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1
2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3 % Copyright (c) 2003-2018 by The University of Queensland
4 % http://www.uq.edu.au
5 %
6 % Primary Business: Queensland, Australia
7 % Licensed under the Apache License, version 2.0
8 % http://www.apache.org/licenses/LICENSE-2.0
9 %
10 % Development until 2012 by Earth Systems Science Computational Center (ESSCC)
11 % Development 2012-2013 by School of Earth Sciences
12 % Development from 2014 by Centre for Geoscience Computing (GeoComp)
13 %
14 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
15
16 \setlength{\unitlength}{1mm}
17
18 \newsavebox{\HLa}
19 \savebox{\HLa}(0,0)
20 {\put(0,0){\circle*{2}}
21 \thicklines \put(1,0){\line(1,0){28}}
22 \put(30,0){\circle*{2}} }
23
24 \newsavebox{\HLathin}
25 \savebox{\HLathin}(0,0)
26 {\put(0,0){\circle{2}}
27 \thinlines \put(1,0){\line(1,0){28}}
28 \put(30,0){\circle{2}} }
29
30 \newsavebox{\VLa}
31 \savebox{\VLa}(0,30)
32 {\put(0,0){\circle*{2}}
33 \thicklines \put(0,1){\line(0,1){28}}
34 \put(0,30){\circle*{2}} }
35
36 \newsavebox{\VLathin}
37 \savebox{\VLathin}(0,30)
38 {\put(0,0){\circle{2}}
39 \thinlines \put(0,1){\line(0,1){28}}
40 \put(0,30){\circle{2}} }
41
42 \newsavebox{\SLax}
43 \savebox{\SLax}(0,30)
44 {\thicklines \put(0,0){\line(-1,1){30}}
45 \put(0,0){\circle*{2}}
46 \put(-30,30){\circle*{2}} }
47
48 \newsavebox{\SLaa}
49 \savebox{\SLaa}(0,15)
50 {\thicklines \put(0,0){\line(-4,3){20}}
51 \put(0,0){\circle*{2}}
52 \put(-20,15){\circle*{2}} }
53
54 \newsavebox{\SLab}
55 \savebox{\SLab}(0,-15)
56 {\thicklines \put(0,0){\line(-4,-3){20}}
57 \put(0,0){\circle*{2}}
58 \put(-20,-15){\circle*{2}} }
59
60 \newsavebox{\SLabthin}
61 \savebox{\SLabthin}(0,-15)
62 {\thinlines \put(-0.7,-0.7){\line(-4,-3){18.7}}
63 \put(0,0){\circle{2}}
64 \put(-20,-15){\circle{2}} }
65
66 \newsavebox{\SLac}
67 \savebox{\SLac}(0,15)
68 {\thicklines \put(0,0){\line(-2,3){10}}
69 \put(0,0){\circle*{2}}
70 \put(-10,15){\circle*{2}} }
71
72 \newsavebox{\SLacthin}
73 \savebox{\SLacthin}(0,15)
74 {\thinlines \put(0,0){\line(-2,3){9.4}}
75 \put(0,0){\circle{2}}
76 \put(-10,15){\circle{2}} }
77
78
79 \newsavebox{\HLd}
80 \savebox{\HLd}(0,0)
81 {\put(0,0){\circle*{2}}
82 \put(10,0){\circle*{2}}
83 \thicklines \put(1,0){\line(1,0){28}}
84 \put(20,0){\circle*{2}}
85 \put(30,0){\circle*{2}} }
86
87 \newsavebox{\HLdthin}
88 \savebox{\HLdthin}(0,0)
89 {\put(0,0){\circle{2}}
90 \put(10,0){\circle{2}}
