2 grid units of the first unit as shared nodes.
    • Longitudinal Array Shift: Copies the base unit and translates it downward by 2 grids (dy = +40 px) and rightward by 1 grid (dx = +20 px). Subsequent stitches are renumbered as 7-12, 13-18, 19-24, and 25-30. Repeating 4 times completes Region 1 (Blue, 30 stitches in total).
    • Parallel Region Shift: Stitches 31-60 (Region 2, Red) are positioned 2 grids to the right (dx = +40 px) and 1 grid upward (dy = -20 px) relative to Region 1. Stitches 61-90 (Region 3, Green) are generated following the same translation rule.

2. Vector Displacement & Inclination Angle

  • Stitch Vector Displacement:
    • 2-Grid Diagonal Vector: dx = -20 px, dy = +20 px, Displacement Length L = √(20² + 20²) = 28.28 px.
    • 3-Grid Diagonal Vector: dx = -40 px, dy = +40 px, Displacement Length L = √(40² + 40²) = 56.57 px.
  • Vector Inclination Angle: All diagonal stitches maintain a constant inclination angle θ = -45°.
  • Translation Matrix: Intra-region unit displacement vector T_unit = (20, 40); Inter-region shift vector T_region = (40, -20).

Module 3: Structural Mechanics & Topology

1. Structural Spine

  • Main Stress Axis: A diagonal line extending at -45° from top-left to bottom-right forms the structural spine. JPG+ 2
  • Shared Overlapping Nodes: The 2 shared grids act as continuous locking points, preventing shear deformation of the rectangular framework under diagonal tension.

2. Tension Balance & Stress Distribution

  • Tension Compensation: Diagonal forces produced by the 2.3.3.2 stitch groups are balanced by the orthogonal warp and weft grid forces of the fabric (Aida Grid).
  • Stress Concentration at Shared Nodes: Shared nodes absorb dual-strand tension, reinforcing the topological rigidity of the diagonal spine and creating a pronounced 3D “Uphill” visual gradient. DOCX

Module 4: SVG Vector API & Dynamic Data

1. HTML/SVG Dynamic Code Card

當前針數:0 / 45 針 0%
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

2. Vector Geometry Parameters

  • ViewBox: 0 0 360 320.
  • Grid System: Orthogonal grid with a step size of 20 px.
  • Start/End Coordinates & Stroke Length:
    • 2-Grid Stitch: dx = 20 px, dy = 20 px. Default stroke-dasharray and stroke-dashoffset set to 29 px.
    • 3-Grid Stitch: dx = 40 px, dy = 40 px. Default stroke-dasharray and stroke-dashoffset set to 57 px.
  • Color System:
    • Region 1 (Blue): #1e50a2
    • Region 2 (Red): #e62f00
    • Region 3 (Green): #2e8b57

Module 5: Visual Gallery

Module 5: Visual Gallery

Front PhotoBack PhotoDesign Draft
Front: Dense green gradient stepped diagonal structureBack: Regular diagonal parallel lines with balanced thread tensionDraft: Hand-drawn geometric coordinates with stitches 1–90 path

Module 6: Algorithm Extensions & Variant Syntax

1. Physical Coverage Ratio

  • Unit Coverage Density: Contains 4 diagonal stitches per unit, yielding an effective surface coverage of approximately 88.5% within a 20×80 px rectangular zone.
  • Gap-Filling Effect: Double stitching at shared nodes eliminates canvas exposure along diagonal seams[cite: 8, 9].

2. Variant Matrix

  • Horizontal Reflection: Converts inclination angle to +45°, altering the visual perception from “Ascending” to “Descending”.
  • Vertical Extension: Increases unit iteration count to generate continuous textile border patterns.

3. Procedural Extension Parameters

  • stepSequence: [2, 3, 3, 2] DOCX
  • unitSpacing: { dx: 20, dy: 40 }
  • regionOffset: { dx: 40, dy: -20 }
  • gapRatio: 0.5
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