diff options
| author | pollney <pollney@c78560ca-4b45-4335-b268-5f3340f3cb52> | 2002-06-10 09:54:03 +0000 |
|---|---|---|
| committer | pollney <pollney@c78560ca-4b45-4335-b268-5f3340f3cb52> | 2002-06-10 09:54:03 +0000 |
| commit | b5cb6c915077b883a637178a3a070b0dae739b83 (patch) | |
| tree | 6aa06e1564a8a65b031e6bec7311760ac2c9e496 | |
| parent | c340c4d5674bf05cada2bb73fd0a04be6e354204 (diff) | |
Added "bitant_rotate" and "quadrant_reflect_rotate" domains for
systems which have a rotational symmetry.
There are some notes describing these domains and the implementation
in the doc directory: rotating_sym.tex
Currently only works for a single processor.
git-svn-id: http://svn.cactuscode.org/arrangements/CactusBase/CartGrid3D/trunk@161 c78560ca-4b45-4335-b268-5f3340f3cb52
28 files changed, 2795 insertions, 65 deletions
diff --git a/doc/fig/rotate_bbh.eps b/doc/fig/rotate_bbh.eps new file mode 100644 index 0000000..a4a2eb0 --- /dev/null +++ b/doc/fig/rotate_bbh.eps @@ -0,0 +1,162 @@ +%!PS-Adobe-2.0 EPSF-2.0 +%%Title: rotate_bbh.eps +%%Creator: fig2dev Version 3.2 Patchlevel 3d +%%CreationDate: Thu Jun 6 19:51:10 2002 +%%For: dp@nbdell15 (Denis Pollney,,,) +%%BoundingBox: 0 0 203 204 +%%Magnification: 1.0000 +%%EndComments +/$F2psDict 200 dict def +$F2psDict begin +$F2psDict /mtrx matrix put +/col-1 {0 setgray} bind def +/col0 {0.000 0.000 0.000 srgb} bind def +/col1 {0.000 0.000 1.000 srgb} bind def +/col2 {0.000 1.000 0.000 srgb} bind def +/col3 {0.000 1.000 1.000 srgb} bind def +/col4 {1.000 0.000 0.000 srgb} bind def +/col5 {1.000 0.000 1.000 srgb} bind def +/col6 {1.000 1.000 0.000 srgb} bind def +/col7 {1.000 1.000 1.000 srgb} bind def +/col8 {0.000 0.000 0.560 srgb} bind def +/col9 {0.000 0.000 0.690 srgb} bind def +/col10 {0.000 0.000 0.820 srgb} bind def +/col11 {0.530 0.810 1.000 srgb} bind def +/col12 {0.000 0.560 0.000 srgb} bind def +/col13 {0.000 0.690 0.000 srgb} bind def +/col14 {0.000 0.820 0.000 srgb} bind def +/col15 {0.000 0.560 0.560 srgb} bind def +/col16 {0.000 0.690 0.690 srgb} bind def +/col17 {0.000 0.820 0.820 srgb} bind def +/col18 {0.560 0.000 0.000 srgb} bind def +/col19 {0.690 0.000 0.000 srgb} bind def +/col20 {0.820 0.000 0.000 srgb} bind def +/col21 {0.560 0.000 0.560 srgb} bind def +/col22 {0.690 0.000 0.690 srgb} bind def +/col23 {0.820 0.000 0.820 srgb} bind def +/col24 {0.500 0.190 0.000 srgb} bind def +/col25 {0.630 0.250 0.000 srgb} bind def +/col26 {0.750 0.380 0.000 srgb} bind def +/col27 {1.000 0.500 0.500 srgb} bind def +/col28 {1.000 0.630 0.630 srgb} bind def +/col29 {1.000 0.750 0.750 srgb} bind def +/col30 {1.000 0.880 0.880 srgb} bind def +/col31 {1.000 0.840 0.000 srgb} bind def + +end +save +newpath 0 204 moveto 0 0 lineto 203 0 lineto 203 204 lineto closepath clip newpath +-78.6 264.4 translate +1 -1 scale + +/cp {closepath} bind def +/ef {eofill} bind def +/gr {grestore} bind def +/gs {gsave} bind def +/sa {save} bind def +/rs {restore} bind def +/l {lineto} bind def +/m {moveto} bind def +/rm {rmoveto} bind def +/n {newpath} bind def +/s {stroke} bind def +/sh {show} bind def +/slc {setlinecap} bind def +/slj {setlinejoin} bind def +/slw {setlinewidth} bind def +/srgb {setrgbcolor} bind def +/rot {rotate} bind def +/sc {scale} bind def +/sd {setdash} bind def +/ff {findfont} bind def +/sf {setfont} bind def +/scf {scalefont} bind def +/sw {stringwidth} bind def +/tr {translate} bind def +/tnt {dup dup currentrgbcolor + 4 -2 roll dup 1 exch sub 3 -1 roll mul add + 4 -2 roll dup 1 exch sub 3 -1 roll mul add + 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} + bind def +/shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul + 4 -2 roll mul srgb} bind def + /DrawEllipse { + /endangle exch def + /startangle exch def + /yrad exch def + /xrad exch def + /y exch def + /x exch def + /savematrix mtrx currentmatrix def + x y tr xrad yrad sc 0 0 1 startangle endangle arc + closepath + savematrix setmatrix + } def + +/$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def +/$F2psEnd {$F2psEnteredState restore end} def + +$F2psBegin +10 setmiterlimit +0 slj 0 slc + 0.06299 0.06299 sc +% +% Fig objects follow +% +% Polyline +7.500 slw +n 2700 1350 m 4050 1350 l 4050 4050 l 2700 4050 l + cp gs col6 1.00 shd ef gr gs col0 s gr +% Ellipse +n 3375 2250 64 64 0 360 DrawEllipse gs 0.00 setgray ef gr gs col0 s gr + +% Ellipse +n 2025 3375 64 64 0 360 DrawEllipse gs 0.00 setgray ef gr gs col0 s gr + +% Polyline +n 1350 1350 m 4050 1350 l 4050 4050 l 1350 4050 l + cp gs col0 s gr +% Polyline +gs clippath +2421 3767 m 2460 3721 l 2346 3623 l 2418 3724 l 2307 3668 l cp +eoclip +n 2115 3465 m + 2430 3735 l gs col0 s gr gr + +% arrowhead +n 2307 3668 m 2418 3724 l 2346 3623 l 2307 3668 l cp gs 0.00 setgray ef gr col0 s +% Polyline +gs clippath +2978 1857 m 2939 1903 l 3053 2001 l 2982 1901 l 3092 1956 l cp +eoclip +n 3285 2160 m + 2970 1890 l gs col0 s gr gr + +% arrowhead +n 3092 1956 m 2982 1901 l 3053 2001 l 3092 1956 l cp gs 0.00 setgray ef gr col0 s +% Polyline +gs clippath +4290 2730 m 4290 2670 l 4139 2670 l 4259 2700 l 4139 2730 l cp +eoclip +n 1260 2700 m + 4275 2700 l gs col0 s gr gr + +% arrowhead +n 4139 2730 m 4259 2700 l 4139 2670 l 4139 2730 l cp gs 0.00 setgray ef gr col0 s +% Polyline +gs clippath +2730 1110 m 2670 1110 l 2670 1261 l 2700 1141 l 2730 1261 l cp +eoclip +n 2700 4185 m + 2700 1125 l gs col0 s gr gr + +% arrowhead +n 2730 1261 m 2700 1141 l 2670 1261 l 2730 1261 l cp gs 0.00 setgray ef gr col0 s +/Helvetica ff 180.00 scf sf +2655 1080 m +gs 1 -1 sc (y) col0 sh gr +/Helvetica ff 180.00 scf sf +4365 2745 m +gs 1 -1 sc (x) col0 sh gr +$F2psEnd +rs diff --git a/doc/fig/rotate_bbh.fig b/doc/fig/rotate_bbh.fig new file mode 100644 index 0000000..970fcb2 --- /dev/null +++ b/doc/fig/rotate_bbh.fig @@ -0,0 +1,29 @@ +#FIG 3.2 +Landscape +Center +Metric +A4 +100.00 +Single +-2 +1200 2 +1 3 0 1 0 0 50 0 20 0.000 1 0.0000 3375 2250 64 64 3375 2250 3439 2250 +1 3 0 1 0 0 50 0 20 0.000 1 0.0000 2025 3375 64 64 2025 3375 2089 3375 +2 2 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 5 + 1350 1350 4050 1350 4050 4050 1350 4050 1350 1350 +2 2 0 1 0 6 60 0 20 0.000 0 0 -1 0 0 5 + 2700 1350 4050 1350 4050 4050 2700 4050 2700 1350 +2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 1 0 2 + 1 1 1.00 60.00 120.00 + 2115 3465 2430 3735 +2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 1 0 2 + 1 1 1.00 60.00 120.00 + 3285 2160 2970 1890 +2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 1 0 2 + 1 1 1.00 60.00 120.00 + 1260 2700 4275 2700 +2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 1 0 2 + 1 1 1.00 60.00 120.00 + 2700 4185 2700 1125 +4 0 0 50 0 16 12 0.0000 4 150 105 2655 1080 y\001 +4 0 0 50 0 16 12 0.0000 4 105 90 4365 2745 x\001 diff --git a/doc/fig/rotate_bitant.eps b/doc/fig/rotate_bitant.eps new file mode 100644 index 0000000..88d0bcb --- /dev/null +++ b/doc/fig/rotate_bitant.eps @@ -0,0 +1,143 @@ +%!PS-Adobe-2.0 EPSF-2.0 +%%Title: rotate_bitant.eps +%%Creator: fig2dev Version 3.2 Patchlevel 3d +%%CreationDate: Sun Jun 9 11:06:24 2002 +%%For: pollney@xeon20.aei-potsdam.mpg.de (Denis Pollney,0.21,1.21,none) +%%BoundingBox: 0 0 165 202 +%%Magnification: 1.0000 +%%EndComments +/$F2psDict 200 dict def +$F2psDict begin +$F2psDict /mtrx matrix put +/col-1 {0 setgray} bind def +/col0 {0.000 0.000 0.000 srgb} bind def +/col1 {0.000 0.000 1.000 srgb} bind def +/col2 {0.000 1.000 0.000 srgb} bind def +/col3 {0.000 1.000 1.000 srgb} bind def +/col4 {1.000 0.000 0.000 srgb} bind def +/col5 {1.000 0.000 1.000 srgb} bind def +/col6 {1.000 1.000 0.000 srgb} bind def +/col7 {1.000 1.000 1.000 srgb} bind def +/col8 {0.000 0.000 0.560 srgb} bind def +/col9 {0.000 0.000 0.690 srgb} bind def +/col10 {0.000 0.000 0.820 srgb} bind def +/col11 {0.530 0.810 1.000 srgb} bind def +/col12 {0.000 0.560 0.000 srgb} bind def +/col13 {0.000 0.690 0.000 srgb} bind def +/col14 {0.000 0.820 0.000 srgb} bind def +/col15 {0.000 0.560 0.560 srgb} bind def +/col16 {0.000 0.690 0.690 srgb} bind def +/col17 {0.000 0.820 0.820 srgb} bind def +/col18 {0.560 0.000 0.000 srgb} bind def +/col19 {0.690 0.000 0.000 srgb} bind def +/col20 {0.820 0.000 0.000 srgb} bind def +/col21 {0.560 0.000 0.560 srgb} bind def +/col22 {0.690 0.000 0.690 srgb} bind def +/col23 {0.820 0.000 0.820 srgb} bind def +/col24 {0.500 0.190 0.000 srgb} bind def +/col25 {0.630 0.250 0.000 srgb} bind def +/col26 {0.750 0.380 0.000 srgb} bind def +/col27 {1.000 0.500 0.500 srgb} bind def +/col28 {1.000 0.630 0.630 srgb} bind def +/col29 {1.000 0.750 0.750 srgb} bind def +/col30 {1.000 0.880 0.880 srgb} bind def +/col31 {1.000 0.840 0.000 srgb} bind def + +end +save +newpath 0 202 moveto 0 0 lineto 165 0 lineto 165 202 lineto closepath clip newpath +-56.7 261.5 translate +1 -1 scale + +/cp {closepath} bind def +/ef {eofill} bind def +/gr {grestore} bind def +/gs {gsave} bind def +/sa {save} bind def +/rs {restore} bind def +/l {lineto} bind def +/m {moveto} bind def +/rm {rmoveto} bind def +/n {newpath} bind def +/s {stroke} bind def +/sh {show} bind def +/slc {setlinecap} bind def +/slj {setlinejoin} bind def +/slw {setlinewidth} bind def +/srgb {setrgbcolor} bind def +/rot {rotate} bind def +/sc {scale} bind def +/sd {setdash} bind def +/ff {findfont} bind def +/sf {setfont} bind def +/scf {scalefont} bind def +/sw {stringwidth} bind def +/tr {translate} bind def +/tnt {dup dup currentrgbcolor + 4 -2 roll dup 1 exch sub 3 -1 roll mul add + 4 -2 roll dup 1 exch sub 3 -1 roll mul add + 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} + bind def +/shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul + 4 -2 roll mul srgb} bind def +/$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def +/$F2psEnd {$F2psEnteredState restore end} def + +$F2psBegin +10 setmiterlimit + 0.06299 0.06299 sc +% +% Fig objects follow +% +% Arc +7.500 slw +gs clippath +1765 3181 m 1774 3122 l 1624 3100 l 1739 3148 l 1615 3159 l cp +1774 2277 m 1765 2218 l 1615 2240 l 1739 2252 l 1624 2299 l cp +eoclip +n 1755.0 2700.0 450.0 -90.0 90.0 arcn +gs col0 s gr + gr + +% arrowhead +n 1615 3159 m 1739 3148 l 1624 3100 l 1615 3159 l cp gs 0.00 setgray ef gr col0 s +% arrowhead +n 1624 2299 m 1739 2252 l 1615 2240 l 1624 2299 l cp gs 0.00 setgray ef gr col0 s +% Polyline +n 1800 1350 m 3150 1350 l 3150 4050 l 1800 4050 l + cp gs col6 1.00 shd ef gr gs col0 s gr +% Polyline +gs clippath +3390 2730 m 3390 2670 l 3239 2670 l 3359 2700 l 3239 2730 l cp +eoclip +n 1710 2700 m + 3375 2700 l gs col0 s gr gr + +% arrowhead +n 3239 2730 m 3359 2700 l 3239 2670 l 3239 2730 l cp gs 0.00 setgray ef gr col0 s +% Polyline +gs clippath +1830 1110 m 1770 1110 l 1770 1261 l 1800 1141 l 1830 1261 l cp +eoclip +n 1800 4140 m + 1800 1125 l gs col0 s gr gr + +% arrowhead +n 1830 1261 m 1800 1141 l 1770 1261 l 1830 1261 l cp gs 0.00 setgray ef gr col0 s +/Helvetica ff 180.00 scf sf +1755 1080 m +gs 1 -1 sc (y) col0 sh gr +/Helvetica ff 180.00 scf sf +3420 2790 m +gs 1 -1 sc (x) col0 sh gr +/Symbol ff 180.00 scf sf +900 2745 m +gs 1 -1 sc (q=p) col0 sh gr +/Helvetica ff 180.00 scf sf +1575 2025 m +gs 1 -1 sc (A) col0 sh gr +/Helvetica ff 180.00 scf sf +1575 3600 m +gs 1 -1 sc (B) col0 sh gr +$F2psEnd +rs diff --git a/doc/fig/rotate_bitant.fig b/doc/fig/rotate_bitant.fig new file mode 100644 index 0000000..ac2e497 --- /dev/null +++ b/doc/fig/rotate_bitant.fig @@ -0,0 +1,25 @@ +#FIG 3.2 +Landscape +Center +Metric +A4 +100.00 +Single +-2 +1200 2 +5 1 0 1 0 7 50 0 -1 0.000 0 1 1 1 1755.000 2700.000 1755 2250 1305 2700 1755 3150 + 1 1 1.00 60.00 120.00 + 1 1 1.00 60.00 120.00 +2 2 0 1 0 6 50 0 20 0.000 0 0 -1 0 0 5 + 1800 1350 3150 1350 3150 4050 1800 4050 1800 1350 +2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 