We define four complex numbers representing the parameters needed to specify an elephantine shape. The real and imaginary parts of these complex numbers are the coefficients of a Fourier coordinate expansion, a powerful tool for reducing the data required to define shapes.
REFERENCES
1.
F.
Dyson
, “A meeting with Enrico Fermi
,” Nature (London)
427
(6972
), 297
(2004
).2.
F. P.
Kuhl
and C. R.
Giardina
, “Elliptic Fourier features of a closed contour
,” Comput. Graph. Image Process.
18
, 236
–258
(1982
).3.
G.
Székely
, A.
Kelemen
, C.
Brechbühler
, and G.
Gerig
, “Segmentation of 2D and 3D objects from MRI volume data using constrained elastic deformations of flexible Fourier contour and surface models
,” Med. Image Anal.
1
(1
), 19
–34
(1996
).4.
K.
Khairy
and J.
Howard
, “Spherical harmonics-based parametric deconvolution of 3D surface images using bending energy minimization
,” Med. Image Anal.
12
(2
), 217
–227
(2008
).5.
The interactive Java applet written by
Rosemary
Kennett
, ⟨physics.syr.edu/courses/java/demos/kennett/Epicycle/Epicycle.html⟩.6.
Interactive Java applet of elliptic descriptors by
F.
Puente León
, ⟨www.vms.ei.tum.de/lehre/vms/fourier/⟩.7.
8.
See supplementary material at http://dx.doi.org/10.1119/1.3254017 for the movie showing the wiggling trunk.
© 2010 American Association of Physics Teachers.
2010
American Association of Physics Teachers
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