Edge-Consistent
Wedge-Gradient Cell Vectorization

Abstract

We present a novel raster-to-vector conversion system designed specifically for the rigorous demands of textile rotary screen engraving and digital printing. Unlike traditional luminosity-based edge tracing (e.g., Potrace), our approach utilizes a hexagonal honeycomb mesh combined with intra-cell wedge gradients to represent continuous-tone imagery with high fidelity while maintaining a strict print-safe SVG subset.

1. Introduction

The textile industry faces a unique challenge in digitization: historical archives exist primarily as fabric swatches or low-resolution scans. Recreating these for modern production requires vectorization that preserves not just shape, but "texture" and "flow". Existing tools often result in "posterization" (banding) or excessive node counts that crash RIP software.

2. Methodology

2.1 Honeycomb Tessellation

We define the image domain $D$ as a set of hexagonal cells $H$. Hexagonal packing offers optimal surface coverage with minimal perimeter. For each cell $c \in H$, we calculate the local color variance $\sigma^2_c$.

2.2 Wedge Decomposition

To capture gradients, each cell is decomposed into 6 triangular wedges $W_1...W_6$. A linear gradient is computed for each wedge, interpolating between the cell centroid color $C_center$ and the edge midpoint color $C_edge$. This ensures $C^0$ continuity across cell boundaries.

3. Print-Safe Constraints

Modern RIPs (Raster Image Processors) are notoriously fragile. Our engine enforces a strict subset of SVG 1.1:

• Permitted: `path`, `linearGradient` (userSpaceOnUse only), `g`, `defs`.
• Forbidden: `filter`, `mask`, `clipPath`, `radialGradient`, `opacity` (on stops).

4. Conclusion

The Sapphire Vector Engine demonstrates that it is possible to achieve photographic fidelity in vector format without resorting to raster embedding or complex mesh gradients unsupported by industrial printers.