Digital distance in the kisrhombille grid with the edge neighborhood
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View abstract on PubMed
Summary
This summary is machine-generated.This study introduces digital distance for kisrhombille tilings, defining neighbor tiles and deriving a distance formula. This provides a new metric for analyzing these geometric patterns.
Area Of Science
- Geometry
- Tessellation Theory
- Discrete Mathematics
Background
- The kisrhombille tiling is a dual tessellation of semi-regular tilings.
- It consists of right-angled triangles in 12 unique orientations.
- A coordinate system is used to formally describe the tile grid.
Purpose Of The Study
- To formally define neighbor tiles within the kisrhombille tiling.
- To introduce the concept of digital distance between tiles.
- To derive a distance formula for the kisrhombille tiling.
Main Methods
- Defined neighbor tiles as those sharing an edge.
- Introduced digital distance as the minimum traversal steps between tiles.
- Derived the distance formula by constructing minimal paths.
Main Results
- Formalized the definition of neighboring tiles in the kisrhombille tiling.
- Established the concept and calculation method for digital distance.
- Derived a novel distance formula applicable to this tiling system.
Conclusions
- The digital distance provides a quantifiable metric for analyzing kisrhombille tilings.
- The derived formula enables precise measurement of separation between tiles.
- This work offers a foundation for further research in geometric network analysis.
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