A world map demonstrating different cartographic projections and their distortion characteristics. This visualization showcases how the same geographic data appears under various map projections (Mercator, Robinson, Mollweide, Orthographic, etc.), revealing how each projection preserves or distorts area, shape, distance, or direction. The plot includes graticule (latitude/longitude grid lines) and optionally Tissot indicatrices to illustrate projection distortion patterns.
#' anyplot.ai
#' map-projections: World Map with Different Projections
#' Library: ggplot2 3.5.1 | R 4.4.1
#' Quality: 85/100 | Created: 2026-05-23
library(ggplot2)
library(maps)
library(ragg)
# Theme tokens
THEME <- Sys.getenv("ANYPLOT_THEME", "light")
PAGE_BG <- if (THEME == "light") "#FAF8F1" else "#1A1A17"
INK <- if (THEME == "light") "#1A1A17" else "#F0EFE8"
INK_SOFT <- if (THEME == "light") "#4A4A44" else "#B8B7B0"
OCEAN_BG <- if (THEME == "light") "#C4DCF0" else "#152030"
LAND_BG <- if (THEME == "light") "#D4C9A8" else "#2A3020"
IMPRINT <- c(
"#009E73", "#C475FD", "#AE3030", "#4467A3",
"#99B314", "#954477", "#BD8233"
)
# --- Mollweide projection math -----------------------------------------------
# Solve 2*theta + sin(2*theta) = pi*sin(lat) via Newton-Raphson
solve_theta <- function(phi_vec) {
sapply(phi_vec, function(p) {
if (is.na(p)) return(NA_real_)
if (abs(p) >= pi / 2 - 1e-9) return(sign(p) * pi / 2)
t <- p
for (i in seq_len(60)) {
delta <- (2 * t + sin(2 * t) - pi * sin(p)) / (2 + 2 * cos(2 * t))
t <- t - delta
if (abs(delta) < 1e-11) break
}
t
})
}
mollweide <- function(lon_deg, lat_deg) {
lon <- lon_deg * pi / 180
lat <- lat_deg * pi / 180
theta <- solve_theta(lat)
data.frame(
x = (2 * sqrt(2) / pi) * lon * cos(theta),
y = sqrt(2) * sin(theta)
)
}
# --- World country boundaries (projected) ------------------------------------
world <- map_data("world")
world_proj <- mollweide(world$long, world$lat)
world$x <- world_proj$x
world$y <- world_proj$y
# --- Projection boundary (Mollweide ellipse: a=2√2, b=√2) -------------------
t_ell <- seq(0, 2 * pi, length.out = 721)
boundary <- data.frame(
x = 2 * sqrt(2) * cos(t_ell),
y = sqrt(2) * sin(t_ell)
)
# --- Graticule (lat/lon grid at 30° intervals) --------------------------------
lat_dense <- seq(-90, 90, length.out = 541)
lon_dense <- seq(-180, 180, length.out = 1081)
meridians <- do.call(rbind, lapply(seq(-180, 180, by = 30), function(lon0) {
pts <- mollweide(rep(lon0, length(lat_dense)), lat_dense)
data.frame(x = pts$x, y = pts$y, group = paste0("mer_", lon0))
}))
parallels <- do.call(rbind, lapply(seq(-90, 90, by = 30), function(lat0) {
pts <- mollweide(lon_dense, rep(lat0, length(lon_dense)))
data.frame(x = pts$x, y = pts$y, group = paste0("par_", lat0))
}))
graticule <- rbind(meridians, parallels)
# --- Tissot indicatrices (small geodesic circles on the sphere) ---------------
# Radius in degrees; longitude offset corrected for latitude (cos projection)
r_deg <- 5
t_circle <- seq(0, 2 * pi, length.out = 73) # 73 pts → closed polygon
lat_centers <- seq(-60, 60, by = 30) # 5 latitude bands
lon_centers <- seq(-150, 150, by = 60) # 6 longitude positions
tissot <- do.call(rbind, lapply(lat_centers, function(lat0) {
cos_lat <- max(cos(lat0 * pi / 180), 0.08)
do.call(rbind, lapply(lon_centers, function(lon0) {
lon_c <- lon0 + r_deg * cos(t_circle) / cos_lat
lat_c <- pmax(pmin(lat0 + r_deg * sin(t_circle), 89.9), -89.9)
pts <- mollweide(lon_c, lat_c)
data.frame(
x = pts$x,
y = pts$y,
group = paste0("t_", lon0, "_", lat0)
)
}))
}))
# --- Equator and prime meridian highlights -----------------------------------
equator <- mollweide(lon_dense, rep(0, length(lon_dense)))
equator$group <- "equator"
prime_merid <- mollweide(rep(0, length(lat_dense)), lat_dense)
prime_merid$group <- "prime"
# --- Plot --------------------------------------------------------------------
p <- ggplot() +
# Ocean fill
geom_polygon(
data = boundary, aes(x = x, y = y),
fill = OCEAN_BG, color = NA
) +
# Land masses (country polygons)
geom_polygon(
data = world, aes(x = x, y = y, group = group),
fill = LAND_BG, color = NA
) +
# Country borders / coastlines
geom_path(
data = world, aes(x = x, y = y, group = group),
color = INK_SOFT, linewidth = 0.10, alpha = 0.55
) +
# Standard graticule (30° grid)
geom_path(
data = graticule, aes(x = x, y = y, group = group),
color = INK_SOFT, linewidth = 0.18, alpha = 0.45
) +
# Equator and prime meridian — slightly bolder
geom_path(
data = equator, aes(x = x, y = y, group = group),
color = INK_SOFT, linewidth = 0.35, alpha = 0.70
) +
geom_path(
data = prime_merid, aes(x = x, y = y, group = group),
color = INK_SOFT, linewidth = 0.35, alpha = 0.70
) +
# Tissot indicatrices — anyplot brand green (position 1)
geom_polygon(
data = tissot, aes(x = x, y = y, group = group),
fill = IMPRINT[1], color = PAGE_BG,
linewidth = 0.06, alpha = 0.78
) +
# Ellipse outline
geom_path(
data = boundary, aes(x = x, y = y),
color = INK_SOFT, linewidth = 0.40
) +
coord_fixed() +
labs(
title = "map-projections · r · ggplot2 · anyplot.ai",
subtitle = "Mollweide equal-area projection · Tissot indicatrices (green) confirm equal-area: every circle covers identical surface"
) +
theme_void(base_size = 8) +
theme(
plot.background = element_rect(fill = PAGE_BG, color = PAGE_BG),
plot.title = element_text(
color = INK, size = 12, hjust = 0.5,
margin = margin(t = 14, b = 6)
),
plot.subtitle = element_text(
color = INK_SOFT, size = 9.5, hjust = 0.5,
margin = margin(b = 12)
),
plot.margin = margin(8, 50, 12, 50)
)
# --- Save --------------------------------------------------------------------
ggsave(
filename = sprintf("plot-%s.png", THEME),
plot = p,
device = ragg::agg_png,
width = 8,
height = 4.5,
units = "in",
dpi = 400
)
Part of World Map with Different Projections on anyplot.ai.