Minimum-distortion continuous cartograms by numerically optimized meshes

TL;DR

An algorithm for creating contiguous cartograms using meshes that uses numerical optimization to minimize cartographic error and distortion by transforming the mesh vertices, and presents a hybrid "best of both worlds" method.

Abstract

We present an algorithm for creating contiguous cartograms using meshes. We use numerical optimization to minimize cartographic error and distortion by transforming the mesh vertices. The vertices can either be optimized in the plane or optimized on the unit sphere and subsequently projected to the plane. We also present a hybrid "best of both worlds" method, where the vertices are optimized on the sphere while anticipating the distortion caused by the final projection to the plane. We show a significant improvement in the preservation of region shapes compared to existing automated methods. Outside the realm of cartograms, we apply this hybrid technique to optimized map projections, creating the Liquid Earth projection.

Figures (11)

• Figure 1: Part of the initial mesh and transformed mesh. Notice how the movement of the mesh vertices shrinks Ireland and Iceland.
• Figure 2: Comparison of shape preservation between the rubber-sheet method (left) and our mesh method (right). The mesh method preserves shapes as much as possible while preserving the connections (or near-connections) to adjacent landmasses. Rubber-sheet examples created with the program F4Carto by Sun odcn-c.
• Figure 3: The initial mesh before and after subdivision.
• Figure 4: A plane cartogram.
• Figure 5: A sphere cartogram shown in orthographic view and projected using the Mollweide projection.