No True North — Daegeun Kim

No True North
Redefined World Map

Open Interactive Map

Github

Interactive Map · Globe Projection · Distortion Analysis

Stack:
D3.js · GeoJSON / TopoJSON · Vanilla JavaScript

Project Overview

This project investigates how the world map changes when the idea of “north” is redefined.

A world map is not a fixed image. It is the result of several decisions: how the globe is oriented, where the map is cut, which projection surface is used, and which distortion is accepted.

This project turns those decisions into an interactive system. Users can select a new north pole, rotate the Earth accordingly, choose a projection type, adjust the seam location, and compare how different maps distort country size and shape.

The project is structured around two main ideas. Projection: how a 3D globe becomes a 2D map. Distortion: what changes during that transformation. The goal is to make the hidden geometry of map projection visible and measurable.

Projection

A projection transforms the spherical surface of the Earth into a flat 2D map. This project explains projection through three geometric surfaces: cylinder, cone, and plane.

Cylindrical

Cylindrical projections place a cylinder around the globe, project the Earth onto the cylinder, and unroll it into a rectangular map. Examples include Mercator, Gall–Peters, and Equirectangular.

Conic

Conic projections place a cone over the globe, project the Earth onto the cone, and unfold it into a flat surface. Examples include Lambert Conformal Conic, Conic Equal Area, and Conic Equidistant.

Azimuthal

Azimuthal projections place a plane tangent to the globe. The point of contact becomes the center of the map. Examples include Azimuthal Equidistant, Lambert Azimuthal Equal-Area, Orthographic, and Stereographic.

In this project, the projection is not only determined by the formula. It is also affected by the orientation of the globe before the projection is applied.

Globe with original north pole orientation

Original orientation

Redefined north

After rotation

The globe remains physically identical, but the coordinate system and pole definition change.

Redefining North

The central idea of the project is that the north pole does not have to remain fixed.

In a conventional world map, the geographic North Pole defines the orientation of the map. This creates the familiar north-up world layout. In this project, the user can choose any location on Earth as the new north pole. The globe is rotated so that the selected location becomes the new pole before the selected projection is applied.

The process: start with the original globe → select a new north pole → rotate the globe so that the selected location becomes the new pole → apply the selected projection → generate a new 2D world map.

This shows that the familiar world map is not only a result of projection type. It is also a result of orientation. Changing the north pole changes which regions appear central, peripheral, continuous, divided, stretched, or compressed.

Default north pole

Redefined north pole

The same equirectangular projection changes dramatically when the north pole is redefined.

Seam Selection

Some projection types require a seam. The seam is the longitude where the world map is cut open. It is especially relevant for cylindrical, pseudocylindrical, and conic projections.

By default, the seam is placed at 180° longitude, the antimeridian. The project allows the user to change the seam location through a controlled seam selection mode. Horizontal scrolling is removed because scrolling can visually shift the map without changing the underlying projection calculation. Instead, the seam is treated as an explicit projection parameter.

The seam affects how the map is visually cut, but it does not affect the measured distortion of a country. If a country is split by the seam, all visible parts of that country keep the same distortion value. Distortion is calculated from the full country geometry, not from seam-clipped fragments.

Distortion

Every flat world map distorts the globe. Because the Earth is spherical, it cannot be flattened into a plane while preserving every geometric property. A projection must sacrifice something.

This project focuses on two types of distortion. Size distortion measures how much larger or smaller a country appears compared to its true area. Shape distortion measures how much the outline of a country changes after size difference is removed.

The two measurements are separated because different projections preserve different properties. The project does not treat distortion as one general error—it separates distortion into measurable components.

Mercator projection with redefined north pole showing size distortion

Mercator — low shape distortion, high size distortion near poles

Gall-Peters projection showing shape distortion

Gall–Peters — low size distortion, high shape distortion

Different projections sacrifice different properties: Mercator preserves local shape but distorts size; Gall–Peters preserves area but distorts shape.

Size Distortion

Size distortion measures how much a country’s displayed area differs from its true geographic area.

This addresses a common issue in world maps: high-latitude countries can appear much larger than they actually are. In Mercator, Greenland appears visually enormous even though its real area is much smaller than Africa and smaller than it appears relative to Australia.

Size distortion example: Greenland on Mercator projection

Greenland on Mercator — a classic example of size distortion at high latitudes.

Size distortion is calculated as:

sizeRatio = currentProjectedCountryArea / trueOrEqualAreaReferenceCountryArea
sizeDistortion = abs(log(sizeRatio))

A sizeRatio of 1.0 means the country appears at its correct area. A ratio of 2.0 means the country appears twice as large as its reference area. A ratio of 0.5 means the country appears half as large. Using abs(log(sizeRatio)) makes enlargement and shrinkage symmetric—a country shown as 2× too large and a country shown as 0.5× too small receive the same distortion magnitude.

The reference area is not the country’s smallest possible appearance in the projection. The reference is the country’s true area, approximated through spherical area or a local equal-area projection. This is important because the smallest projected version of a country is not necessarily the correct version: some projections may shrink regions, so the smallest appearance cannot be treated as the accurate baseline. The intended question is: how large does this country appear compared to its true area?

Shape Distortion

Shape distortion measures how much a country’s outline changes after size difference is removed.

