Connecting Scripts: Building bridges between Latin and Hangul

Hangul is the writing system that is unique to Korean, having been designed by King Se-jong 571 years ago. In the age of globalization, we are in need of multi-script fonts to produce multi-language documents. Hangul will often be combined with Latin, the most familiar script. How can a hangul typeface be connected to its equivalent latin, without losing its inherent nature?