Tilametriikat

Tilametriikat, in its broad Finnish usage, refers to spatial metrics—the study and application of distance and similarity measures in space. The term encompasses both theoretical aspects from metric geometry and practical methods used in geographic information systems (GIS), robotics, and computer vision.

In mathematics, a metric is a function d: X × X → [0, ∞) that assigns a nonnegative distance between any two points in a set X and satisfies four conditions: non-negativity, identity of indiscernibles, symmetry, and the triangle inequality. Spatial metrics define the geometry of a space and enable formal notions of closeness, proximity, and shortest paths. Common examples include Euclidean distance (L2), Manhattan distance (L1), and Chebyshev distance (L∞), as well as the broader family of Minkowski metrics. For geographic applications, distances on the Earth’s surface are often computed with spherical formulas such as the Haversine or Vincenty methods.

In discrete spaces such as grids or networks, tilametriikat cover 4- and 8-neighborhood distances, graph-based shortest-path distances, and least-cost paths where different cell costs or directions influence the measured distance. Anisotropic or weighted metrics account for directionality or varying traversal costs, while resistance-like metrics model connectivity in complex terrains.

Applications span urban planning, navigation, robotics, remote sensing, and computer vision. The choice of metric affects pathfinding, clustering, and spatial inference, influencing both accuracy and computational efficiency. Variants and relaxations, such as quasi-metrics or metric tensors, address spaces where symmetry or the triangle inequality may not hold strictly. See also metric space, distance, and GIS.