91 \thinlines \multiput(1,0)(10,0){3}{\line(1,0){8}}
92 \put(20,0){\circle{2}}
93 \put(30,0){\circle{2}} }
94
95 \newsavebox{\VLd}
96 \savebox{\VLd}(0,30)
97 {\put(0,0){\circle*{2}}
98 \put(0,10){\circle*{2}}
99 \thicklines \put(0,1){\line(0,1){28}}
100 \put(0,20){\circle*{2}}
101 \put(0,30){\circle*{2}} }
102
103 \newsavebox{\VLdthin}
104 \savebox{\VLdthin}(0,30)
105 {\put(0,0){\circle{2}}
106 \put(0,10){\circle{2}}
107 \thinlines \multiput(0,1)(0,10){3}{\line(0,1){8}}
108 \put(0,20){\circle{2}}
109 \put(0,30){\circle{2}} }
110
111 \newsavebox{\SLf}
112 \savebox{\SLf}(0,30)
113 {\thicklines \put(0,0){\line(-1,1){30}}
114 \put(0,0){\circle*{2}}
115 \put(-10,10){\circle*{2}}
116 \put(-20,20){\circle*{2}}
117 \put(-30,30){\circle*{2}} }
118
119 \newsavebox{\SLad}
120 \savebox{\SLad}(0,15)
121 {\thicklines \put(0,0){\line(-4,3){20}}
122 \put(0,0){\circle*{2}}
123 \put(-6.66,5){\circle*{2}}
124 \put(-13.33,10){\circle*{2}}
125 \put(-20,15){\circle*{2}} }
126
127 \newsavebox{\SLbd}
128 \savebox{\SLbd}(0,-15)
129 {\thicklines \put(0,0){\line(-4,-3){20}}
130 \put(0,0){\circle*{2}}
131 \put(-6.66,-5){\circle*{2}}
132 \put(-13.33,-10){\circle*{2}}
133 \put(-20,-15){\circle*{2}} }
134
135 \newsavebox{\SLbdthin}
136 \savebox{\SLbdthin}(0,-15)
137 {\thinlines \multiput(-0.7,-0.7)(-6.66,-5){3}{\line(-4,-3){5.1}}
138 \put(0,0){\circle{2}}
139 \put(-6.66,-5){\circle{2}}
140 \put(-13.33,-10){\circle{2}}
141 \put(-20,-15){\circle{2}} }
142
143 \newsavebox{\SLcd}
144 \savebox{\SLcd}(0,15)
145 {\thicklines \put(0,0){\line(-2,3){10}}
146 \put(0,0){\circle*{2}}
147 \put(-3.33,5){\circle*{2}}
148 \put(-6.66,10){\circle*{2}}
149 \put(-10,15){\circle*{2}} }
150
151 \newsavebox{\SLcdthin}
152 \savebox{\SLcdthin}(0,15)
153 {\thinlines \multiput(-0.6,0.8)(-3.33,5){3}{\line(-2,3){2.35}}
154 \put(0,0){\circle{2}}
155 \put(-3.33,5){\circle{2}}
156 \put(-6.66,10){\circle{2}}
157 \put(-10,15){\circle{2}} }
158
159 \newsavebox{\HLe}
160 \savebox{\HLe}(0,0)
161 {\put(0,0){\circle*{2}}
162 \put(15,0){\circle*{2}}
163 \thicklines \put(1,0){\line(1,0){28}}
164 \put(30,0){\circle*{2}} }
165
166 \newsavebox{\HLethin}
167 \savebox{\HLethin}(0,0)
168 {\put(0,0){\circle{2}}
169 \put(15,0){\circle{2}}
170 \thinlines \multiput(1,0)(15,0){2}{\line(1,0){13}}
171 \put(30,0){\circle{2}} }
172
173 \newsavebox{\VLe}
174 \savebox{\VLe}(0,30)
175 {\put(0,0){\circle*{2}}
176 \put(0,15){\circle*{2}}
177 \thicklines \put(0,1){\line(0,1){28}}
178 \put(0,30){\circle*{2}} }
179
180 \newsavebox{\VLethin}
181 \savebox{\VLethin}(0,30)
