THE UNIVERSITY OF CALGARY Eric Snively A ... - Ohio University

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$Introduction to Numerical Math and Matlab ... - Ohio University$

conversion. Volume-to-nuages facilitates spacing of images on the z-mis, with the units being the number of pixels. Z-axis dimensions can be fractions of a pixel, to ensure maximum fidelity to the proportions of the modeled object. The program asks for the size of each image in the x and y dimensions (in this case 512 pixels each), and then asks for the z dimension between slices. From the length of the original specimen (TMP 94.12.602), scale bars on the CT images, and the x and y pixel dimensions, I calculated the necessary z-axis spacing between images. The physical width of MT II is 7 cm at a position corresponding to slice 131. The length of the rnetatarsal is 49.9 cm, or 7.13 times 7 cm, over the distance covered by 54 slices. On slice 131, the width of the image of MT II is 1 15.45 pixels. Therefore, to calailate the length L of the 3D model in pixels: (9) Lmodel= Wirnage X 7.1 3 =823 pixels To calculate the z-axis spacing (k,) between the slices: (1 0) Gadng = Lm& slices(=54) =l5.24 pixels The result of 15.24 pixels between slices of each metatarsal ensured that the 3D model matched the proportions of the fossil. With the dimension variables entered into volume~to~nuages, I specified output file for the NUAGES edge detection and modeling software. An initial NUAGES file requires the .cnt suffix (specifying contour or edge data for the file). The resulting .cnt files for each metatarsal were then subject to processing by
this program. NUAGES typically found one curve per image or two if a medulary cavity was present in a given region of the metatamal. 4. 30 modeling and finife element mesh generation To create a 30 model fram image slices stacked along the z-axis, NUAGES formulates connectivrty between cuwes according to user-supplied commands. These commands also facilitate mesh creation. For example, the -tri command generates a tn'angular surface mesh, and tetra creates a tetrahedral volumetric rnesh. For finite element analysis, a votumetric mesh with tetrahedral elements was chosen as the reconstructed 30 model. Other commands entered into NUAGES ensured that the number of tetrahedra within the mesh was suffciently high for informative stress analysis, but low enough for efficient proœssing by MARC finite etement software. These commands were entered as preprocessing options into NUAGES (-popt in the NUAGES command Iine, followed by the appropnate commands and arguments). for example, the command -approx reduces the number of elements by deleting vertices (points in spacej. if three points form an angle that is less than a specified nurnber of degrees, one of those points is deleted. The result is a straight Iine between two vertices; the Iine becomes one side of a larger tetrahedral element. Large-scale contours are retained whenever three points subtend an angle greater than the specified amount. Therefore, if a small angle is chosen, extraneous vertices are deleted, but fidelity to the original shape is
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THE UNIVERSITY OF CALGARY Functiona
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Many figures in this thesis use col
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ACKNOWLEûGEM ENTS Many friends and
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Approval page Acknowledgements Tabi
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CONCLUDING COMMENTS Figures for Cha
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CHAPTER 5: Mechanical and phylogene
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LIST OF FIGURES Figure 1 .l. Phylog
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Figure 3.6. Osteological correlates
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AMNH GI HMN IVPP MOR NMC OMNH PIN P
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and constructional morphology revea
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1985, Bryant and Seymour 1990). If
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surfaces of a Tyrannosaurus rex spe
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3. Troodontidae (Figure 1.2): Trwdo
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Hypothesized functions of the tyran
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1. Atomization (Chapters 2 and 3).
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Figure 1.1. P hylogenetic diagram o
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Figure 1.2. Phylogenetic diagram of
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Figure 1 .S. Skeletal restorations
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did not quantify the degree of prox
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qualitative debate over arctometata
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This hypothesis focuses on tyrannos
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Table 2.1. Theropod and Plafeosauru
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specimens in the figures reflects a
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were not attempted. While this limi
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Chapter 3). 1 now address variation
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- Ç6'P 1 68'€tr 1 L'OC 99'66 L'9
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Table 2.3: Log-transformed values f
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experiences a sharp laterally indin
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ecause it can be cursorily dassifie
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arctometatarsalian specimens, the l
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) Shaf€ and region of proximal ar
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a) Ginglymus. Figure 2.14 shows the
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) Shaft and region of proximal arti
