The cross-section of a blade is the primary way of determining its function and place in history.
Early Viking and medieval European blades tended to have a lenticular cross-section. This type of design lacks a strong central ridge in the middle of the blade. The flexibility these blades have illustrates the purpose that they served as primarily cutting weapons that could also be used for thrusting.
With the improvement in the defensive capabilities of armor in the High and Late Middle Ages, the cross-section of the sword blade adapted to suit the needs of warriors. Swords began to favour rigidity over flexibility as more rigid blades allowed for the stronger thrusts that were used to pierce armour. These blades were made with a diamond cross-section, which could be more or less acute, depending on the purpose of the blade. Weapons such as the estoc, for example, would have little to no cutting edge, but they would be very rigid and strong on the thrust. This is opposed by the longsword which was usually a multi-purpose weapon used for both thrusting and cutting.
The diamond cross-section could also be hollow ground for greater edge sharpness and thrust efficiency, while retaining strong central ridges.