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: makie 0.22.10 | Julia 1.11.9
# Quality: 86/100 | Created: 2026-05-23
using CairoMakie
using Colors
using Random
Random.seed!(42)
const THEME = get(ENV, "ANYPLOT_THEME", "light")
const PAGE_BG = THEME == "light" ? colorant"#FAF8F1" : colorant"#1A1A17"
const ELEVATED_BG = THEME == "light" ? colorant"#FFFDF6" : colorant"#242420"
const INK = THEME == "light" ? colorant"#1A1A17" : colorant"#F0EFE8"
const INK_SOFT = THEME == "light" ? colorant"#4A4A44" : colorant"#B8B7B0"
const BRAND = colorant"#009E73"
d2r(x) = x * π / 180.0
# --- Projection functions ---
function proj_mercator(lon_deg, lat_deg)
lat = clamp(lat_deg, -85.0, 85.0)
return d2r(lon_deg), log(tan(π / 4 + d2r(lat) / 2))
end
function mollweide_theta(lat_deg)
abs(lat_deg) >= 89.9 && return sign(lat_deg) * (π / 2)
phi = d2r(lat_deg)
theta = phi
rhs = π * sin(phi)
for _ in 1:60
denom = 2.0 + 2.0 * cos(2theta)
abs(denom) < 1e-14 && break
theta -= (2theta + sin(2theta) - rhs) / denom
end
return theta
end
function proj_mollweide(lon_deg, lat_deg)
theta = mollweide_theta(lat_deg)
return (2sqrt(2) / π) * d2r(lon_deg) * cos(theta), sqrt(2) * sin(theta)
end
function proj_orthographic(lon_deg, lat_deg)
lam = d2r(lon_deg)
phi = d2r(lat_deg)
cos(phi) * cos(lam) < 0.0 && return (NaN, NaN)
return cos(phi) * sin(lam), sin(phi)
end
const EE_M = sqrt(3.0) / 2.0
const EE_A1 = 1.340264
const EE_A2 = -0.081106
const EE_A3 = 0.000893
const EE_A4 = 0.003796
function proj_equal_earth(lon_deg, lat_deg)
lam = d2r(lon_deg)
phi = d2r(lat_deg)
theta = asin(clamp(EE_M * sin(phi), -1.0, 1.0))
theta2 = theta * theta
P = EE_A1 + theta2 * (EE_A2 + theta2 * (EE_A3 + theta2 * EE_A4))
return lam * cos(theta) / (EE_M * P), theta * P
end
# --- Simplified continent outlines (lon, lat) in degrees, roughly clockwise ---
const CONTINENT_POLYS = [
# Africa
[(-5.4,36.0),(10.0,37.3),(12.0,33.0),(25.0,31.3),(32.5,31.0),
(36.5,22.0),(43.0,14.8),(50.0,11.8),(42.5,11.5),(42.0,0.0),
(40.5,-10.0),(35.5,-20.0),(33.0,-27.0),(26.5,-30.8),(18.8,-34.8),
(16.5,-29.5),(12.5,-17.0),(9.5,-5.5),(8.5,1.0),(2.5,4.8),
(-3.0,4.8),(-8.5,4.5),(-15.0,11.0),(-17.5,14.7),(-17.0,21.0),
(-13.0,27.7),(-5.4,36.0)],
# Eurasia (simplified — Malay Peninsula omitted for clean outline)
[(-9.0,37.0),(-4.5,48.5),(2.0,51.0),(8.0,57.5),(17.5,57.5),
(22.0,59.5),(28.0,65.5),(32.0,70.0),(50.0,74.0),(80.0,74.0),
(110.0,73.5),(130.0,72.5),(143.0,70.0),(141.0,52.0),(135.5,43.0),
(130.5,35.5),(121.5,29.5),(114.0,21.5),(105.0,10.0),(80.0,9.0),
(77.5,8.5),(80.0,22.0),(68.0,22.0),(61.0,24.0),(55.5,23.0),
(44.0,12.0),(43.5,11.5),(45.0,15.0),(37.0,22.0),(32.5,29.0),
(34.5,36.5),(36.0,36.5),(29.5,41.0),(26.5,41.5),(22.0,40.0),
(14.5,40.5),(13.0,38.0),(13.0,44.5),(7.5,44.0),(1.5,43.5),
(-2.5,44.0),(-9.0,37.0)],
# North America
[(-168.0,71.0),(-140.0,72.5),(-100.0,73.0),(-80.0,73.0),
(-65.0,63.0),(-53.0,47.0),(-66.5,44.5),(-70.5,43.0),
(-75.5,35.0),(-81.0,25.0),(-87.0,16.0),(-83.5,10.5),
(-77.5,8.0),(-84.0,10.0),(-90.0,14.0),(-97.0,19.0),
(-104.0,19.0),(-110.0,23.5),(-118.0,32.0),(-120.5,34.5),
(-124.0,46.0),(-130.0,55.0),(-137.0,60.0),(-152.0,60.0),
