Case Study: Canvas-017

Module 1: Metadata Table

ItemMetadata Content
Case IDCanvas-017
Perceptual ImpressionUphill / Elevation
Basic StructureRectangular diagonal fill structure (2-3-3-2 continuous stepped grid structure)
Thread SpecificationDMC Embroidery Floss No. 25 (3 strands folded in half)
Color SchemeLight Green, Medium Green, Dark Green (equivalent to Blue, Red, and Yellow paths in the animation)
Stitching DirectionTop-left diagonal extending continuously toward the bottom-right
Syntax TypeSequential Translation Syntax

Module 2: Starting Logic & Vector Operations

1. Stitch Sequence & Region Translation

  • Phase①Base Unit Block (Stitches 1–6):
    • Stitches 1–2: Long diagonal spanning 2 grid squares (top-right to bottom-left, angle at 45°).
    • Stitches 3–4: Long diagonal spanning 3 grid squares.
    • Stitches 5–6: Long diagonal spanning 3 grid squares.
  • Phase②Region 1 Sequential Extension (Blue Path, Stitches 1–30):
    • Translate the base pattern (Stitches 1–6) downward by 2 grids and rightward by 1 grid. Repeat 4 times to generate stitches 7–12, 13–18, 19–24, and 25–30 in sequence, completing Region 1 (Blue Path).
  • Phase③Region 2 Translation (Red Path, Stitches 31–60):
    • Translate Region 1 (1–30) as a whole rightward by 2 grids and upward by 1 grid to generate stitches 31–60 (Red Path / Medium Green Thread).
  • Phase④Region 3 Translation (Yellow Path, Stitches 61–90):
    • Translate Region 2 (31–60) rightward by 2 grids and upward by 1 grid to generate stitches 61–90 (Yellow Path / Dark Green Thread).

2. Vector Angles & Geometric Parameters

  • Diagonal Vector Angle: The top-right to bottom-left diagonal inclination is  (vector direction ).
  • Physical Span Length:
    • 2-grid short diagonal: Length is approx. 5.1 mm (SVG equivalent length: 28.28 px).
    • 3-grid long diagonal: Length is approx. 10.1 mm (SVG equivalent length: 56.57 px).

Module 3: Structural Mechanics & Topology

1. Stepped Connection Mechanics & Visual Elevation

  • Sequential Interlocking: Using a vector step translation of “2 right, 1 up,” the stitches overlap tightly at the boundaries, eliminating gaps.
  • Uphill Perception: The layered color bands extending from bottom-left to top-right create a continuous upward dynamic visual tension.

2. Tension Balance Mechanism

  • Parallel  diagonal stitches are packed tightly together. The physical friction against the fabric base accumulated through repetitive translation keeps the canvas flat without warping or puckering.

Module 4: SVG Vector Syntax & Interactive Demo Code

1. SVG Geometric Parameters

  • ViewBox: -20 -20 320 220
  • Grid System: Dashed line grid with 20-unit spacing (c017_grid_line).
  • Color Mapping: Blue main path (#3b82f6) corresponds to Light Green; Red main path (#ef4444) corresponds to Medium Green; Yellow main path (#eab308) corresponds to Dark Green.

2. Interactive Card Embed Code (WordPress Ready)

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

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

  • Physical Coverage: The stepped parallel diagonal filling provides over  coverage without fabric gaps.
  • Variant Matrix:
    • stepSequence = [2, 3, 3, 2]
    • translationStep = () (Shift 2 units right, 1 unit up)
    • repeatCount = 5 times (intra-region) / 3 regions (overall)
  • Procedural Extension Logic: Adjust the translation vector and three-color gradient offsets to generate continuous geometric embroidery patterns with topographic gradient wrapping.
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