These representations of China are from Joseph Needham's Science and Civilization in China.

A schematic of the Empire

"The traditional conception of the radiation of ancient Chinese culture from its imperial centre (from the Shi Ching Thu Shuo). Proceeding outward from the metropolitan area, we have in concentric rectangles, (a) the royal domains, (b) the lands of the tributary feudal princes and lords, (c) the 'zone of pacification', i.e., the marches, where Chinese civilization was in course of adoption, (d) the zone of allied barbarians, (e) the zone of cultureless savagery..."
(from The Shorter Science & Civilization in China, vol 2 pg. 239)

Map of the Tracks of Yü the Great, ca. 1100 AD

(pg. 266)