A triangle-based logic for affine-invariant querying of spatial and spatio-temporal data

TL;DR

This paper introduces a triangle-based query language for spatial and spatio-temporal databases that is affine-invariant, expressive, and intuitive, addressing issues of incompatibility due to coordinate system differences.

Contribution

It proposes a novel triangle logic that is affine-generic, expressive like first-order logic over reals, and suitable for spatial and spatio-temporal data.

Findings

The triangle logic is affine-invariant and expressive.

It matches the expressive power of affine-generic first-order logic.

The language is simple and intuitive for practical use.

Abstract

In spatial databases, incompatibilities often arise due to different choices of origin or unit of measurement (e.g., centimeters versus inches). By representing and querying the data in an affine-invariant manner, we can avoid these incompatibilities. In practice, spatial (resp., spatio-temporal) data is often represented as a finite union of triangles (resp., moving triangles). As two arbitrary triangles are equal up to a unique affinity of the plane, they seem perfect candidates as basic units for an affine-invariant query language. We propose a so-called "triangle logic", a query language that is affine-generic and has triangles as basic elements. We show that this language has the same expressive power as the affine-generic fragment of first-order logic over the reals on triangle databases. We illustrate that the proposed language is simple and intuitive. It can also serve as a first step towards a "moving-triangle logic" for spatio-temporal data.