Elliptical Fourier Analysis - EFAResults Worksheet

Each row on the EFAResults worksheet (shown below in 3 panels) refers to a single valve outline.

Column A (yellowed) is used only to select valve (specimen) outlines to be reproduced from the elliptical Fourier coefficients.
Columns B through K contain descriptive, identification and processing information about each valve.
Sampling (column F) refers to the number of points in the smoothed-and-sampled outline subjected to EFA.
Length (column H) is based on the difference in the maximum and minimum x-coordinate values of rotation-standardized specimens.
Area (column I) is calculating using Eves' (1972) m
ethod for two-dimensional polygons.

Column L refers to the number of harmonics extracted in the EFA.
Columns M to ED (potentially) contain the elliptical Fourier coefficients which describe the valve; data for 3 harmonics are shown in the above panel from the worksheet. All coefficients are in sets of 4 (a, b, c, d), except those of the zeroth harmonic, a(0) and c(0), which indicate the x- and y-coordinates, respectively, of the outline centroid. If the outline has been size-normalized using the Rohlf-Archie option in the Invariance (EFA) frame, then coefficient a(1) will be 1.0, coefficients b(1) and c(1) will be zero, and the value of coefficient d(1) will indicate the ellipticity of this first harmonic ellipse.

Harmonic amplitudes are listed for each harmonic beginning in column EH; the above panel illustrates only 3 of them for 3 valves.

Updated 1 July 2009 RKE