doc/user/finleyelements.tex


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Copyright (c) 2003-2018 by The University of Queensland
% http://www.uq.edu.au
%
% Primary Business: Queensland, Australia
% Licensed under the Apache License, version 2.0
% http://www.apache.org/licenses/LICENSE-2.0
%
% Development until 2012 by Earth Systems Science Computational Center (ESSCC)
% Development 2012-2013 by School of Earth Sciences
% Development from 2014 by Centre for Geoscience Computing (GeoComp)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\setlength{\unitlength}{1mm}

\newsavebox{\HLa}
\savebox{\HLa}(0,0)
  {\put(0,0){\circle*{2}}
   \thicklines \put(1,0){\line(1,0){28}}
   \put(30,0){\circle*{2}} }

\newsavebox{\HLathin}
\savebox{\HLathin}(0,0)
  {\put(0,0){\circle{2}}
   \thinlines \put(1,0){\line(1,0){28}}
   \put(30,0){\circle{2}} }

\newsavebox{\VLa}
\savebox{\VLa}(0,30)
  {\put(0,0){\circle*{2}}
   \thicklines \put(0,1){\line(0,1){28}}
   \put(0,30){\circle*{2}} }

\newsavebox{\VLathin}
\savebox{\VLathin}(0,30)
  {\put(0,0){\circle{2}}
   \thinlines \put(0,1){\line(0,1){28}}
   \put(0,30){\circle{2}} }

\newsavebox{\SLax}
\savebox{\SLax}(0,30)
  {\thicklines \put(0,0){\line(-1,1){30}}
   \put(0,0){\circle*{2}}
   \put(-30,30){\circle*{2}} }

\newsavebox{\SLaa}
\savebox{\SLaa}(0,15)
  {\thicklines \put(0,0){\line(-4,3){20}}
   \put(0,0){\circle*{2}}
   \put(-20,15){\circle*{2}} }

\newsavebox{\SLab}
\savebox{\SLab}(0,-15)
  {\thicklines \put(0,0){\line(-4,-3){20}}
   \put(0,0){\circle*{2}}
   \put(-20,-15){\circle*{2}} }

\newsavebox{\SLabthin}
\savebox{\SLabthin}(0,-15)
  {\thinlines \put(-0.7,-0.7){\line(-4,-3){18.7}}
   \put(0,0){\circle{2}}
   \put(-20,-15){\circle{2}} }

\newsavebox{\SLac}
\savebox{\SLac}(0,15)
  {\thicklines \put(0,0){\line(-2,3){10}}
   \put(0,0){\circle*{2}}
   \put(-10,15){\circle*{2}} }

\newsavebox{\SLacthin}
\savebox{\SLacthin}(0,15)
  {\thinlines \put(0,0){\line(-2,3){9.4}}
   \put(0,0){\circle{2}}
   \put(-10,15){\circle{2}} }


\newsavebox{\HLd}
\savebox{\HLd}(0,0)
  {\put(0,0){\circle*{2}}
   \put(10,0){\circle*{2}}
   \thicklines \put(1,0){\line(1,0){28}}
   \put(20,0){\circle*{2}}
   \put(30,0){\circle*{2}} }

\newsavebox{\HLdthin}
\savebox{\HLdthin}(0,0)
  {\put(0,0){\circle{2}}
   \put(10,0){\circle{2}}
   \thinlines \multiput(1,0)(10,0){3}{\line(1,0){8}}
   \put(20,0){\circle{2}}
   \put(30,0){\circle{2}} }

\newsavebox{\VLd}
\savebox{\VLd}(0,30)
  {\put(0,0){\circle*{2}}
   \put(0,10){\circle*{2}}
   \thicklines \put(0,1){\line(0,1){28}}
   \put(0,20){\circle*{2}}
   \put(0,30){\circle*{2}} }

\newsavebox{\VLdthin}
\savebox{\VLdthin}(0,30)
  {\put(0,0){\circle{2}}
   \put(0,10){\circle{2}}
   \thinlines \multiput(0,1)(0,10){3}{\line(0,1){8}}
   \put(0,20){\circle{2}}
   \put(0,30){\circle{2}} }

\newsavebox{\SLf}
\savebox{\SLf}(0,30)
  {\thicklines \put(0,0){\line(-1,1){30}}
   \put(0,0){\circle*{2}}
   \put(-10,10){\circle*{2}}
   \put(-20,20){\circle*{2}}
   \put(-30,30){\circle*{2}} }