1 0 2 + 1 1 1.00 60.00 120.00 + 1710 2700 3375 2700 +2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 1 0 2 + 1 1 1.00 60.00 120.00 + 1800 4140 1800 1125 +4 0 0 50 0 16 12 0.0000 4 150 105 1755 1080 y\001 +4 0 0 50 0 16 12 0.0000 4 105 90 3420 2790 x\001 +4 0 0 50 0 32 12 0.0000 4 135 315 900 2745 q=p\001 +4 0 0 50 0 16 12 0.0000 4 135 135 1575 2025 A\001 +4 0 0 50 0 16 12 0.0000 4 135 120 1575 3600 B\001 diff --git a/doc/fig/rotate_bitant.fig.bak b/doc/fig/rotate_bitant.fig.bak new file mode 100644 index 0000000..cbf06fa --- /dev/null +++ b/doc/fig/rotate_bitant.fig.bak @@ -0,0 +1,25 @@ +#FIG 3.2 +Landscape +Center +Metric +A4 +100.00 +Single +-2 +1200 2 +5 1 0 1 0 7 50 0 -1 0.000 0 1 1 1 1755.000 2700.000 1755 2250 1305 2700 1755 3150 + 1 1 1.00 60.00 120.00 + 1 1 1.00 60.00 120.00 +2 2 0 1 0 6 50 0 20 0.000 0 0 -1 0 0 5 + 1800 1350 3150 1350 3150 4050 1800 4050 1800 1350 +2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 1 0 2 + 1 1 1.00 60.00 120.00 + 1710 2700 3375 2700 +2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 1 0 2 + 1 1 1.00 60.00 120.00 + 1800 4140 1800 1125 +4 0 0 50 0 16 12 0.0000 4 150 105 1755 1080 y\001 +4 0 0 50 0 16 12 0.0000 4 105 90 3420 2790 x\001 +4 0 0 50 0 32 12 0.0000 4 135 315 900 2745 q=p\001 +4 0 0 50 0 16 12 0.0000 4 135 135 1575 2025 A\001 +4 0 0 50 0 16 12 0.0000 4 135 120 1575 3825 B\001 diff --git a/doc/fig/rotate_bitant_example.eps b/doc/fig/rotate_bitant_example.eps new file mode 100644 index 0000000..91254da --- /dev/null +++ b/doc/fig/rotate_bitant_example.eps @@ -0,0 +1,193 @@ +%!PS-Adobe-2.0 EPSF-2.0 +%%Title: rotate_bitant_example.eps +%%Creator: fig2dev Version 3.2 Patchlevel 3d +%%CreationDate: Sat Jun 8 19:19:08 2002 +%%For: dp@nbdell15 (Denis Pollney,,,) +%%BoundingBox: 0 0 302 269 +%%Magnification: 1.0000 +%%EndComments +/$F2psDict 200 dict def +$F2psDict begin +$F2psDict /mtrx matrix put +/col-1 {0 setgray} bind def +/col0 {0.000 0.000 0.000 srgb} bind def +/col1 {0.000 0.000 1.000 srgb} bind def +/col2 {0.000 1.000 0.000 srgb} bind def +/col3 {0.000 1.000 1.000 srgb} bind def +/col4 {1.000 0.000 0.000 srgb} bind def +/col5 {1.000 0.000 1.000 srgb} bind def +/col6 {1.000 1.000 0.000 srgb} bind def +/col7 {1.000 1.000 1.000 srgb} bind def +/col8 {0.000 0.000 0.560 srgb} bind def +/col9 {0.000 0.000 0.690 srgb} bind def +/col10 {0.000 0.000 0.820 srgb} bind def +/col11 {0.530 0.810 1.000 srgb} bind def +/col12 {0.000 0.560 0.000 srgb} bind def +/col13 {0.000 0.690 0.000 srgb} bind def +/col14 {0.000 0.820 0.000 srgb} bind def +/col15 {0.000 0.560 0.560 srgb} bind def +/col16 {0.000 0.690 0.690 srgb} bind def +/col17 {0.000 0.820 0.820 srgb} bind def +/col18 {0.560 0.000 0.000 srgb} bind def +/col19 {0.690 0.000 0.000 srgb} bind def +/col20 {0.820 0.000 0.000 srgb} bind def +/col21 {0.560 0.000 0.560 srgb} bind def +/col22 {0.690 0.000 0.690 srgb} bind def +/col23 {0.820 0.000 0.820 srgb} bind def +/col24 {0.500 0.190 0.000 srgb} bind def +/col25 {0.630 0.250 0.000 srgb} bind def +/col26 {0.750 0.380 0.000 srgb} bind def +/col27 {1.000 0.500 0.500 srgb} bind def +/col28 {1.000 0.630 0.630 srgb} bind def +/col29 {1.000 0.750 0.750 srgb} bind def +/col30 {1.000 0.880 0.880 srgb} bind def +/col31 {1.000 0.840 0.000 srgb} bind def + +end +save +newpath 0 269 moveto 0 0 lineto 302 0 lineto 302 269 lineto closepath clip newpath +-65.2 315.4 translate +1 -1 scale + +/cp {closepath} bind def +/ef {eofill} bind def +/gr {grestore} bind def +/gs {gsave} bind def +/sa {save} bind def +/rs {restore} bind def +/l {lineto} bind def +/m {moveto} bind def +/rm {rmoveto} bind def +/n {newpath} bind def +/s {stroke} bind def +/sh {show} bind def +/slc {setlinecap} bind def +/slj {setlinejoin} bind def +/slw {setlinewidth} bind def +/srgb {setrgbcolor} bind def +/rot {rotate} bind def +/sc {scale} bind def +/sd {setdash} bind def +/ff {findfont} bind def +/sf {setfont} bind def +/scf {scalefont} bind def +/sw {stringwidth} bind def +/tr {translate} bind def +/tnt {dup dup currentrgbcolor + 4 -2 roll dup 1 exch sub 3 -1 roll mul add + 4 -2 roll dup 1 exch sub 3 -1 roll mul add + 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} + bind def +/shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul + 4 -2 roll mul srgb} bind def + /DrawEllipse { + /endangle exch def + /startangle exch def + /yrad exch def + /xrad exch def + /y exch def + /x exch def + /savematrix mtrx currentmatrix def + x y tr xrad yrad sc 0 0 1 startangle endangle arc + closepath + savematrix setmatrix + } def + +/$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def +/$F2psEnd {$F2psEnteredState restore end} def + +$F2psBegin +10 setmiterlimit +0 slj 0 slc + 0.06299 0.06299 sc +% +% Fig objects follow +% +% Polyline +7.500 slw +n 1800 2250 m 3375 2250 l 3375 4725 l 1800 4725 l + cp gs col6 1.00 shd ef gr gs col0 s gr +% Polyline +n 3375 1350 m 1800 2250 l 3375 2250 l 4950 1350 l + cp gs col6 1.00 shd ef gr gs col0 s gr +% Polyline +n 3375 2250 m 4950 1350 l 4950 3825 l 3375 4725 l + cp gs col6 1.00 shd ef gr gs col0 s gr +% Ellipse +n 2700 1350 315 135 0 360 DrawEllipse gs col0 s gr + +% Polyline +gs clippath +1142 3806 m 1171 3858 l 1303 3783 l 1184 3817 l 1273 3731 l cp +eoclip +n 1800 3465 m + 1170 3825 l gs col0 s gr gr + +% arrowhead +n 1273 3731 m 1184 3817 l 1303 3783 l 1273 3731 l cp gs 0.00 setgray ef gr col0 s +% Polyline + [60] 0 sd +n 3375 1350 m + 3375 3825 l gs col0 s gr [] 0 sd +% Polyline + [60] 0 sd +n 3375 3825 m + 4950 3825 l gs col0 s gr [] 0 sd +% Polyline + [60] 0 sd +n 3375 3825 m + 1800 4725 l gs col0 s gr [] 0 sd +% Polyline + [60] 0 sd +n 2700 1755 m + 2700 4725 l gs col0 s gr [] 0 sd +% Polyline + [60] 0 sd +n 1805 3474 m + 4145 2124 l gs col0 s gr [] 0 sd +% Polyline + [60] 0 sd +n 4140 2970 m + 1575 2970 l gs col0 s gr [] 0 sd +% Polyline +gs clippath +5685 3000 m 5685 2940 l 5534 2940 l 5654 2970 l 5534 3000 l cp +eoclip +n 4140 2970 m + 5670 2970 l gs col0 s gr gr + +% arrowhead +n 5534 3000 m 5654 2970 l 5534 2940 l 5534 3000 l cp gs 0.00 setgray ef gr col0 s +% Polyline +n 2700 4725 m + 2700 4995 l gs col0 s gr +% Polyline + [60] 0 sd +n 1800 2970 m + 1575 2970 l gs col0 s gr [] 0 sd +% Polyline +gs clippath +2730 885 m 2670 885 l 2670 1036 l 2700 916 l 2730 1036 l cp +eoclip +n 2700 1710 m + 2700 900 l gs col0 s gr gr + +% arrowhead +n 2730 1036 m 2700 916 l 2670 1036 l 2730 1036 l cp gs 0.00 setgray ef gr col0 s +/Helvetica ff 180.00 scf sf +1035 3960 m +gs 1 -1 sc (x) col0 sh gr +/Helvetica ff 180.00 scf sf +2655 855 m +gs 1 -1 sc (z) col0 sh gr +/Helvetica ff 180.00 scf sf +5715 3015 m +gs 1 -1 sc (y) col0 sh gr +/Helvetica ff 180.00 scf sf +1710 1305 m +gs 1 -1 sc (rotation) col0 sh gr +/Helvetica ff 180.00 scf sf +1845 1485 m +gs 1 -1 sc (axis) col0 sh gr +$F2psEnd +rs diff --git a/doc/fig/rotate_bitant_example.fig b/doc/fig/rotate_bitant_example.fig new file mode 100644 index 0000000..38d3e2d --- /dev/null +++ b/doc/fig/rotate_bitant_example.fig @@ -0,0 +1,46 @@ +#FIG 3.2 +Landscape +Center +Metric +A4 +100.00 +Single +-2 +1200 2 +1 1 0 1 0 7 50 0 -1 0.000 1 0.0000 2700 1350 315 135 2700 1350 3015 1350 +2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 1 0 2 + 1 1 1.00 60.00 120.00 + 1800 3465 1170 3825 +2 1 1 1 0 7 50 0 -1 4.000 0 0 -1 0 0 2 + 3375 1350 3375 3825 +2 1 1 1 0 7 50 0 -1 4.000 0 0 -1 0 0 2 + 3375 3825 4950 3825 +2 1 1 1 0 7 50 0 -1 4.000 0 0 -1 0 0 2 + 3375 3825 1800 4725 +2 1 1 1 0 7 50 0 -1 4.000 0 0 -1 0 0 2 + 2700 1755 2700 4725 +2 1 1 1 0 7 50 0 -1 4.000 0 0 -1 0 0 2 + 1805 3474 4145 2124 +2 1 1 1 0 7 50 0 -1 4.000 0 0 -1 0 0 2 + 4140 2970 1575 2970 +2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 1 0 2 + 1 1 1.00 60.00 120.00 + 4140 2970 5670 2970 +2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2 + 2700 4725 2700 4995 +2 2 0 1 0 6 60 0 20 0.000 0 0 -1 0 0 5 + 1800 2250 3375 2250 3375 4725 1800 4725 1800 2250 +2 3 0 1 0 6 60 0 20 0.000 0 0 -1 0 0 5 + 3375 1350 1800 2250 3375 2250 4950 1350 3375 1350 +2 3 0 1 0 6 60 0 20 0.000 0 0 -1 0 0 5 + 3375 2250 4950 1350 4950 3825 3375 4725 3375 2250 +2 1 1 1 0 7 50 0 -1 4.000 0 0 -1 0 0 2 + 1800 2970 1575 2970 +2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 1 0 2 + 1 1 1.00 60.00 120.00 + 2700 1710 2700 900 +4 0 0 50 0 16 12 0.0000 4 105 90 1035 3960 x\001 +4 0 0 50 0 16 12 0.0000 4 105 90 2655 855 z\001 +4 0 0 50 0 16 12 0.0000 4 150 105 5715 3015 y\001 +4 0 0 50 0 16 12 0.0000 4 135 615 1710 1305 rotation\001 +4 0 0 50 0 16 12 0.0000 4 135 330 1845 1485 axis\001 diff --git a/doc/fig/rotate_general.eps b/doc/fig/rotate_general.eps new file mode 100644 index 0000000..5d48bed --- /dev/null +++ b/doc/fig/rotate_general.eps @@ -0,0 +1,138 @@ +%!PS-Adobe-2.0 EPSF-2.0 +%%Title: rotate_general.eps +%%Creator: fig2dev Version 3.2 Patchlevel 3d +%%CreationDate: Sun Jun 9 11:03:43 2002 +%%For: pollney@xeon20.aei-potsdam.mpg.de (Denis Pollney,0.21,1.21,none) +%%BoundingBox: 0 0 154 158 +%%Magnification: 1.0000 +%%EndComments +/$F2psDict 200 dict def +$F2psDict begin +$F2psDict /mtrx matrix put +/col-1 {0 setgray} bind def +/col0 {0.000 0.000 0.000 srgb} bind def +/col1 {0.000 0.000 1.000 srgb} bind def +/col2 {0.000 1.000 0.000 srgb} bind def +/col3 {0.000 1.000 1.000 srgb} bind def +/col4 {1.000 0.000 0.000 srgb} bind def +/col5 {1.000 0.000 1.000 srgb} bind def +/col6 {1.000 1.000 0.000 srgb} bind def +/col7 {1.000 1.000 1.000 srgb} bind def +/col8 {0.000 0.000 0.560 srgb} bind def +/col9 {0.000 0.000 0.690 srgb} bind def +/col10 {0.000 0.000 0.820 srgb} bind def +/col11 {0.530 0.810 1.000 srgb} bind def +/col12 {0.000 0.560 0.000 srgb} bind def +/col13 {0.000 0.690 0.000 srgb} bind def +/col14 {0.000 0.820 0.000 srgb} bind def +/col15 {0.000 0.560 0.560 srgb} bind def +/col16 {0.000 0.690 0.690 srgb} bind def +/col17 {0.000 0.820 0.820 srgb} bind def +/col18 {0.560 0.000 0.000 srgb} bind def +/col19 {0.690 0.000 0.000 srgb} bind def +/col20 {0.820 0.000 0.000 srgb} bind def +/col21 {0.560 0.000 0.560 srgb} bind def +/col22 {0.690 0.000 0.690 srgb} bind def +/col23 {0.820 0.000 0.820 srgb} bind def +/col24 {0.500 0.190 0.000 srgb} bind def +/col25 {0.630 0.250 0.000 srgb} bind def +/col26 {0.750 0.380 0.000 srgb} bind def +/col27 {1.000 0.500 0.500 srgb} bind def +/col28 {1.000 0.630 0.630 srgb} bind def +/col29 {1.000 0.750 0.750 srgb} bind def +/col30 {1.000 0.880 0.880 srgb} bind def +/col31 {1.000 0.840 0.000 srgb} bind def + +end +save +newpath 0 158 moveto 0 0 lineto 154 0 lineto 154 158 lineto closepath clip newpath +-73.7 241.7 translate +1 -1 scale + +/cp {closepath} bind def +/ef {eofill} bind def +/gr {grestore} bind def +/gs {gsave} bind def +/sa {save} bind def +/rs {restore} bind def +/l {lineto} bind def +/m {moveto} bind def +/rm {rmoveto} bind def +/n {newpath} bind def +/s {stroke} bind def +/sh {show} bind def +/slc {setlinecap} bind def +/slj {setlinejoin} bind def +/slw {setlinewidth} bind def +/srgb {setrgbcolor} bind def +/rot {rotate} bind def +/sc {scale} bind def +/sd {setdash} bind def +/ff {findfont} bind def +/sf {setfont} bind def +/scf {scalefont} bind def +/sw {stringwidth} bind def +/tr {translate} bind def +/tnt {dup dup currentrgbcolor + 4 -2 roll dup 1 exch sub 3 -1 roll mul add + 4 -2 roll dup 1 exch sub 3 -1 roll mul add + 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} + bind def +/shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul + 4 -2 roll mul srgb} bind def + /DrawEllipse { + /endangle exch def + /startangle exch def + /yrad exch def + /xrad exch def + /y exch def + /x exch def + /savematrix mtrx currentmatrix def + x y tr xrad yrad sc 0 0 1 startangle endangle arc + closepath + savematrix setmatrix + } def + +/$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def +/$F2psEnd {$F2psEnteredState restore end} def + +$F2psBegin +10 setmiterlimit + 0.06299 0.06299 sc +% +% Fig objects follow +% +% Arc +7.500 slw +gs clippath +2053 2808 m 2022 2756 l 1892 2833 l 2011 2798 l 1923 2885 l cp +2022 2193 m 2053 2141 l 1923 2064 l 2011 2152 l 1892 2116 l cp +eoclip +n 1761.0 2475.0 411.0 -50.0 50.0 arcn +gs col0 s gr + gr + +% arrowhead +n 1923 2885 m 2011 2798 l 1892 2833 l 1923 2885 l cp gs 0.00 setgray ef gr col0 s +% arrowhead +n 1892 2116 m 2011 2152 l 1923 2064 l 1892 2116 l cp gs 0.00 setgray ef gr col0 s +% Ellipse +n 1800 2475 45 45 0 360 DrawEllipse gs 0.00 setgray ef gr gs col0 s gr + +% Polyline +n 1800 2475 m 3600 1350 l 3600 3825 l + 1800 2475 l cp gs col6 1.00 shd ef gr gs col0 s gr +/Symbol ff 180.00 scf sf +1170 2475 m +gs 1 -1 sc (q) col0 sh gr +/Helvetica ff 180.00 scf sf +2340 1980 m +gs 1 -1 sc (A) col0 sh gr +/Helvetica ff 180.00 scf sf +2340 3240 m +gs 1 -1 sc (B) col0 sh gr +/Helvetica ff 180.00 scf sf +2925 2610 m +gs 1 -1 sc (Grid) col0 sh gr +$F2psEnd +rs diff --git a/doc/fig/rotate_general.fig b/doc/fig/rotate_general.fig new file mode 100644 index 0000000..5658283 --- /dev/null +++ b/doc/fig/rotate_general.fig @@ -0,0 +1,19 @@ +#FIG 3.2 +Landscape +Center +Metric +A4 +100.00 +Single +-2 +1200 2 +5 1 0 1 0 7 50 0 -1 0.000 0 1 1 1 1761.000 2475.000 2025 2160 1350 2475 2025 2790 + 1 1 1.00 60.00 120.00 + 1 1 1.00 60.00 120.00 +1 3 0 1 0 0 50 0 20 0.000 1 0.0000 1800 2475 45 45 1800 2475 1845 2475 +2 1 0 1 0 6 50 0 20 0.000 0 0 -1 0 0 4 + 1800 2475 3600 1350 3600 3825 1800 2475 +4 0 0 50 0 32 12 0.0000 4 135 105 1170 2475 q\001 +4 0 0 50 0 16 12 0.0000 4 135 135 2340 1980 A\001 +4 0 0 50 0 16 12 0.0000 4 135 120 2340 3240 B\001 +4 0 0 50 0 16 12 0.0000 4 135 345 2925 2610 Grid\001 diff --git a/doc/fig/rotate_general.fig.bak b/doc/fig/rotate_general.fig.bak new file mode 100644 index 0000000..eb39772 --- /dev/null +++ b/doc/fig/rotate_general.fig.bak @@ -0,0 +1,18 @@ +#FIG 3.2 +Landscape +Center +Metric +A4 +100.00 +Single +-2 +1200 2 +5 1 0 1 0 7 50 0 -1 0.000 0 1 1 0 1761.000 2475.000 2025 2160 1350 2475 2025 2790 + 1 1 1.00 60.00 120.00 +1 3 0 1 0 0 50 0 20 0.000 1 0.0000 1800 2475 45 45 1800 2475 1845 2475 +2 1 0 1 0 6 50 0 20 0.000 0 0 -1 0 0 4 + 1800 2475 3600 1350 3600 3825 1800 2475 +4 0 0 50 0 32 12 0.0000 4 135 105 1170 2475 q\001 +4 0 0 50 0 16 12 0.0000 4 135 135 2340 1980 A\001 +4 0 0 50 0 16 12 0.0000 4 135 120 2340 3240 B\001 +4 0 0 50 0 16 12 0.0000 4 135 345 2925 2610 Grid\001 diff --git a/doc/fig/rotate_grid.eps b/doc/fig/rotate_grid.eps new file mode 100644 index 0000000..a725f92 --- /dev/null +++ b/doc/fig/rotate_grid.eps @@ -0,0 +1,197 @@ +%!PS-Adobe-2.0 EPSF-2.0 +%%Title: rotate_grid.eps +%%Creator: fig2dev Version 3.2 Patchlevel 3d +%%CreationDate: Sat Jun 8 18:10:26 2002 +%%For: dp@nbdell15 (Denis Pollney,,,) +%%BoundingBox: 0 0 290 261 +%%Magnification: 1.0000 +%%EndComments +/$F2psDict 200 dict def +$F2psDict begin +$F2psDict /mtrx matrix put +/col-1 {0 setgray} bind def +/col0 {0.000 0.000 0.000 srgb} bind def +/col1 {0.000 0.000 1.000 srgb} bind def +/col2 {0.000 1.000 0.000 srgb} bind def +/col3 {0.000 1.000 1.000 srgb} bind def +/col4 {1.000 0.000 0.000 srgb} bind def +/col5 {1.000 0.000 1.000 srgb} bind def +/col6 {1.000 1.000 0.000 srgb} bind def +/col7 {1.000 1.000 1.000 srgb} bind def +/col8 {0.000 0.000 0.560 srgb} bind def +/col9 {0.000 0.000 0.690 srgb} bind def +/col10 {0.000 0.000 0.820 srgb} bind def +/col11 {0.530 0.810 1.000 srgb} bind def +/col12 {0.000 0.560 0.000 srgb} bind def +/col13 {0.000 0.690 0.000 srgb} bind def +/col14 {0.000 0.820 0.000 srgb} bind def +/col15 {0.000 0.560 0.560 srgb} bind def +/col16 {0.000 0.690 0.690 srgb} bind def +/col17 {0.000 0.820 0.820 srgb} bind def +/col18 {0.560 0.000 0.000 srgb} bind def +/col19 {0.690 0.000 0.000 srgb} bind def +/col20 {0.820 0.000 0.000 srgb} bind def +/col21 {0.560 0.000 0.560 srgb} bind def +/col22 {0.690 0.000 0.690 srgb} bind def +/col23 {0.820 0.000 0.820 srgb} bind def +/col24 {0.500 0.190 0.000 srgb} bind def +/col25 {0.630 0.250 0.000 srgb} bind def +/col26 {0.750 0.380 0.000 srgb} bind def +/col27 {1.000 0.500 0.500 srgb} bind def +/col28 {1.000 0.630 0.630 srgb} bind def +/col29 {1.000 0.750 0.750 srgb} bind def +/col30 {1.000 0.880 0.880 srgb} bind def +/col31 {1.000 0.840 0.000 srgb} bind def + +end +save +newpath 0 261 moveto 0 0 lineto 290 0 lineto 290 261 lineto closepath clip newpath +-59.5 346.6 translate +1 -1 scale + +/cp {closepath} bind def +/ef {eofill} bind def +/gr {grestore} bind def +/gs {gsave} bind def +/sa {save} bind def +/rs {restore} bind def +/l {lineto} bind def +/m {moveto} bind def +/rm {rmoveto} bind def +/n {newpath} bind def +/s {stroke} bind def +/sh {show} bind def +/slc {setlinecap} bind def +/slj {setlinejoin} bind def +/slw {setlinewidth} bind def +/srgb {setrgbcolor} bind def +/rot {rotate} bind def +/sc {scale} bind def +/sd {setdash} bind def +/ff {findfont} bind def +/sf {setfont} bind def +/scf {scalefont} bind def +/sw {stringwidth} bind def +/tr {translate} bind def +/tnt {dup dup currentrgbcolor + 4 -2 roll dup 1 exch sub 3 -1 roll mul add + 4 -2 roll dup 1 exch sub 3 -1 roll mul add + 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} + bind def +/shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul + 4 -2 roll mul srgb} bind def +/$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def +/$F2psEnd {$F2psEnteredState restore end} def + +$F2psBegin +10 setmiterlimit +0 slj 0 slc + 0.06299 0.06299 sc +% +% Fig objects follow +% +% Polyline +7.500 slw +n 1800 1800 m 5175 1800 l 5175 5400 l 1800 5400 l + cp gs col6 1.00 shd ef gr gs col0 s gr +% Polyline +n 2070 1800 m + 2070 2565 l gs col0 s gr +% Polyline +n 2430 2070 m + 1800 2070 l gs col0 s gr +% Polyline +n 2430 2295 m + 