Minimum-distortion continuous cartograms by numerically optimized meshes

TL;DR

This paper introduces a numerical optimization algorithm for creating contiguous cartograms with minimal distortion, improving shape preservation and applying the method to novel map projections like the Liquid Earth.

Contribution

It develops a hybrid mesh optimization technique that accounts for projection distortion, enhancing cartogram accuracy and introducing the Liquid Earth projection.

Findings

Significant improvement in shape preservation over existing methods

Effective hybrid sphere-plane optimization approach

Application to innovative map projections like Liquid Earth

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.