\newsavebox{\SLad}
\savebox{\SLad}(0,15)
  {\thicklines \put(0,0){\line(-4,3){20}}
   \put(0,0){\circle*{2}}
   \put(-6.66,5){\circle*{2}}
   \put(-13.33,10){\circle*{2}}
   \put(-20,15){\circle*{2}} }

\newsavebox{\SLbd}
\savebox{\SLbd}(0,-15)
  {\thicklines \put(0,0){\line(-4,-3){20}}
   \put(0,0){\circle*{2}}
   \put(-6.66,-5){\circle*{2}}
   \put(-13.33,-10){\circle*{2}}
   \put(-20,-15){\circle*{2}} }

\newsavebox{\SLbdthin}
\savebox{\SLbdthin}(0,-15)
  {\thinlines \multiput(-0.7,-0.7)(-6.66,-5){3}{\line(-4,-3){5.1}}
   \put(0,0){\circle{2}}
   \put(-6.66,-5){\circle{2}}
   \put(-13.33,-10){\circle{2}}
   \put(-20,-15){\circle{2}} }

\newsavebox{\SLcd}
\savebox{\SLcd}(0,15)
  {\thicklines \put(0,0){\line(-2,3){10}}
   \put(0,0){\circle*{2}}
   \put(-3.33,5){\circle*{2}}
   \put(-6.66,10){\circle*{2}}
   \put(-10,15){\circle*{2}} }

\newsavebox{\SLcdthin}
\savebox{\SLcdthin}(0,15)
  {\thinlines \multiput(-0.6,0.8)(-3.33,5){3}{\line(-2,3){2.35}}
   \put(0,0){\circle{2}}
   \put(-3.33,5){\circle{2}}
   \put(-6.66,10){\circle{2}}
   \put(-10,15){\circle{2}} }

\newsavebox{\HLe}
\savebox{\HLe}(0,0)
  {\put(0,0){\circle*{2}}
   \put(15,0){\circle*{2}}
   \thicklines \put(1,0){\line(1,0){28}}
   \put(30,0){\circle*{2}} }

\newsavebox{\HLethin}
\savebox{\HLethin}(0,0)
  {\put(0,0){\circle{2}}
   \put(15,0){\circle{2}}
   \thinlines \multiput(1,0)(15,0){2}{\line(1,0){13}}
   \put(30,0){\circle{2}} }

\newsavebox{\VLe}
\savebox{\VLe}(0,30)
  {\put(0,0){\circle*{2}}
   \put(0,15){\circle*{2}}
   \thicklines \put(0,1){\line(0,1){28}}
   \put(0,30){\circle*{2}} }

\newsavebox{\VLethin}
\savebox{\VLethin}(0,30)
  {\put(0,0){\circle{2}}
   \put(0,15){\circle{2}}
   \thinlines \multiput(0,1)(0,15){2}{\line(0,1){13}}
   \put(0,30){\circle{2}} }

\newsavebox{\SLe}
\savebox{\SLe}(0,30)
  {\thicklines \put(0,0){\line(-1,1){30}}
   \put(0,0){\circle*{2}}
   \put(-15,15){\circle*{2}}
   \put(-30,30){\circle*{2}} }

\newsavebox{\SLae}
\savebox{\SLae}(0,15)
  {\thicklines \put(0,0){\line(-4,3){20}}
   \put(0,0){\circle*{2}}
   \put(-10,7.5){\circle*{2}}
   \put(-20,15){\circle*{2}} }

\newsavebox{\SLbe}
\savebox{\SLbe}(0,-15)
  {\thicklines \put(0,0){\line(-4,-3){20}}
   \put(0,0){\circle*{2}}
   \put(-10,-7.5){\circle*{2}}
   \put(-20,-15){\circle*{2}} }

\newsavebox{\SLbethin}
\savebox{\SLbethin}(0,-15)
  {\thinlines \multiput(-0.7,-0.7)(-10,-7.5){2}{\line(-4,-3){8.4}}
   \put(0,0){\circle{2}}
   \put(-10,-7.5){\circle{2}}
   \put(-20,-15){\circle{2}} }

\newsavebox{\SLce}
\savebox{\SLce}(0,15)
  {\thicklines \put(0,0){\line(-2,3){10}}
   \put(0,0){\circle*{2}}
   \put(-5,7.5){\circle*{2}}
   \put(-10,15){\circle*{2}} }

