Using Delaunay Triangles To Build Desire Lines
Corresponding Author: Pedro Camargo, Veitch Lister Consulting
Presented By: Pedro Camargo, Veitch Lister Consulting
Abstract
Desire lines are still one of the most used tools for quick analysis of transportation movements and to convey “big-picture” results about such movements, especially because desire lines are independent of the existing of an underlying network, which allows for their construction before modeling networks are prepared.
Despite its usefulness, desire lines yield very poor maps when the number of filled cells in a matrix is too large, which is the case for our current transportation models with their many thousands of Traffic Analysis Zones (TAZs).
Alternatives such showing only the largest flows and aggregating matrices are resources often used by transport planners to circumvent the visualization issues caused by large and disperse matrices, but it those are resources that often consume considerable time, thus making the use of desire lines much less convenient than it was initially designed to be.
In order to circumvent the poor quality provided by these standard desire lines, this paper proposes an algorithm based on an all-or-assignment of the demand matrix onto a minimal network connecting all the centroids, instead of just generating straight lines from all origins to all destinations.
In turn, we implement this algorithm based on a novel interpretation of minimal networks, which are derived from Delaunay Triangles. This paper also discusses the impact of these new network properties in the analysis outcomes for testing cases for models available from Australia, Brazil and United States encompassing urban and regional modelling, as well as passenger and freight demand matrices.
The implementation of this resource as an open source software was made within the AequilibraE Add-on for QGIS.