Case Study: Canvas-012

Computational Embroidery Syntax Card

Module 1: Metadata Table

Property / Item	Description & Technical Specifications
Case ID	Canvas-012
Perceptual Impression	“Wing & Diagonal Stitches” architecture offering dynamic geometric rhythm; combines layered diagonal stitch groupings with calculated grid spacing to generate depth, geometric tension, and light interaction.
Basic Structure	Wing & Diagonal Stitch syntax; primary modules consist of 2-3-4-3-2 grid diagonal stitch sequences with a 1-grid empty interval, interwoven with four sets of 2×2 diagonal stitches.
Thread Specification	DMC No. 25 embroidery floss / 4 strands (folded, equivalent to 4 strands).
Color Palette	Primary: Green; Accent: Sky Blue, Off-White
Stitching Direction	Two-phase execution: ① Green wing & diagonal foundation array (bottom-left to top-right) → ② Center filling (Sky Blue & Off-White); extending from top-left to bottom-right at a 45° diagonal angle.

Module 2: Starting & Vector Operations

• Starting Rule: The initial anchor is set at the top-left corner. Phase ① (Green wing and diagonal structure) is executed first along a 45° slope from top-left to bottom-right. Phase ② completes the bottom-left corner, top-right corner, and central sky blue/off-white fills.
• Phase ① Green Diagonal & Wing Sequence (Stitches 1–20, Dual-Block System):
  • Right Block (Stitches 1–10): Sequential execution across 3, 1, 2, 2, 1 grid lengths:
    • Stitches 1–2 (3 Grids): Start (340, 220) $\rightarrow$ End (460, 100)
    • Stitches 3–4 (1 Grid): Start (420, 220) $\rightarrow$ End (460, 180)
    • Stitches 5–6 (2 Grids): Start (380, 220) $\rightarrow$ End (460, 140)
    • Stitches 7–8 (2 Grids): Start (340, 180) $\rightarrow$ End (420, 100)
    • Stitches 9–10 (1 Grid): Start (340, 140) $\rightarrow$ End (380, 100)
  • Left Block (Stitches 11–20): Parallel mirror translation to the left region ($\Delta x = -280\text{px}$):
    • Stitches 11–12 (3 Grids): Start (60, 220) $\rightarrow$ End (180, 100)
    • Stitches 13–14 (1 Grid): Start (140, 220) $\rightarrow$ End (180, 180)
    • Stitches 15–16 (2 Grids): Start (100, 220) $\rightarrow$ End (180, 140)
    • Stitches 17–18 (2 Grids): Start (60, 180) $\rightarrow$ End (140, 100)
    • Stitches 19–20 (1 Grid): Start (60, 140) $\rightarrow$ End (100, 100)
• Vector & Angle Computations:
  • Stitch Angle: All main diagonal lines maintain a consistent $-45^\circ$ inclination (constrained by grid coordinates).
  • Physical Dimension Mapping: 1-grid span $\approx 6.1\text{ mm}$; 2-grid span $\approx 12.1\text{ mm}$; 3-grid span $\approx 18.1\text{ mm}$; 4-grid span $\approx 24.2\text{ mm}$.

Module 3: Structural Mechanics & Topology

• Core Topological Node Network:
  • Long diagonal stitches (4-grid and 3-grid spans) serve as the structural backbone, flanked symmetrically by shorter 2-grid and 1-grid stitches to form stable, wing-like geometric units.
  • Parallel pathways of green, sky blue, and off-white threads construct a dual-texture topological grid across the canvas.
• Structural Tension Analysis:
  • Symmetric Tension Balance: Uniform $45^\circ$ angles distribute pulling forces evenly across warp and weft threads, preventing fabric distortion across large filled areas.
  • Grid Interlocking Stability: The 1-grid empty interval acts as a strain relief zone, locking foundation threads securely to eliminate sagging or loosening.

Module 4: Vector API & Dynamic SVG Widget

SVG Vector Parameters:

• ViewBox: 0 0 520 320
• Grid Baseline: 40 x 40 px System (Centroid Grid Offset)
• Phase ① Right Block Vectors (Stitches 1–10):
  • Stitches 1–2 (3 Grids): Start (340, 220) $\rightarrow$ End (460, 100) | Stroke Color: #16a34a
  • Stitches 3–4 (1 Grid): Start (420, 220) $\rightarrow$ End (460, 180) | Stroke Color: #16a34a
  • Stitches 5–6 (2 Grids): Start (380, 220) $\rightarrow$ End (460, 140) | Stroke Color: #16a34a
  • Stitches 7–8 (2 Grids): Start (340, 180) $\rightarrow$ End (420, 100) | Stroke Color: #16a34a
  • Stitches 9–10 (1 Grid): Start (340, 140) $\rightarrow$ End (380, 100) | Stroke Color: #16a34a
• Phase ① Left Block Vectors (Stitches 11–20):
  • Translated along the diagonal axis ($\Delta x = -280\text{px}, \Delta y = 0\text{px}$), completing the dual-block symmetric layout.

Module 5: Visual Gallery

Front View (Physical Embroidery)	Back View (Structure Analysis)	Design Blueprint (Hand-drawn Diagram)
CP_012_4.jpg	CV_012B_4.jpg	CV_012H_4.jpg

Module 6: Algorithm Extensions & Variant Syntax

• Thread Physicality & Coverage:
  • Substrate: Optimized for 18-count Mono Canvas (40px grid spacing coordinate system).
  • Volumetric Density: Combined wing and diagonal stitching creates tactile, elevated wing-like contours while maintaining precise grid alignment.
• Stitch Variant Matrix:
  • Dual-Color Gradient Variant: Filling central empty intervals with Sky Blue and Off-White strands generates high-contrast dynamic relief against the green foundation.
• Procedural Extension Parameters:
  • stepSequence: [2, 3, 4, 3, 2] grid span sequence.
  • unitSpacing: 1 grid (precise empty space left when transitioning between wing units along the 45° slope).
  • diagonalCluster: 2 grids depth $\times$ 2 rows (four-set diagonal stitch cluster).
  • gapRatio: Adjustable gap ratio to customize visual porosity and dynamic contrast.