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1 ksteube 1811
2 jfenwick 3989 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3 jfenwick 6651 % Copyright (c) 2003-2018 by The University of Queensland
4 jfenwick 3989 % http://www.uq.edu.au
5 gross 625 %
6 ksteube 1811 % Primary Business: Queensland, Australia
7 jfenwick 6112 % Licensed under the Apache License, version 2.0
8     % http://www.apache.org/licenses/LICENSE-2.0
9 ksteube 1316 %
10 jfenwick 3989 % Development until 2012 by Earth Systems Science Computational Center (ESSCC)
11 jfenwick 4657 % Development 2012-2013 by School of Earth Sciences
12     % Development from 2014 by Centre for Geoscience Computing (GeoComp)
13 jfenwick 3989 %
14     %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
15 ksteube 1316
16 jgs 102 \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 jfenwick 3311 \begin{center}
237     \begin{picture}(150,160) \thicklines
238 jgs 102
239 jfenwick 3311 \put(20,155){\circle*{2}}
240     \put(15,145){\parbox[t]{45mm}
241 jgs 102 \finleyelement{Point1}}
242    
243 jfenwick 3311 \put(90,155){\usebox{\HLa}}
244     \put(90,145){\parbox[t]{45mm}
245     \finleyelement{Line2} }
246 jgs 102
247 jfenwick 3311 \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 jgs 102 \finleyelement{Tri3} }
252    
253 jfenwick 3311 \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 jgs 102 \finleyelement{Rec4} }
259    
260 jfenwick 3311 \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 jgs 102 \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 caltinay 4286 % numbering the lines:
285 jfenwick 3311 % 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 jgs 102 \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 jfenwick 3311 \end{center}
316 jgs 102 \end{figure}
317     %=====================================================================
318     %
319     %
320     % order 2
321     % -------
322     % (boxes in 'fesubelm')
323    
324    
325     \begin{figure}
326 jfenwick 3311 \begin{center}
327 jgs 102 \setlength{\unitlength}{1mm}
328 jfenwick 3311 \begin{picture}(150,160) \thicklines
329 jgs 102
330 jfenwick 3311 \put(20,155){\circle*{2}}
331     \put(15,145){\parbox[t]{45mm}
332 jgs 102 \finleyelement{Point1} }
333    
334 jfenwick 3311 \put(90,155){\usebox{\HLe}}
335     \put(90,145){\parbox[t]{45mm}
336 gross 2748 \finleyelement{Line3} and \finleyelement{Line3Macro} }
337 jgs 102
338 jfenwick 3311 \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 jgs 102 \finleyelement{Tri6} }
343    
344 jfenwick 3311 \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 jgs 102 \finleyelement{Rec8} }
350    
351 jfenwick 3311 \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 gross 2748 \finleyelement{Tet10} and \finleyelement{Tet10Macro}}
359 jgs 102
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 caltinay 4286 % numbering the lines:
377 jfenwick 3311 % 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 jgs 102 \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 gross 2748 \caption{\label{FINLEY.FIG:2} Elements of order 2 and macro elements}
434 jfenwick 3311 \end{center}
435 jgs 102 \end{figure}
436    
437     %
438     % additional elements
439     %
440     \begin{figure}
441 jfenwick 3311 \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 jgs 102 \end{picture}
460 jfenwick 3311 \caption{\label{FINLEY.FIG:4}\finleyelement{Rec9} and \finleyelement{Rec9Macro}}
461     \end{center}
462 jgs 102 \end{figure}

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