A Square Equal-area Map Projection with Low Angular Distortion, Minimal Cusps, and Closed-form Solutions

TL;DR

This paper introduces a new square equal-area map projection with low angular distortion, minimal cusps, and closed-form solutions, enabling efficient real-time visualization and seamless tiling.

Contribution

It presents the first square equal-area projection combining low distortion, minimal cusps, and closed-form solutions, suitable for real-time and panoramic applications.

Findings

Lower angular distortion than previous projections

Seamless tiling enabled by quincuncial arrangement

Closed-form solutions facilitate real-time visualization

Abstract

A novel square equal-area map projection is proposed. The projection combines closed-form forward and inverse solutions with relatively low angular distortion and minimal cusps, a combination of properties not manifested by any previously published square equal-area projection. Thus, the new projection has lower angular distortion than any previously published square equal-area projection with a closed-form solution. Utilizing a quincuncial arrangement, the new projection places the north pole at the center of the square and divides the south pole between its four corners; the projection can be seamlessly tiled. The existence of closed-form solutions makes the projection suitable for real-time visualization applications, both in cartography and in other areas, such as for the display of panoramic images.