Since Starship has to feed its engines in two kind of situations :
-during ascent, acceleration is colinear to Starship's longitudinal axis.
-at the end of the belly dive, acceleration is normal to Starship's longitudinal axis.
Why is the bottom of both LOX and LCH4 tanks curved the way they are? At first glance it looks like having a central piping/engine feeding, is the most efficient and safest solution to feed engines during ascent, yet it requires using header tanks to restart after belly dive.
Wouldn't a reversed curvature combined with radial feeding allow the engines to work in both configurations, without needing header tanks? (radial feeding located at belly side)