Simpson's rules (ship stability)

Simpson's rules are a set of rules used in ship stability and naval architecture, to calculate the areas and volumes of irregular figures.

[1] This is an application of Simpson's rule for finding the values of an integral, here interpreted as the area under a curve.

[5] This estimates the area in the left half of the figure for Simpson's 1st Rule while using all three pieces of data.

For instance, in the latter, Simpson's 3rd rule is used to find the volume between two co-ordinates.

To calculate the entire area / volume, Simpson's first rule is used.