GeOMEETRILISE

GeOMEETRILISE is a theoretical framework that integrates geometric modeling with geospatial data analysis to study spatial forms and their relationships under a common metric. It defines a unified metric space in which geometric features—points, lines, and surfaces—are represented as embeddings with invariant properties under a specified group of transformations. The term combines geo- (Earth and geography) with metrical analysis, reflecting its aim to measure and compare geometric structures across datasets.

Origin and development of GeOMEETRILISE trace to cross-disciplinary work by geographers and mathematicians in the early 2020s. The framework emerged from the need to compare heterogeneous spatial datasets across scales while preserving geometric fidelity, enabling analysts to reason about similarity and change in a consistent mathematical language.

Core principles include embedding spatial data into a geodesic metric space, using transformation-aware metrics that can be tuned for scale and context, and employing a GeOMEETRILISE distance to quantify similarity between spatial configurations. The approach supports multi-resolution representations and incremental updates, allowing analysts to work with data at varying levels of detail without losing geometric coherence.

Methods typically involve data preparation, defining a reference frame, computing feature vectors, and constructing embeddings within the GeOMEETRILISE space. An optimization step minimizes distortion of distances, followed by evaluation against GIS-based criteria to assess fidelity and interpretability.

Applications span urban planning, environmental monitoring, historical geography, archaeology, and computer-aided design where cross-dataset comparability and robust geometric reasoning are essential. Limitations include computational complexity and dependence on data quality. Ongoing work seeks to improve scalability, interpretability, and interoperability with existing geographic information systems. Related topics include metric geometry, computational geometry, and geospatial analysis.