1800 2295 l gs col0 s gr +% Polyline +n 1530 4635 m + 1530 5400 l gs col0 s gr +% Polyline +n 1800 5400 m 1260 5400 l 1260 1800 l 1800 1800 l + cp gs col0 s gr +% Polyline +n 2430 2520 m + 1800 2520 l gs col0 s gr +% Polyline +n 2340 1800 m + 2340 2565 l gs col0 s gr +% Polyline +n 1260 5175 m + 1800 5175 l gs col0 s gr +% Polyline +n 1260 4950 m + 1800 4950 l gs col0 s gr +% Polyline +n 1260 4725 m + 1800 4725 l gs col0 s gr +% Polyline +gs clippath +1830 1560 m 1770 1560 l 1770 1711 l 1800 1591 l 1830 1711 l cp +eoclip +n 1800 5490 m + 1800 1575 l gs col0 s gr gr + +% arrowhead +n 1830 1711 m 1800 1591 l 1770 1711 l 1830 1711 l cp gs 0.00 setgray ef gr col0 s +% Polyline +gs clippath +5415 3630 m 5415 3570 l 5264 3570 l 5384 3600 l 5264 3630 l cp +eoclip +n 1125 3600 m + 5400 3600 l gs col0 s gr gr + +% arrowhead +n 5264 3630 m 5384 3600 l 5264 3570 l 5264 3630 l cp gs 0.00 setgray ef gr col0 s +/Helvetica ff 180.00 scf sf +1845 2025 m +gs 1 -1 sc (00 01) col0 sh gr +/Helvetica ff 180.00 scf sf +1845 2250 m +gs 1 -1 sc (10 11) col0 sh gr +/Helvetica ff 180.00 scf sf +1845 2475 m +gs 1 -1 sc (20 21) col0 sh gr +/Helvetica ff 180.00 scf sf +1305 5130 m +gs 1 -1 sc (11 10) col0 sh gr +/Helvetica ff 180.00 scf sf +1305 5355 m +gs 1 -1 sc (01 00) col0 sh gr +/Helvetica ff 180.00 scf sf +1305 4905 m +gs 1 -1 sc (21 20) col0 sh gr +/Helvetica ff 180.00 scf sf +3105 2880 m +gs 1 -1 sc (physical grid) col0 sh gr +/Helvetica ff 180.00 scf sf +1575 4095 m +gs 1 -1 sc 90.0 rot (ghost zones) col0 sh gr +/Helvetica ff 180.00 scf sf +1800 1485 m +gs 1 -1 sc (y) col0 sh gr +/Helvetica ff 180.00 scf sf +5445 3690 m +gs 1 -1 sc (x) col0 sh gr +/Helvetica ff 180.00 scf sf +1935 1755 m +gs 1 -1 sc (0) col0 sh gr +/Helvetica ff 180.00 scf sf +2160 1755 m +gs 1 -1 sc (1) col0 sh gr +/Helvetica ff 180.00 scf sf +4995 1755 m +gs 1 -1 sc (n) col0 sh gr +/Helvetica ff 180.00 scf sf +945 1980 m +gs 1 -1 sc (0) col0 sh gr +/Helvetica ff 180.00 scf sf +945 2205 m +gs 1 -1 sc (1) col0 sh gr +/Helvetica ff 180.00 scf sf +945 5400 m +gs 1 -1 sc (m) col0 sh gr +/Times-Roman ff 180.00 scf sf +945 2430 m +gs 1 -1 sc (2) col0 sh gr +$F2psEnd +rs diff --git a/doc/fig/rotate_grid.fig b/doc/fig/rotate_grid.fig new file mode 100644 index 0000000..f2897c2 --- /dev/null +++ b/doc/fig/rotate_grid.fig @@ -0,0 +1,54 @@ +#FIG 3.2 +Landscape +Center +Metric +A4 +100.00 +Single +-2 +1200 2 +2 2 0 1 0 6 60 0 20 0.000 0 0 -1 0 0 5 + 1800 1800 5175 1800 5175 5400 1800 5400 1800 1800 +2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2 + 2070 1800 2070 2565 +2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2 + 2430 2070 1800 2070 +2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2 + 2430 2295 1800 2295 +2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2 + 1530 4635 1530 5400 +2 2 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 5 + 1800 5400 1260 5400 1260 1800 1800 1800 1800 5400 +2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2 + 2430 2520 1800 2520 +2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2 + 2340 1800 2340 2565 +2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2 + 1260 5175 1800 5175 +2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2 + 1260 4950 1800 4950 +2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2 + 1260 4725 1800 4725 +2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 1 0 2 + 1 1 1.00 60.00 120.00 + 1800 5490 1800 1575 +2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 1 0 2 + 1 1 1.00 60.00 120.00 + 1125 3600 5400 3600 +4 0 0 50 0 16 12 0.0000 4 135 480 1845 2025 00 01\001 +4 0 0 50 0 16 12 0.0000 4 135 480 1845 2250 10 11\001 +4 0 0 50 0 16 12 0.0000 4 135 480 1845 2475 20 21\001 +4 0 0 50 0 16 12 0.0000 4 135 480 1305 5130 11 10\001 +4 0 0 50 0 16 12 0.0000 4 135 480 1305 5355 01 00\001 +4 0 0 50 0 16 12 0.0000 4 135 480 1305 4905 21 20\001 +4 0 0 50 0 16 12 0.0000 4 180 1080 3105 2880 physical grid\001 +4 0 0 50 0 16 12 1.5708 4 180 1005 1575 4095 ghost zones\001 +4 0 0 50 0 16 12 0.0000 4 150 105 1800 1485 y\001 +4 0 0 50 0 16 12 0.0000 4 105 90 5445 3690 x\001 +4 0 0 50 0 16 12 0.0000 4 135 105 1935 1755 0\001 +4 0 0 50 0 16 12 0.0000 4 135 105 2160 1755 1\001 +4 0 0 50 0 16 12 0.0000 4 105 105 4995 1755 n\001 +4 0 0 50 0 16 12 0.0000 4 135 105 945 1980 0\001 +4 0 0 50 0 16 12 0.0000 4 135 105 945 2205 1\001 +4 0 0 50 0 16 12 0.0000 4 105 135 945 5400 m\001 +4 0 0 50 0 0 12 0.0000 4 135 90 945 2430 2\001 diff --git a/doc/fig/rotate_octant.eps b/doc/fig/rotate_octant.eps new file mode 100644 index 0000000..2fa5e69 --- /dev/null +++ b/doc/fig/rotate_octant.eps @@ -0,0 +1,143 @@ +%!PS-Adobe-2.0 EPSF-2.0 +%%Title: rotate_octant.eps +%%Creator: fig2dev Version 3.2 Patchlevel 3d +%%CreationDate: Sun Jun 9 11:05:54 2002 +%%For: pollney@xeon20.aei-potsdam.mpg.de (Denis Pollney,0.21,1.21,none) +%%BoundingBox: 0 0 148 130 +%%Magnification: 1.0000 +%%EndComments +/$F2psDict 200 dict def +$F2psDict begin +$F2psDict /mtrx matrix put +/col-1 {0 setgray} bind def +/col0 {0.000 0.000 0.000 srgb} bind def +/col1 {0.000 0.000 1.000 srgb} bind def +/col2 {0.000 1.000 0.000 srgb} bind def +/col3 {0.000 1.000 1.000 srgb} bind def +/col4 {1.000 0.000 0.000 srgb} bind def +/col5 {1.000 0.000 1.000 srgb} bind def +/col6 {1.000 1.000 0.000 srgb} bind def +/col7 {1.000 1.000 1.000 srgb} bind def +/col8 {0.000 0.000 0.560 srgb} bind def +/col9 {0.000 0.000 0.690 srgb} bind def +/col10 {0.000 0.000 0.820 srgb} bind def +/col11 {0.530 0.810 1.000 srgb} bind def +/col12 {0.000 0.560 0.000 srgb} bind def +/col13 {0.000 0.690 0.000 srgb} bind def +/col14 {0.000 0.820 0.000 srgb} bind def +/col15 {0.000 0.560 0.560 srgb} bind def +/col16 {0.000 0.690 0.690 srgb} bind def +/col17 {0.000 0.820 0.820 srgb} bind def +/col18 {0.560 0.000 0.000 srgb} bind def +/col19 {0.690 0.000 0.000 srgb} bind def +/col20 {0.820 0.000 0.000 