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Article: A description of the generating curve of bivalves with straight hinges

Publication: Palaeontology
Volume: 25
Part: 1
Publication Date: January 1982
Page(s): 109 117
Author(s): Margaret Jennifer Rogers
Addition Information

How to Cite

ROGERS, M. 1982. A description of the generating curve of bivalves with straight hinges. Palaeontology25, 1, 109–117.

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The Palaeontological Association (Free Access)


A method of describing the whole of the generating curve of a lamellibranch is sought. When lengths and angles are used to describe an outline, much of the outline remains undefined. A curve can be fitted to an outline and the coefficients in the particular approximation employed then define the outline. Reasons are given for fitting a Tchebychev polynominal, rather than a spline, or Fourier series containing both sine and cosine terms. Polar coordinates r and 6 are calculated for each point on a digitized outline. Cos 6, rather than 6 is chosen as the independent variable when the Tchebychev coefficients are calculated. It is found that about 100 irregular spaced data points are required to produce stable coefficients, and that adequate numerical accuracy is obtained when the outline is described by the first six coefficients. These six coefficients can also be used as shape discriminators. As the value of c0 is a measure of size, it can be used to standardize the other coefficients. The standardized coefficients can be used to compare the shape of the generating curve of shells of different sizes.
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