This separation is essential. If two projected country shapes are compared directly without size normalization, size distortion incorrectly affects shape distortion. For example, Mercator enlarges high-latitude countries. If the enlarged country outline is directly compared with a reference outline, it may appear to have high shape distortion even though Mercator preserves local shape. To avoid this, shape distortion is calculated after normalizing size.

Shape distortion example: Russia outline comparison

Russia’s outline compared across projections after size normalization.

Shape distortion process:

01 Project the country using the current map projection.
02 Project the same country using a local reference projection.
03 Move both shapes to the same centroid.
04 Scale both shapes to the same area.
05 Align the shapes to maximize overlap.
06 Calculate the maximum IoU (intersection over union).
07 Compute shape distortion from the similarity score.

shapeSimilarity = maxIoU(normalizedCurrentShape, normalizedReferenceShape)
shapeDistortion = 1 − shapeSimilarity

If the normalized shapes overlap perfectly, IoU is 1 and shape distortion is 0. If the shapes overlap poorly, IoU decreases and shape distortion increases. This method ensures that shape distortion measures outline deformation, not area enlargement or shrinkage. It explains why a projection like Mercator can have high size distortion but relatively low shape distortion.

Standardized Distortion Scale

Distortion values are standardized across all projections. The project does not normalize distortion separately for each map—this was an important design decision.

If each projection used its own minimum and maximum distortion range, every projection would fill the full color range. A low-distortion projection would appear highly distorted simply because it has a relative maximum within its own map. That would answer “which countries are most distorted within this projection?”—but the project needs to answer “how distorted is this projection compared to other projections?”

Therefore, size and shape distortion use fixed global maximum values, keeping the distortion scale consistent across Mercator, Gall–Peters, conic, pseudocylindrical, and azimuthal projections.

Incorrect normalizedSize = sizeDistortion / maxSizeDistortionInCurrentMap
normalizedShape = shapeDistortion / maxShapeDistortionInCurrentMap

Correct normalizedSize = sizeDistortion / globalSizeDistortionMax
normalizedShape = shapeDistortion / globalShapeDistortionMax

Projection Tradeoffs

The distortion system reveals the tradeoff between preserving size and preserving shape. Every projection family makes a different choice.

Mercator	Preserves local shape and angles. Low shape distortion, but high size distortion near the poles.
Gall–Peters	Preserves area. Low size distortion, but high shape distortion.
Equal-area	Prioritizes correct area. Generally lower size distortion, but may deform shape.
Conformal	Prioritizes local shape and angle. Generally lower shape distortion, but may strongly distort area.
Azimuthal	Lowest distortion near the projection center. Distortion increases toward the edge, depending on the specific azimuthal method.

The purpose of the tool is not to find one correct map, but to show what each map preserves and what it sacrifices.

Methodology

The full workflow from globe to distortion-evaluated map:

01 Treat the Earth as a globe.
02 The user selects a new north pole.
03 Rotate the globe so that the selected location becomes the new north pole.
04 Apply the selected projection.
05 For seam-based projections, the seam determines where the map is cut.
06 Evaluate each country as a full geographic object.
07 Calculate size distortion from the area ratio against a true reference area.
08 Calculate shape distortion from normalized outline comparison (area equalized before comparison).
09 Apply the standardized global distortion scale across all projections.
10 Render the result with per-country distortion values.

Distortion is calculated per country, not from random Tissot circles or clipped screen fragments. The seam is ignored in distortion measurement.

Development Decisions

Each choice in the distortion system was made deliberately. These decisions define what the tool measures and what it does not.

— Distortion is measured per country. The project focuses on recognizable landmasses and how they visually change on world maps.
— The default world map is not treated as distortion-free. It is only one projection orientation among many.
— Size distortion uses true or equal-area reference area, not the smallest possible projected size.
— Shape distortion removes size difference before comparing outlines. This prevents size distortion from contaminating shape distortion.
— Distortion values use a global standardized scale, not a separate scale for each projection. This allows meaningful cross-projection comparison.
— The seam affects visual cutting only. It does not affect country distortion measurement.
— Only size and shape distortion are included. Distance, direction, and scale distortion are excluded to keep the project focused on visual perception of world maps.

Implementation

The interactive tool is implemented as a static web application. The main technical challenge is not only drawing different projections, but keeping distortion measurement consistent across projection types, pole orientations, and seam positions.

Projections	D3.js geographic projections
Country geometry	TopoJSON / GeoJSON country outlines
Globe rotation	Custom rotation for redefining the north pole
Seam control	Projection-specific seam parameter
Size distortion	Country-level area ratio against equal-area reference
Shape distortion	Country-level normalized outline comparison using max IoU
Distortion scale	Standardized global maximum, consistent across all projections
Controls	Projection type, pole location, seam position, distortion mode

Reflection

This project shows that world maps are designed systems, not neutral images.

Changing the north pole changes the structure of the map. Changing the projection changes what is preserved and what is sacrificed. Changing the seam changes where the world is cut.

By making these decisions interactive, the project reveals that the familiar world map is only one of many possible representations of the Earth. The final tool is both a projection experiment and a distortion analysis system. It shows how the globe becomes a map, and how that transformation changes the perceived size and shape of the world.