\newsavebox{\SLcethin}
\savebox{\SLcethin}(0,15)
  {\thinlines \multiput(-0.6,0.8)(-5,7.5){2}{\line(-2,3){3.9}}
   \put(0,0){\circle{2}}
   \put(-5,7.5){\circle{2}}
   \put(-10,15){\circle{2}} }

%=====================================================================
%
%   order 1
%   -------
%

\begin{figure}
\begin{center}
\begin{picture}(150,160) \thicklines

\put(20,155){\circle*{2}}
\put(15,145){\parbox[t]{45mm}
             \finleyelement{Point1}}

\put(90,155){\usebox{\HLa}}
\put(90,145){\parbox[t]{45mm}
             \finleyelement{Line2} }

\put(10,95){\usebox{\HLa}}
\put(40,95){\usebox{\SLax}}
\put(10,95){\usebox{\VLa}}
\put(10,85){\parbox[t]{45mm}
             \finleyelement{Tri3} }

\put(90,95){\usebox{\HLa}}
\put(90,125){\usebox{\HLa}}
\put(90,95){\usebox{\VLa}}
\put(120,95){\usebox{\VLa}}
\put(90,85){\parbox[t]{45mm}
             \finleyelement{Rec4} }

\put(10,20){\usebox{\HLa}}
\put(40,20){\usebox{\SLax}}
\put(10,20){\usebox{\VLa}}
\put(40,20){\usebox{\SLac}}
\put(30,35){\usebox{\SLabthin}}
\put(30,35){\usebox{\SLaa}}
\put(10,10 ){\parbox[t]{45mm}
             \finleyelement{Tet4} }

\put(90,20){\usebox{\HLa}}
\put(90,50){\usebox{\HLa}}
\put(90,20){\usebox{\VLa}}
\put(120,20){\usebox{\VLa}}
\put(110,35){\usebox{\SLabthin}}
\put(140,35){\usebox{\SLab}}
\put(110,65){\usebox{\SLab}}
\put(140,65){\usebox{\SLab}}
\put(110,35){\usebox{\HLathin}}
\put(110,65){\usebox{\HLa}}
\put(110,35){\usebox{\VLathin}}
\put(140,35){\usebox{\VLa}}
\put(90,10 ){\parbox[t]{45mm}
             \finleyelement{Hex8} }

% numbering the lines:
 % Point
\put(19,158){{\it 1}}
% line
\put(89,158){{\it 1}} 
\put(119,158){{\it 2}}
% Triangle
\put(6,124){{\it 3}}
\put(6,94){{\it 1}}
\put(43,94){{\it 2}}
% quadrilateral
\put(86,124){{\it 4}}
\put(86,94){{\it 1}}
\put(123,124){{\it 3}}
\put(123,94){{\it 2}}
% Tetrahedron
\put(6,49){{\it 4}}
\put(6,19){{\it 1}}
\put(43,19){{\it 2}}
\put(33,34){{\it 3}}
% Hexahedron
\put(86,49){{\it 5}} 
\put(86,19){{\it 1}}
\put(123,49){{\it 6}}
\put(123,19){{\it 2}}
\put(106,64){{\it 8}}
\put(106,34){{\it 4}}
\put(143,64){{\it 7}}
\put(143,34){{\it 3}}
\end{picture}
\caption{\label{FINLEY.FIG:1} Elements of order 1}
\end{center}
\end{figure}
%=====================================================================
%
%
%   order 2
%   -------
%   (boxes in 'fesubelm')


\begin{figure}
\begin{center}
\setlength{\unitlength}{1mm}
\begin{picture}(150,160) \thicklines

\put(20,155){\circle*{2}}
\put(15,145){\parbox[t]{45mm}
             \finleyelement{Point1} }

\put(90,155){\usebox{\HLe}}
\put(90,145){\parbox[t]{45mm}
             \finleyelement{Line3} and \finleyelement{Line3Macro} }

\put(10,95){\usebox{\HLe}}
\put(40,95){\usebox{\SLe}}
\put(10,95){\usebox{\VLe}}
\put(10,85){\parbox[t]{45mm}
             \finleyelement{Tri6} }

\put(90,95){\usebox{\HLe}}
\put(90,125){\usebox{\HLe}}
\put(90,95){\usebox{\VLe}}
\put(120,95){\usebox{\VLe}}
\put(90,85){\parbox[t]{45mm}
             \finleyelement{Rec8} }

