Analysis of Artifact Shape Using Fourier Series in Closed Form

AbstractStandardized, quantified characterization of artifact shape is still problematic insofar as both intuitive shape typologies and multivariate analyses of shape attributes are limited to narrowly defined classes of artifacts exhibiting homologous morphological landmarks. The Fourier series in closed form is introduced as a mathematical description of irregular, two-dimensional shape, where the relative contributions of 20 standard components of shape, or “harmonics,” are given in a series equation which can also regenerate the shape of the artifact as precisely as required. This method permits cross-class inspection of the variance of shapes of artifacts, and lends itself to classifications of shape or to intra-class analyses of variance. The level of descriptive precision may be set by the investigator in accordance with research interests. Applications of the method to archaeological samples, and different analyses of the data generated by the method, are discussed.