182 {\put(0,0){\circle{2}}
183 \put(0,15){\circle{2}}
184 \thinlines \multiput(0,1)(0,15){2}{\line(0,1){13}}
185 \put(0,30){\circle{2}} }
186
187 \newsavebox{\SLe}
188 \savebox{\SLe}(0,30)
189 {\thicklines \put(0,0){\line(-1,1){30}}
190 \put(0,0){\circle*{2}}
191 \put(-15,15){\circle*{2}}
192 \put(-30,30){\circle*{2}} }
193
194 \newsavebox{\SLae}
195 \savebox{\SLae}(0,15)
196 {\thicklines \put(0,0){\line(-4,3){20}}
197 \put(0,0){\circle*{2}}
198 \put(-10,7.5){\circle*{2}}
199 \put(-20,15){\circle*{2}} }
200
201 \newsavebox{\SLbe}
202 \savebox{\SLbe}(0,-15)
203 {\thicklines \put(0,0){\line(-4,-3){20}}
204 \put(0,0){\circle*{2}}
205 \put(-10,-7.5){\circle*{2}}
206 \put(-20,-15){\circle*{2}} }
207
208 \newsavebox{\SLbethin}
209 \savebox{\SLbethin}(0,-15)
210 {\thinlines \multiput(-0.7,-0.7)(-10,-7.5){2}{\line(-4,-3){8.4}}
211 \put(0,0){\circle{2}}
212 \put(-10,-7.5){\circle{2}}
213 \put(-20,-15){\circle{2}} }
214
215 \newsavebox{\SLce}
216 \savebox{\SLce}(0,15)
217 {\thicklines \put(0,0){\line(-2,3){10}}
218 \put(0,0){\circle*{2}}
219 \put(-5,7.5){\circle*{2}}
220 \put(-10,15){\circle*{2}} }
221
222 \newsavebox{\SLcethin}
223 \savebox{\SLcethin}(0,15)
224 {\thinlines \multiput(-0.6,0.8)(-5,7.5){2}{\line(-2,3){3.9}}
225 \put(0,0){\circle{2}}
226 \put(-5,7.5){\circle{2}}
227 \put(-10,15){\circle{2}} }
228
229 %=====================================================================
230 %
231 % order 1
232 % -------
233 %
234
235 \begin{figure}
236 \begin{center}
237 \begin{picture}(150,160) \thicklines
238
239 \put(20,155){\circle*{2}}
240 \put(15,145){\parbox[t]{45mm}
241 \finleyelement{Point1}}
242
243 \put(90,155){\usebox{\HLa}}
244 \put(90,145){\parbox[t]{45mm}
245 \finleyelement{Line2} }
246
247 \put(10,95){\usebox{\HLa}}
248 \put(40,95){\usebox{\SLax}}
249 \put(10,95){\usebox{\VLa}}
250 \put(10,85){\parbox[t]{45mm}
251 \finleyelement{Tri3} }
252
253 \put(90,95){\usebox{\HLa}}
254 \put(90,125){\usebox{\HLa}}
255 \put(90,95){\usebox{\VLa}}
256 \put(120,95){\usebox{\VLa}}
257 \put(90,85){\parbox[t]{45mm}
258 \finleyelement{Rec4} }
259
260 \put(10,20){\usebox{\HLa}}
261 \put(40,20){\usebox{\SLax}}
262 \put(10,20){\usebox{\VLa}}
263 \put(40,20){\usebox{\SLac}}
264 \put(30,35){\usebox{\SLabthin}}
265 \put(30,35){\usebox{\SLaa}}
266 \put(10,10 ){\parbox[t]{45mm}
267 \finleyelement{Tet4} }
268
269 \put(90,20){\usebox{\HLa}}
270 \put(90,50){\usebox{\HLa}}
271 \put(90,20){\usebox{\VLa}}
272 \put(120,20){\usebox{\VLa}}
273 \put(110,35){\usebox{\SLabthin}}