(-165.0,62.0),(-168.0,65.0),(-168.0,71.0)],
# South America
[(-80.0,8.0),(-75.0,10.5),(-63.0,10.5),(-60.0,6.5),
(-51.0,4.0),(-50.0,0.0),(-51.0,-3.0),(-36.0,-5.0),
(-35.0,-8.0),(-37.5,-12.0),(-39.0,-23.0),(-43.0,-23.0),
(-48.0,-28.5),(-52.0,-34.0),(-58.0,-34.0),(-62.0,-38.0),
(-65.0,-40.0),(-65.5,-45.0),(-65.5,-55.0),(-68.5,-54.5),
(-73.0,-50.0),(-75.0,-42.0),(-72.0,-36.0),(-72.0,-30.0),
(-70.0,-18.0),(-76.0,-2.0),(-80.0,0.0),(-80.0,8.0)],
# Australia
[(114.0,-22.0),(114.0,-34.0),(117.0,-35.5),(122.0,-34.0),
(126.0,-34.0),(131.0,-31.0),(132.0,-29.0),(125.0,-14.0),
(130.0,-12.0),(136.0,-12.0),(137.0,-16.0),(141.0,-16.0),
(145.0,-14.5),(146.5,-19.0),(149.0,-21.0),(153.5,-28.0),
(152.0,-33.0),(150.5,-37.0),(148.0,-38.5),(146.0,-39.0),
(143.5,-39.0),(141.0,-38.5),(132.0,-33.0),(126.0,-34.0),
(122.0,-34.0),(117.0,-35.5),(114.0,-34.0),(114.0,-22.0)],
# Antarctica — coastal ring then south-pole closure
[(-180.0,-70.0),(-170.0,-72.0),(-160.0,-70.0),(-150.0,-68.0),
(-140.0,-70.0),(-130.0,-72.0),(-120.0,-70.0),(-110.0,-68.0),
(-100.0,-70.0),(-90.0,-72.0),(-80.0,-70.0),(-70.0,-68.0),
(-60.0,-70.0),(-50.0,-72.0),(-40.0,-70.0),(-30.0,-68.0),
(-20.0,-70.0),(-10.0,-72.0),(0.0,-70.0),(10.0,-68.0),
(20.0,-70.0),(30.0,-72.0),(40.0,-70.0),(50.0,-68.0),
(60.0,-70.0),(70.0,-72.0),(80.0,-70.0),(90.0,-68.0),
(100.0,-70.0),(110.0,-72.0),(120.0,-70.0),(130.0,-68.0),
(140.0,-70.0),(150.0,-72.0),(160.0,-70.0),(170.0,-68.0),
(180.0,-70.0),(90.0,-89.9),(0.0,-89.9),(-90.0,-89.9),
(-180.0,-70.0)],
# Greenland (illustrates Mercator distortion)
[(-44.0,83.0),(-18.0,77.0),(-12.0,76.0),(-18.0,73.0),
(-27.5,71.0),(-25.0,69.0),(-17.0,67.5),(-22.0,65.0),
(-25.0,65.0),(-38.0,65.5),(-45.0,60.5),(-52.0,66.0),
(-57.0,68.0),(-60.0,72.0),(-67.0,77.0),(-68.0,80.0),
(-60.0,83.0),(-44.0,83.0)],
]
# --- Drawing helpers ---
function draw_lines_nan!(ax, xs, ys; color, linewidth)
n = length(xs)
i = 1
while i <= n
if !isnan(xs[i]) && !isnan(ys[i])
j = i + 1
while j <= n && !isnan(xs[j]) && !isnan(ys[j])
j += 1
end
j > i + 1 && lines!(ax, xs[i:j-1], ys[i:j-1]; color=color, linewidth=linewidth)
i = j
else
i += 1
end
end
end
function draw_continents!(ax, proj_fn; fill_color, stroke_color)
for poly_ll in CONTINENT_POLYS
pts = Point2f[]
for (lon, lat) in poly_ll
x, y = proj_fn(lon, lat)
!isnan(x) && !isnan(y) && push!(pts, Point2f(x, y))
end
length(pts) >= 3 && poly!(ax, pts;
color=fill_color,
strokecolor=stroke_color,
strokewidth=0.7)
end
end
function draw_graticule!(ax, proj_fn; lon_step=30, lat_step=30, n_pts=200,
color=BRAND, linewidth=0.7)
for lon in -180:lon_step:180
lats = range(-89.9, 89.9; length=n_pts)
xs = Float64[]; ys = Float64[]
for lat in lats
x, y = proj_fn(lon, lat)
push!(xs, x); push!(ys, y)
end
draw_lines_nan!(ax, xs, ys; color=color, linewidth=linewidth)
end
for lat in -90:lat_step:90
lons = range(-180, 180; length=n_pts)
xs = Float64[]; ys = Float64[]
for lon in lons
x, y = proj_fn(lon, lat)
push!(xs, x); push!(ys, y)
end
draw_lines_nan!(ax, xs, ys; color=color, linewidth=linewidth)
end
end
function draw_tissot!(ax, proj_fn; fill_color=BRAND, r_deg=7.0, n_pts=60)
for lon in -150:60:150, lat in -60:30:60
cos_lat = max(cosd(lat), 0.01)
