Area Computation by Coordinates

Area computation by coordinates has become the conventional method for application purposes. The structure and forms of the equations used for this method are investigated in this study. Various factors that result in a negative value of the computed area are also explored. Examples are provided to illustrate that the value of area is independent of the location of origin. If sign conventions are followed faithfully in various quadrants, the numerical answer will be the same. Traditionally, a negative area is considered as meaningless. This article demonstrated some potentially useful information provided by the sign of the area. To improve accuracy, two interpolation schemes, cubic spline and Akima's 1970 quasi-Hermite spline, are tested with numerical examples. For the limited examples experienced, both algorithms have demonstrated the potential for accuracy improvement. However, there is no conclusive evidence on which algorithm is the better one.