274 \put(140,35){\usebox{\SLab}}
275 \put(110,65){\usebox{\SLab}}
276 \put(140,65){\usebox{\SLab}}
277 \put(110,35){\usebox{\HLathin}}
278 \put(110,65){\usebox{\HLa}}
279 \put(110,35){\usebox{\VLathin}}
280 \put(140,35){\usebox{\VLa}}
281 \put(90,10 ){\parbox[t]{45mm}
282 \finleyelement{Hex8} }
283
284 % numbering the lines:
285 % Point
286 \put(19,158){{\it 1}}
287 % line
288 \put(89,158){{\it 1}}
289 \put(119,158){{\it 2}}
290 % Triangle
291 \put(6,124){{\it 3}}
292 \put(6,94){{\it 1}}
293 \put(43,94){{\it 2}}
294 % quadrilateral
295 \put(86,124){{\it 4}}
296 \put(86,94){{\it 1}}
297 \put(123,124){{\it 3}}
298 \put(123,94){{\it 2}}
299 % Tetrahedron
300 \put(6,49){{\it 4}}
301 \put(6,19){{\it 1}}
302 \put(43,19){{\it 2}}
303 \put(33,34){{\it 3}}
304 % Hexahedron
305 \put(86,49){{\it 5}}
306 \put(86,19){{\it 1}}
307 \put(123,49){{\it 6}}
308 \put(123,19){{\it 2}}
309 \put(106,64){{\it 8}}
310 \put(106,34){{\it 4}}
311 \put(143,64){{\it 7}}
312 \put(143,34){{\it 3}}
313 \end{picture}
314 \caption{\label{FINLEY.FIG:1} Elements of order 1}
315 \end{center}
316 \end{figure}
317 %=====================================================================
318 %
319 %
320 % order 2
321 % -------
322 % (boxes in 'fesubelm')
323
324
325 \begin{figure}
326 \begin{center}
327 \setlength{\unitlength}{1mm}
328 \begin{picture}(150,160) \thicklines
329
330 \put(20,155){\circle*{2}}
331 \put(15,145){\parbox[t]{45mm}
332 \finleyelement{Point1} }
333
334 \put(90,155){\usebox{\HLe}}
335 \put(90,145){\parbox[t]{45mm}
336 \finleyelement{Line3} and \finleyelement{Line3Macro} }
337
338 \put(10,95){\usebox{\HLe}}
339 \put(40,95){\usebox{\SLe}}
340 \put(10,95){\usebox{\VLe}}
341 \put(10,85){\parbox[t]{45mm}
342 \finleyelement{Tri6} }
343
344 \put(90,95){\usebox{\HLe}}
345 \put(90,125){\usebox{\HLe}}
346 \put(90,95){\usebox{\VLe}}
347 \put(120,95){\usebox{\VLe}}
348 \put(90,85){\parbox[t]{45mm}
349 \finleyelement{Rec8} }
350
351 \put(10,20){\usebox{\HLe}}
352 \put(40,20){\usebox{\SLe}}
353 \put(10,20){\usebox{\VLe}}
354 \put(40,20){\usebox{\SLce}}
355 \put(30,35){\usebox{\SLbethin}}
356 \put(30,35){\usebox{\SLae}}
357 \put(10,10 ){\parbox[t]{45mm}
358 \finleyelement{Tet10} and \finleyelement{Tet10Macro}}
359
360 \put(90,20){\usebox{\HLe}}
361 \put(90,50){\usebox{\HLe}}
362 \put(90,20){\usebox{\VLe}}
363 \put(120,20){\usebox{\VLe}}
364 \put(110,35){\usebox{\SLbethin}}
365 \put(140,35){\usebox{\SLbe}}
366 \put(110,65){\usebox{\SLbe}}
367 \put(140,65){\usebox{\SLbe}}
