Using a Natural Constraint to Approximate Area and Volume

. This paper presents methods to calculate the 2D area (or the 3D volume) enclosed by a plane curve (or space surface) without analytical expression. One property of our methods is that the error of the measurement is proportional to the square of the measuring unit when the unit is small enough. Finally, we point out a property common to calculating area and volume using the corresponding algorithm. This property can be used as a constraint to increase the accuracy of the estimation. 1. Background In many engineering fields, we often need to calculate the area of a plane region or the volume of a 3D space region. Generally speaking, if we know the analytical expression of the curve bounding the plane region, we can easily calculate the area of the region by integration. The same applies to the calculation of the volume of a 3D region. But in many fields, such as computer vision or surveying and mapping, we often do not know the analytical expressions of the bounding curve for the pl..