Obtaining The Origin-Destination Matrix In Euclidean Distances By Means Of Haversine's Law For The Transport Analysis Zones (Tazs) Of The City Of San Juan De Pasto

Abstract

Intermediate Andean cities require updated and georeferenced origin-destination (O-D) matrices to support evidence-based transport planning. San Juan de Pasto, with 184 Transport Analysis Zones (ZAT) and complex topography, lacks a spatially explicit and methodologically rigorous open-access distance matrix. This research generates a 184×184 Euclidean-geodesic distance matrix through application of the Haversine law to geographic coordinates of centroids in the WGS84 system. The matrix calculates 33,856 origin-destination pairs using spherical trigonometry with Earth's mean radius of 6,371 km, producing distances with numerical tolerance below 10⁻⁶ km. Statistical analysis of 33,672 interzonal distances reveals a mean distance of 5.47 km (standard deviation 2.15 km, coefficient of variation 39.3%), characterizing a compact intermediate city with evident spatial stratification: densely occupied central core (mean <2.4 km), medium urban periphery (3–7 km) containing 39.78% of pairs, and periurban zones (>8 km) where spatial friction acts as an accessibility barrier. The matrix exhibits perfect symmetry without outliers, validating mathematical consistency and computational integrity. Results provide a homogeneous and replicable technical baseline that enables calibration of gravity models for trip distribution, calculation of cumulative accessibility indicators, evaluation of optimization scenarios for the Strategic Public Transport System (SETP), and territorial equity analysis in access to urban services. The methodology is cost-effective, open-source, and replicable in intermediate Latin American cities lacking automatic fare collection systems, establishing rigorous technical precedent that transcends geometric input to become a strategic tool underpinning sustainable, equitable, and innovative urban mobility in Andean contexts.