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Numerical methods for the reconstruction of fossil material in three dimensions

Published online by Cambridge University Press:  01 May 2009

J. H. Doveton
Affiliation:
Kansas Geological Survey, 1930 Avenue ‘A’, Campus West, The University of Kansas, Lawrence, Kansas 66044, USA

Summary

Distances measured between homologous reference points on fragmentary fossil material can be used to recover a three-dimensional framework by operations of standard matrix algebra. A procedure that combines both linear and non-linear algorithms is described and illustrated in a simple reconstruction of Waptia fieldensis. The approach attempts to provide a modelling process in which a palaeontologist can explore the geometrical consequences of fossil measurements through continuous interaction with programmed reconstructions.

Type
Articles
Copyright
Copyright © Cambridge University Press 1979

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References

Ahuja, D. V. & Coons, S. A. 1968. Geometry for construction and display. IBM Systems 7, 188205.CrossRefGoogle Scholar
Brower, J. C. 1973. Ontogeny of a Miocene pelecypod. J. Int. Ass. Math. Geol. 5, 7390.CrossRefGoogle Scholar
Coons, S. A. 1967. Surfaces for computer-aided design of space forms. MIT Tech. Rep. MAC-TR-41.CrossRefGoogle Scholar
Davis, J. C. 1973. Statistics and Data Analysis in Geology. New York: John Wiley.Google Scholar
Golledge, R. G. & Rushton, G. 1972. Multidimensional Scaling: Review and Geographical Applications, Tech. Paper Ass. Am. Geogr. no. 10.Google Scholar
Gould, P. 1967. On the geographic interpretation of eigenvalues: an initial exploration. Trans. Inst. Br. Geogr. 42, 5386.CrossRefGoogle Scholar
Gould, S. J. 1967. Evolutionary patterns in pelycosaurian reptiles; a factor analytical study. Evolution. 21, 385401.CrossRefGoogle Scholar
Howarth, R. J. 1973. Preliminary assessment of a non-linear mapping algorithm in a geological context. J. Int. Ass. Math. Geology 5, 3957.CrossRefGoogle Scholar
Meyrink, G. 1915. Der Golem, trans. Pemberton, M. 1928. Boston: Houghton Mifflin.Google Scholar
Rogers, D. F. & Adams, J. A. 1976. Mathematical Elements for Computer Graphics. New York: McGraw-Hill.Google Scholar
Sammon, J. W. Jr. 1969. A non-linear mapping for data structure analysis. IEEE Trans. Computers C-18 5, 401–9.CrossRefGoogle Scholar
Scheidegger, A. E. 1965. On the statistics of the orientation of bedding planes, grain axes, and similar sedimentological data. Prof. Pap. U.S. geol. Surv. 525-C, 164–7.Google Scholar
Tipper, J. C. 1976. The study of geological objects in three dimensions by the computerized reconstruction of serial sections. J. Geol. 84, 476484.CrossRefGoogle Scholar
Tipper, J. C. 1977. Three dimensional analysis of geological forms. J. Geol. 85, 591611.CrossRefGoogle Scholar
Torgerson, W. S. 1958. Theory and Methods of Scaling. New York: John Wiley.Google Scholar
Westbroek, P. & Hesper, B. (in press). Computer-mediated storage and steric respresentation of serial sections.Google Scholar
Woodcock, N. H. 1977. Specification of fabric shapes using an eigenvalue method. Bull. geol. Soc. Am. 88, 1231–6.2.0.CO;2>CrossRefGoogle Scholar