Multi-Scale Quantitative Direction-Relation Matrix for Cardinal Directions

Existing qualitative direction-relation matrix models employ rigid classification schemes, limiting their ability to differentiate directional relationships between multiple targets within the same directional tile. This paper proposes two quantitative matrix models for qualitative direction-relation with differing levels of precision. Based on directional tile partitioning derived from qualitative direction-relation models, the new models achieve quantitative expression of qualitative directionality through two distinct descriptive parameters: order and coordinate. The order matrix utilizes angular and displacement measurements as sequential variables, capturing the directional sequence characteristics within the same directional tile. The coordinate matrix employs direction-relation coordinates as matrix elements, integrating directional and distance relationships to identify the distribution of targets at varying distances along the same line of sight. These two novel models operate at distinct scales and achieve soft classification of directional relationships, substantially enhancing descriptive precision. Furthermore, they serve as foundational quantitative frameworks for the qualitative direction-relation models, establishing a bridge between quantitative and qualitative models. Experimental assessment confirms that the new models substantially improve directional relationship precision through their quantitative elements while supporting various application domains.