Fresnel Map

The Codex Atlanticus 221v-b depicts a diagram with a set of consecutive circles. Each crescent has the same area as the central circle. Utilised by the likes of Fresnel and March, this geometric technique has been applied in multiple spheres such as architecture and civil engineering.

I utilised Fresnel’s circles as part of a novel mapping technique in which each ‘doughnut’ (or annuli) has the same area as the central circle. This visual technique, created in early 2020 during my doctoral research, is well-suited to addressing the Modifiable Areal Unit Problem (MAUP). More information can be found in my PhD thesis.

An open source R package, fmap, has been created to produce Fresnel Maps and is available on Github.

library(fmap)
library(sf)
library(dplyr)

# Load the sf datasets of cholera deaths and Soho pumps
data(cholera_deaths, soho_pumps)

# Filter the Broad Street Pump from the Soho pumps dataset
bstreet_pump <- soho_pumps %>% filter(soho.pump == "Broad Street")

# Visualise the Fresnel Map
fmap_plot(radius_inner = 125, ncircles = 8, geo_centre = bstreet_pump, geo_points = cholera_deaths, sum = "cholera.deaths")