368 \put(110,35){\usebox{\HLethin}}
369 \put(110,65){\usebox{\HLe}}
370 \put(110,35){\usebox{\VLethin}}
371 \put(140,35){\usebox{\VLe}}
372 \put(90,10 ){\parbox[t]{45mm}
373 \finleyelement{Hex20} }
374
375
376 % numbering the lines:
377 % Point
378 \put(19,158){{\it 1}}
379 % line
380 \put(89,158){{\it 1}}
381 \put(104,158){{\it 3}}
382 \put(119,158){{\it 2}}
383 % Triangle
384 \put(6,124){{\it 3}}
385 \put(6,109){{\it 6}}
386 \put(6,94){{\it 1}}
387 \put(28,109){{\it 5}}
388 \put(43,94){{\it 2}}
389 \put(24,90){{\it 4}}
390 % quaTrilateral
391 \put(104,90){{\it 5}}
392 \put(86,124){{\it 4}}
393 \put(86,109){{\it 8}}
394 \put(86,94){{\it 1}}
395 \put(104,128){{\it 7}}
396 \put(123,124){{\it 3}}
397 \put(123,109){{\it 6}}
398 \put(123,94){{\it 2}}
399 % Tetrahedron
400 \put(24,15){{\it 5}}
401 \put(6,49){{\it 4}}
402 \put(6,34){{\it 8}}
403 \put(6,19){{\it 1}}
404 \put(21,34){{\it 9}}
405 \put(43,19){{\it 2}}
406 \put(16,26.5){{\it 7}}
407 \put(38,26.5){{\it 6}}
408 \put(33,34){{\it 3}}
409 \put(22.5,41.5){{\it 10}}
410 % Hexahedron
411 \put(104,15){{\it 9}}
412 \put(86,49){{\it 5}}
413 \put(85,34){{\it 13}}
414 \put(86,19){{\it 1}}
415 \put(104,52){{\it 17}}
416 \put(123,49){{\it 6}}
417 \put(115,37){{\it 14}}
418 \put(123,19){{\it 2}}
419 \put(125,37){{\it 11}}
420 \put(106,64){{\it 8}}
421 \put(112,46){{\it 16}}
422 \put(106,34){{\it 4}}
423 \put(124,68){{\it 19}}
424 \put(143,64){{\it 7}}
425 \put(142,49){{\it 15}}
426 \put(143,34){{\it 3}}
427 \put(94.5,26.5){{\it 12}}
428 \put(132.5,26.5){{\it 10}}
429 \put(94.5,56.5){{\it 20}}
430 \put(132.5,56.5){{\it 18}}
431
432 \end{picture}
433 \caption{\label{FINLEY.FIG:2} Elements of order 2 and macro elements}
434 \end{center}
435 \end{figure}
436
437 %
438 % additional elements
439 %
440 \begin{figure}
441 \begin{center}
442 \begin{picture}(50,50) \thicklines
443 \put(10,10){\usebox{\HLe}}
444 \put(10,40){\usebox{\HLe}}
445 \put(10,10){\usebox{\VLe}}
446 \put(40,10){\usebox{\VLe}}
447 \put(25,25){\circle*{2}}
448 % \put(50,085){\parbox[t]{45mm}
449 % \finleyelement{Rec9} and \finleyelement{Rec9Macro}}
450 \put(24,5){{\it 5}}
451 \put(6,39){{\it 4}}
452 \put(6,24){{\it 8}}
453 \put(6,9){{\it 1}}
454 \put(24,43){{\it 7}}
455 \put(43,43){{\it 3}}
456 \put(43,25){{\it 6}}
457 \put(43,9){{\it 2}}
458 \put(24,20){{\it 9}}
459 \end{picture}
460 \caption{\label{FINLEY.FIG:4}\finleyelement{Rec9} and \finleyelement{Rec9Macro}}
461 \end{center}
462 \end{figure}

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