A moment based metric for 2-D and 3-D packing

The most common metric used today to evaluate the effectiveness of a packing technique is the percentage of space used. An inherent limitation of this metric is its inability to differentiate between two different packing arrangements of the same set of objects. This paper proposes an alternative metric for both the 2-D and 3-D cases, called the point moment metric, and expands on the theory behind the proposed metric. The metric is based on evaluating the compactness of the remaining free space in a packing arrangement. This measure is the ratio of a defined moment calculated for the current free space and the initial free packing space. The developed metric can be extended to N-dimensional packing problems, where N={1, 2, ... }. The arbitrary 3-D shape packing problem is used as an illustration of an application of the metric. The point moment metric has not been developed to replace the measurement of the percentage of volume used but rather to complement it by allowing efficient comparison of apparently equivalent packing arrangements using the same volume of space. It is not suited for comparing two packing arrangements occupying different volumes.