\put(10,20){\usebox{\HLe}}
\put(40,20){\usebox{\SLe}}
\put(10,20){\usebox{\VLe}}
\put(40,20){\usebox{\SLce}}
\put(30,35){\usebox{\SLbethin}}
\put(30,35){\usebox{\SLae}}
\put(10,10 ){\parbox[t]{45mm}
             \finleyelement{Tet10} and \finleyelement{Tet10Macro}}

\put(90,20){\usebox{\HLe}}
\put(90,50){\usebox{\HLe}}
\put(90,20){\usebox{\VLe}}
\put(120,20){\usebox{\VLe}}
\put(110,35){\usebox{\SLbethin}}
\put(140,35){\usebox{\SLbe}}
\put(110,65){\usebox{\SLbe}}
\put(140,65){\usebox{\SLbe}}
\put(110,35){\usebox{\HLethin}}
\put(110,65){\usebox{\HLe}}
\put(110,35){\usebox{\VLethin}}
\put(140,35){\usebox{\VLe}}
\put(90,10 ){\parbox[t]{45mm}
             \finleyelement{Hex20} }


% numbering the lines:
% Point
\put(19,158){{\it 1}} 
% line
\put(89,158){{\it 1}} 
\put(104,158){{\it 3}}
\put(119,158){{\it 2}}
% Triangle
\put(6,124){{\it 3}} 
\put(6,109){{\it 6}}
\put(6,94){{\it 1}}
\put(28,109){{\it 5}}
\put(43,94){{\it 2}}
\put(24,90){{\it 4}}
% quaTrilateral
\put(104,90){{\it 5}} 
\put(86,124){{\it 4}}
\put(86,109){{\it 8}}
\put(86,94){{\it 1}}
\put(104,128){{\it 7}}
\put(123,124){{\it 3}}
\put(123,109){{\it 6}}
\put(123,94){{\it 2}}
% Tetrahedron
\put(24,15){{\it 5}} 
\put(6,49){{\it 4}}
\put(6,34){{\it 8}}
\put(6,19){{\it 1}}
\put(21,34){{\it 9}}
\put(43,19){{\it 2}}
\put(16,26.5){{\it 7}}
\put(38,26.5){{\it 6}}
\put(33,34){{\it 3}}
\put(22.5,41.5){{\it 10}}
% Hexahedron
\put(104,15){{\it 9}} 
\put(86,49){{\it 5}}
\put(85,34){{\it 13}}
\put(86,19){{\it 1}}
\put(104,52){{\it 17}}
\put(123,49){{\it 6}}
\put(115,37){{\it 14}}
\put(123,19){{\it 2}}
\put(125,37){{\it 11}}
\put(106,64){{\it 8}}
\put(112,46){{\it 16}}
\put(106,34){{\it 4}}
\put(124,68){{\it 19}}
\put(143,64){{\it 7}}
\put(142,49){{\it 15}}
\put(143,34){{\it 3}}
\put(94.5,26.5){{\it 12}}
\put(132.5,26.5){{\it 10}}
\put(94.5,56.5){{\it 20}}
\put(132.5,56.5){{\it 18}}

\end{picture}
\caption{\label{FINLEY.FIG:2} Elements of order 2 and macro elements}
\end{center}
\end{figure}

%
% additional elements
%
\begin{figure}
\begin{center}
\begin{picture}(50,50) \thicklines
\put(10,10){\usebox{\HLe}}
\put(10,40){\usebox{\HLe}}
\put(10,10){\usebox{\VLe}}
\put(40,10){\usebox{\VLe}}
\put(25,25){\circle*{2}}
% \put(50,085){\parbox[t]{45mm}
%              \finleyelement{Rec9} and  \finleyelement{Rec9Macro}}
\put(24,5){{\it 5}}
\put(6,39){{\it 4}}
\put(6,24){{\it 8}}
\put(6,9){{\it 1}}
\put(24,43){{\it 7}}
\put(43,43){{\it 3}}
\put(43,25){{\it 6}}
\put(43,9){{\it 2}}
\put(24,20){{\it 9}}
\end{picture}
\caption{\label{FINLEY.FIG:4}\finleyelement{Rec9} and  \finleyelement{Rec9Macro}}
\end{center}
\end{figure}
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}
Name	Value
svn:eol-style	native
svn:keywords	Author Date Id Revision