pts = Point2f[]
any_nan = false
for k in 0:n_pts-1
ang = 2π * k / n_pts
x, y = proj_fn(lon + r_deg * sin(ang) / cos_lat,
clamp(lat + r_deg * cos(ang), -89.0, 89.0))
if isnan(x) || isnan(y)
any_nan = true
else
push!(pts, Point2f(x, y))
end
end
!any_nan && length(pts) >= 3 && poly!(ax, pts;
color=(fill_color, 0.20f0),
strokecolor=(fill_color, 0.85f0),
strokewidth=0.9)
end
end
# --- Projection boundary shapes ---
function boundary_rect(x0, x1, y0, y1)
[Point2f(x0, y0), Point2f(x1, y0), Point2f(x1, y1), Point2f(x0, y1)]
end
function boundary_ellipse(a, b; n=300)
ts = range(0, 2π; length=n)
[Point2f(a * cos(t), b * sin(t)) for t in ts]
end
function boundary_equal_earth(; n=200)
lats = collect(range(-90, 90; length=n))
right = [Point2f(proj_equal_earth(180, lat)...) for lat in lats]
top_pole = [Point2f(proj_equal_earth(lon, 90)...) for lon in range(180, -180; length=60)]
left = [Point2f(proj_equal_earth(-180, lat)...) for lat in reverse(lats)]
bot_pole = [Point2f(proj_equal_earth(lon, -90)...) for lon in range(-180, 180; length=60)]
vcat(right, top_pole, left, bot_pole)
end
# --- Layout ---
const merc_y85 = proj_mercator(0, 85.0)[2]
const grat_alpha = THEME == "light" ? 0.55f0 : 0.70f0
const grat_color = RGBAf(Float32(BRAND.r), Float32(BRAND.g), Float32(BRAND.b), grat_alpha)
const bord_color = RGBAf(Float32(INK_SOFT.r), Float32(INK_SOFT.g), Float32(INK_SOFT.b), 1.0f0)
const land_stroke = RGBAf(Float32(INK_SOFT.r), Float32(INK_SOFT.g), Float32(INK_SOFT.b), 0.8f0)
fig = Figure(size=(1600, 900), fontsize=14, backgroundcolor=PAGE_BG)
Label(fig[0, 1:2];
text="map-projections · julia · makie · anyplot.ai",
fontsize=20, color=INK, tellwidth=false, padding=(0, 0, 6, 0))
specs = [
(proj_mercator, "Mercator — Conformal", 1, 1,
boundary_rect(-π, π, -merc_y85, merc_y85),
(-π * 1.06, π * 1.06, -merc_y85 * 1.08, merc_y85 * 1.08)),
(proj_mollweide, "Mollweide — Equal-Area", 1, 2,
boundary_ellipse(2sqrt(2), sqrt(2)),
(-3.05, 3.05, -1.52, 1.52)),
(proj_orthographic, "Orthographic — Perspective", 2, 1,
boundary_ellipse(1.0, 1.0),
(-1.12, 1.12, -1.12, 1.12)),
(proj_equal_earth, "Equal Earth — Equal-Area", 2, 2,
boundary_equal_earth(),
(-2.9, 2.9, -1.48, 1.48)),
]
for (proj_fn, title, row, col, bnd_pts, (xlo, xhi, ylo, yhi)) in specs
ax = Axis(fig[row, col];
title = title,
titlesize = 16,
titlecolor = INK,
backgroundcolor = PAGE_BG,
topspinevisible = false,
rightspinevisible = false,
leftspinevisible = false,
bottomspinevisible = false,
xticksvisible = false,
yticksvisible = false,
xticklabelsvisible = false,
yticklabelsvisible = false,
xgridvisible = false,
ygridvisible = false,
)
xlims!(ax, xlo, xhi)
ylims!(ax, ylo, yhi)
poly!(ax, bnd_pts; color=ELEVATED_BG, strokewidth=0)
draw_graticule!(ax, proj_fn; color=grat_color, linewidth=0.7)
draw_continents!(ax, proj_fn; fill_color=ELEVATED_BG, stroke_color=land_stroke)
draw_tissot!(ax, proj_fn; fill_color=BRAND)
poly!(ax, bnd_pts; color=(:white, 0.0f0), strokecolor=bord_color, strokewidth=1.5)
end
rowgap!(fig.layout, 8)
colgap!(fig.layout, 8)
save("plot-$(THEME).png", fig; px_per_unit=2)
Part of World Map with Different Projections on anyplot.ai.