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measurements of width pV2S%TU-DE an
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Table 2.4b Variancelmeasurement eac
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the largest sum of linear measureme
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Table 2.5: Specimen statistics Herr
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and Sinraptor dongi specimens. With
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In addition, a hook like proximal a
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oth physical narrowing and elongati
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1s the MT 111 shape segregation fun
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tyrannosaurids, ornithomimid, and t
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proximal constriction, white EImisa
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Figure 2.2. Tyrannosaurid, trwdonti
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Figure 2.4. Dromaeosaurid and carno
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- Anterior (flexor) surface medial
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Figure 2.7. Left MT III of Tyrannos
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Figure 2.8. Left MT III of Gorgosau
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Figure 2.9. Left MT III of an omith
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Figure 2.10. Left metatarsus of Tmd
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Figure 2.1 1. Left MT III of Elmisa
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Figure 2.12. Right MT III of Deinon
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Figure 2.13. Left MT III of Allosau
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Figure 2.14. Left metatarsus of Sin
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Figure 2.15. Plots of MT Ill specir
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Figure 2.16. Plot of third metatars
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tv . ... . Ri. . . .
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Figure 2.19. Plot of third metatars
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CHAPTER 3: Tensile keystone model o
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dynamically transmitted Iommotor fo
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Table 3.1 . Metatarsi examined in t
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interrnetatarsal dynamics in these
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compelled analysis of movement evid
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Once prepared, TMP 94.1 2.602 and i
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Daspletosaurus tomsus (MOR 590), an
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2. Freedom of movement inferred fro
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Table 3.2. Surface areas of intemet
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phylogenetic bracketing Wtmer 1995)
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4) Forces from anterior displacerne
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e expected for tyrannosaurid interm
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The preceding discussion derives fr
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weapons sparring), and the arctomet
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Figure 3.1. Schematic representatio
Page 163: Figure 3.3. CT reconstruction of ri
Page 167: Figure 3.5. MT II (left element) an
Page 171: Figure 3.7. Osteological correlates
Page 175: Figure 3.9. Osteological correlates
Page 179: Figure 3.1 1 ae. The metatarsal rec
Page 187: Figure 3.13. Ligament contribution
Page 191 and 192: Figure 3.15. Anatorny of the equid
Page 193: Figure 3.16. Cornparison of loading
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Page 198 and 199: The practicality of the finite elem
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Page 202 and 203: A FORCE INPUTS AND MATERIAL PROPERT
Page 204 and 205: Alexander et al. (1 979) rewrded a
Page 206 and 207: The preceding loading regime entait
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Page 210 and 211: 2. Preparation of data for contour
Page 212 and 213: . - Elastic modulus (GP4 Ex EY Ez P
Page 216 and 217: maintained. An angle of 2 degrees p
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Page 224: Figure 4.1. Initial loads and bound
Page 228: Figure 4.3. Finite element mesh of
Page 232: Figure 4.5. Strain distribution in
Page 236 and 237: CHAPTER 5: Mechanical and evolution
Page 238 and 239: y distal intermetatarsal ligaments,
Page 240 and 241: Probable fundion of the tyrannosaur
Page 242 and 243: Ornitholestes, and camosaurs) incre
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Page 248 and 249: face of the skull met part of the m
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Page 262 and 263: Proximal intermetatarsal ligaments
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witti a surfeit of potentially supp
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Figure 5.2. Phylogeny of the Therop
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Bock W.J. and von Wahlert G. Evolut
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Cume P.J. 1997. Theropoda. In: Fari
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Grenard S. 1991. Handbook of Alliga
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Liem K.F. and Osse J.W.M. 1975. Bio
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Richtsmeier J.T. and Cheverud J.M.
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Woo S., Maynard J., Butler O. 1987.
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Different variables in a PCA will h
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THE UNIVERSITY OF CALGARY Eric Snively A ... - Ohio University

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