srgb} bind def +/col21 {0.560 0.000 0.560 srgb} bind def +/col22 {0.690 0.000 0.690 srgb} bind def +/col23 {0.820 0.000 0.820 srgb} bind def +/col24 {0.500 0.190 0.000 srgb} bind def +/col25 {0.630 0.250 0.000 srgb} bind def +/col26 {0.750 0.380 0.000 srgb} bind def +/col27 {1.000 0.500 0.500 srgb} bind def +/col28 {1.000 0.630 0.630 srgb} bind def +/col29 {1.000 0.750 0.750 srgb} bind def +/col30 {1.000 0.880 0.880 srgb} bind def +/col31 {1.000 0.840 0.000 srgb} bind def + +end +save +newpath 0 130 moveto 0 0 lineto 148 0 lineto 148 130 lineto closepath clip newpath +-31.2 218.0 translate +1 -1 scale + +/cp {closepath} bind def +/ef {eofill} bind def +/gr {grestore} bind def +/gs {gsave} bind def +/sa {save} bind def +/rs {restore} bind def +/l {lineto} bind def +/m {moveto} bind def +/rm {rmoveto} bind def +/n {newpath} bind def +/s {stroke} bind def +/sh {show} bind def +/slc {setlinecap} bind def +/slj {setlinejoin} bind def +/slw {setlinewidth} bind def +/srgb {setrgbcolor} bind def +/rot {rotate} bind def +/sc {scale} bind def +/sd {setdash} bind def +/ff {findfont} bind def +/sf {setfont} bind def +/scf {scalefont} bind def +/sw {stringwidth} bind def +/tr {translate} bind def +/tnt {dup dup currentrgbcolor + 4 -2 roll dup 1 exch sub 3 -1 roll mul add + 4 -2 roll dup 1 exch sub 3 -1 roll mul add + 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} + bind def +/shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul + 4 -2 roll mul srgb} bind def +/$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def +/$F2psEnd {$F2psEnteredState restore end} def + +$F2psBegin +10 setmiterlimit + 0.06299 0.06299 sc +% +% Fig objects follow +% +% Arc +7.500 slw +gs clippath +1833 3011 m 1777 2990 l 1724 3132 l 1794 3030 l 1780 3152 l cp +1327 2499 m 1311 2442 l 1165 2482 l 1289 2479 l 1181 2539 l cp +eoclip +n 1357.6 2923.7 451.8 -96.7 11.7 arcn +gs col0 s gr + gr + +% arrowhead +n 1780 3152 m 1794 3030 l 1724 3132 l 1780 3152 l cp gs 0.00 setgray ef gr col0 s +% arrowhead +n 1181 2539 m 1289 2479 l 1165 2482 l 1181 2539 l cp gs 0.00 setgray ef gr col0 s +% Polyline +n 1350 1800 m 2475 1800 l 2475 2925 l 1350 2925 l + cp gs col6 1.00 shd ef gr gs col0 s gr +% Polyline +gs clippath +2715 2955 m 2715 2895 l 2564 2895 l 2684 2925 l 2564 2955 l cp +eoclip +n 1260 2925 m + 2700 2925 l gs col0 s gr gr + +% arrowhead +n 2564 2955 m 2684 2925 l 2564 2895 l 2564 2955 l cp gs 0.00 setgray ef gr col0 s +% Polyline +gs clippath +1380 1560 m 1320 1560 l 1320 1711 l 1350 1591 l 1380 1711 l cp +eoclip +n 1350 3015 m + 1350 1575 l gs col0 s gr gr + +% arrowhead +n 1380 1711 m 1350 1591 l 1320 1711 l 1380 1711 l cp gs 0.00 setgray ef gr col0 s +/Symbol ff 180.00 scf sf +495 3420 m +gs 1 -1 sc (q=3p/2) col0 sh gr +/Helvetica ff 180.00 scf sf +1305 1530 m +gs 1 -1 sc (y) col0 sh gr +/Helvetica ff 180.00 scf sf +2745 3015 m +gs 1 -1 sc (x) col0 sh gr +/Helvetica ff 180.00 scf sf +1125 2250 m +gs 1 -1 sc (A) col0 sh gr +/Helvetica ff 180.00 scf sf +1935 3150 m +gs 1 -1 sc (B) col0 sh gr +$F2psEnd +rs diff --git a/doc/fig/rotate_octant.fig b/doc/fig/rotate_octant.fig new file mode 100644 index 0000000..83d2834 --- /dev/null +++ b/doc/fig/rotate_octant.fig @@ -0,0 +1,25 @@ +#FIG 3.2 +Landscape +Center +Metric +A4 +100.00 +Single +-2 +1200 2 +5 1 0 1 0 7 50 0 -1 0.000 0 1 1 1 1357.558 2923.697 1305 2475 1035 3240 1800 3015 + 1 1 1.00 60.00 120.00 + 1 1 1.00 60.00 120.00 +2 2 0 1 0 6 50 0 20 0.000 0 0 -1 0 0 5 + 1350 1800 2475 1800 2475 2925 1350 2925 1350 1800 +2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 1 0 2 + 1 1 1.00 60.00 120.00 + 1260 2925 2700 2925 +2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 1 0 2 + 1 1 1.00 60.00 120.00 + 1350 3015 1350 1575 +4 0 0 50 0 32 12 0.0000 4 135 540 495 3420 q=3p/2\001 +4 0 0 50 0 16 12 0.0000 4 150 105 1305 1530 y\001 +4 0 0 50 0 16 12 0.0000 4 105 90 2745 3015 x\001 +4 0 0 50 0 16 12 0.0000 4 135 135 1125 2250 A\001 +4 0 0 50 0 16 12 0.0000 4 135 120 1935 3150 B\001 diff --git a/doc/fig/rotate_octant.fig.bak b/doc/fig/rotate_octant.fig.bak new file mode 100644 index 0000000..ff81b04 --- /dev/null +++ b/doc/fig/rotate_octant.fig.bak @@ -0,0 +1,23 @@ +#FIG 3.2 +Landscape +Center +Metric +A4 +100.00 +Single +-2 +1200 2 +5 1 0 1 0 7 50 0 -1 0.000 0 1 1 1 1357.558 2923.697 1305 2475 1035 3240 1800 3015 + 1 1 1.00 60.00 120.00 + 1 1 1.00 60.00 120.00 +2 2 0 1 0 6 50 0 20 0.000 0 0 -1 0 0 5 + 1350 1800 2475 1800 2475 2925 1350 2925 1350 1800 +2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 1 0 2 + 1 1 1.00 60.00 120.00 + 1260 2925 2700 2925 +2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 1 0 2 + 1 1 1.00 60.00 120.00 + 1350 3015 1350 1575 +4 0 0 50 0 32 12 0.0000 4 135 540 495 3420 q=3p/2\001 +4 0 0 50 0 16 12 0.0000 4 150 105 1305 1530 y\001 +4 0 0 50 0 16 12 0.0000 4 105 90 2745 3015 x\001 diff --git a/doc/fig/rotate_quadrant_example.eps b/doc/fig/rotate_quadrant_example.eps new file mode 100644 index 0000000..100013a --- /dev/null +++ b/doc/fig/rotate_quadrant_example.eps @@ -0,0 +1,200 @@ +%!PS-Adobe-2.0 EPSF-2.0 +%%Title: rotate_quadrant_example.eps +%%Creator: fig2dev Version 3.2 Patchlevel 3d +%%CreationDate: Sat Jun 8 19:04:20 2002 +%%For: dp@nbdell15 (Denis Pollney,,,) +%%BoundingBox: 0 0 302 203 +%%Magnification: 1.0000 +%%EndComments +/$F2psDict 200 dict def +$F2psDict begin +$F2psDict /mtrx matrix put +/col-1 {0 setgray} bind def +/col0 {0.000 0.000 0.000 srgb} bind def +/col1 {0.000 0.000 1.000 srgb} bind def +/col2 {0.000 1.000 0.000 srgb} bind def +/col3 {0.000 1.000 1.000 srgb} bind def +/col4 {1.000 0.000 0.000 srgb} bind def +/col5 {1.000 0.000 1.000 srgb} bind def +/col6 {1.000 1.000 0.000 srgb} bind def +/col7 {1.000 1.000 1.000 srgb} bind def +/col8 {0.000 0.000 0.560 srgb} bind def +/col9 {0.000 0.000 0.690 srgb} bind def +/col10 {0.000 0.000 0.820 srgb} bind def +/col11 {0.530 0.810 1.000 srgb} bind def +/col12 {0.000 0.560 0.000 srgb} bind def +/col13 {0.000 0.690 0.000 srgb} bind def +/col14 {0.000 0.820 0.000 srgb} bind def +/col15 {0.000 0.560 0.560 srgb} bind def +/col16 {0.000 0.690 0.690 srgb} bind def +/col17 {0.000 0.820 0.820 srgb} bind def +/col18 {0.560 0.000 0.000 srgb} bind def +/col19 {0.690 0.000 0.000 srgb} bind def +/col20 {0.820 0.000 0.000 srgb} bind def +/col21 {0.560 0.000 0.560 srgb} bind def +/col22 {0.690 0.000 0.690 srgb} bind def +/col23 {0.820 0.000 0.820 srgb} bind def +/col24 {0.500 0.190 0.000 srgb} bind def +/col25 {0.630 0.250 0.000 srgb} bind def +/col26 {0.750 0.380 0.000 srgb} bind def +/col27 {1.000 0.500 0.500 srgb} bind def +/col28 {1.000 0.630 0.630 srgb} bind def +/col29 {1.000 0.750 0.750 srgb} bind def +/col30 {1.000 0.880 0.880 srgb} bind def +/col31 {1.000 0.840 0.000 srgb} bind def + +end +save +newpath 0 203 moveto 0 0 lineto 302 0 lineto 302 203 lineto closepath clip newpath +-65.2 249.4 translate +1 -1 scale + +/cp {closepath} bind def +/ef {eofill} bind def +/gr {grestore} bind def +/gs {gsave} bind def +/sa {save} bind def +/rs {restore} bind def +/l {lineto} bind def +/m {moveto} bind def +/rm {rmoveto} bind def +/n {newpath} bind def +/s {stroke} bind def +/sh {show} bind def +/slc {setlinecap} bind def +/slj {setlinejoin} bind def +/slw {setlinewidth} bind def +/srgb {setrgbcolor} bind def +/rot {rotate} bind def +/sc {scale} bind def +/sd {setdash} bind def +/ff {findfont} bind def +/sf {setfont} bind def +/scf {scalefont} bind def +/sw {stringwidth} bind def +/tr {translate} bind def +/tnt {dup dup currentrgbcolor + 4 -2 roll dup 1 exch sub 3 -1 roll mul add + 4 -2 roll dup 1 exch sub 3 -1 roll mul add + 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} + bind def +/shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul + 4 -2 roll mul srgb} bind def + /DrawEllipse { + /endangle exch def + /startangle exch def + /yrad exch def + /xrad exch def + /y exch def + /x exch def + /savematrix mtrx currentmatrix def + x y tr xrad yrad sc 0 0 1 startangle endangle arc + closepath + savematrix setmatrix + } def + +/$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def +/$F2psEnd {$F2psEnteredState restore end} def + +$F2psBegin +10 setmiterlimit +0 slj 0 slc + 0.06299 0.06299 sc +% +% Fig objects follow +% +% Polyline +7.500 slw +n 3375 1350 m 1800 2250 l 3375 2250 l 4950 1350 l 3375 1350 l + cp gs col6 1.00 shd ef gr gs col0 s gr +% Polyline +n 1800 2250 m 3375 2250 l 3375 3465 l 1800 3465 l + cp gs col6 1.00 shd ef gr gs col0 s gr +% Polyline +n 3375 2250 m 3375 3465 l 4950 2520 l 4950 1350 l 3375 2250 l + cp gs col6 1.00 shd ef gr gs col0 s gr +% Ellipse +n 2700 1350 315 135 0 360 DrawEllipse gs col0 s gr + +% Polyline +gs clippath +1142 3806 m 1171 3858 l 1303 3783 l 1184 3817 l 1273 3731 l cp +eoclip +n 1800 3465 m + 1170 3825 l gs col0 s gr gr + +% arrowhead +n 1273 3731 m 1184 3817 l 1303 3783 l 1273 3731 l cp gs 0.00 setgray ef gr col0 s +% Polyline + [60] 0 sd +n 1805 3474 m + 4145 2124 l gs col0 s gr [] 0 sd +% Polyline + [60] 0 sd +n 4140 2970 m + 1575 2970 l gs col0 s gr [] 0 sd +% Polyline +gs clippath +5685 3000 m 5685 2940 l 5534 2940 l 5654 2970 l 5534 3000 l cp +eoclip +n 4140 2970 m + 5670 2970 l gs col0 s gr gr + +% arrowhead +n 5534 3000 m 5654 2970 l 5534 2940 l 5534 3000 l cp gs 0.00 setgray ef gr col0 s +% Polyline + [60] 0 sd +n 1800 2970 m + 1575 2970 l gs col0 s gr [] 0 sd +% Polyline +gs clippath +2730 885 m 2670 885 l 2670 1036 l 2700 916 l 2730 1036 l cp +eoclip +n 2700 1710 m + 2700 900 l gs col0 s gr gr + +% arrowhead +n 2730 1036 m 2700 916 l 2670 1036 l 2730 1036 l cp gs 0.00 setgray ef gr col0 s +% Polyline + [60] 0 sd +n 3375 1350 m + 3375 2250 l gs col0 s gr [] 0 sd +% Polyline + [60] 0 sd +n 2700 1755 m + 2700 3465 l gs col0 s gr [] 0 sd +% Polyline +n 2700 3465 m + 2700 3825 l gs col0 s gr +% Polyline +gs clippath +3075 3660 m 3135 3660 l 3135 3509 l 3105 3629 l 3075 3509 l cp +3135 3225 m 3075 3225 l 3075 3376 l 3105 3256 l 3135 3376 l cp +eoclip +n 3105 3240 m + 3105 3645 l gs col0 s gr gr + +% arrowhead +n 3135 3376 m 3105 3256 l 3075 3376 l 3135 3376 l cp gs 0.00 setgray ef gr col0 s +% arrowhead +n 3075 3509 m 3105 3629 l 3135 3509 l 3075 3509 l cp gs 0.00 setgray ef gr col0 s +/Helvetica ff 180.00 scf sf +1035 3960 m +gs 1 -1 sc (x) col0 sh gr +/Helvetica ff 180.00 scf sf +2655 855 m +gs 1 -1 sc (z) col0 sh gr +/Helvetica ff 180.00 scf sf +5715 3015 m +gs 1 -1 sc (y) col0 sh gr +/Helvetica ff 180.00 scf sf +3240 3690 m +gs 1 -1 sc (reflection plane) col0 sh gr +/Helvetica ff 180.00 scf sf +1755 1395 m +gs 1 -1 sc (rotation) col0 sh gr +/Helvetica ff 180.00 scf sf +1890 1575 m +gs 1 -1 sc (axis) col0 sh gr +$F2psEnd +rs diff --git a/doc/fig/rotate_quadrant_example.fig b/doc/fig/rotate_quadrant_example.fig new file mode 100644 index 0000000..1b8b9df --- /dev/null +++ b/doc/fig/rotate_quadrant_example.fig @@ -0,0 +1,47 @@ +#FIG 3.2 +Landscape +Center +Metric +A4 +100.00 +Single +-2 +1200 2 +1 1 0 1 0 7 50 0 -1 0.000 1 0.0000 2700 1350 315 135 2700 1350 3015 1350 +2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 1 0 2 + 1 1 1.00 60.00 120.00 + 1800 3465 1170 3825 +2 1 1 1 0 7 50 0 -1 4.000 0 0 -1 0 0 2 + 1805 3474 4145 2124 +2 1 1 1 0 7 50 0 -1 4.000 0 0 -1 0 0 2 + 4140 2970 1575 2970 +2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 1 0 2 + 1 1 1.00 60.00 120.00 + 4140 2970 5670 2970 +2 3 0 1 0 6 60 0 20 0.000 0 0 -1 0 0 6 + 3375 1350 1800 2250 3375 2250 4950 1350 3375 1350 3375 1350 +2 1 1 1 0 7 50 0 -1 4.000 0 0 -1 0 0 2 + 1800 2970 1575 2970 +2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 1 0 2 + 1 1 1.00 60.00 120.00 + 2700 1710 2700 900 +2 1 1 1 0 7 50 0 -1 4.000 0 0 -1 0 0 2 + 3375 1350 3375 2250 +2 2 0 1 0 6 60 0 20 0.000 0 0 -1 0 0 5 + 1800 2250 3375 2250 3375 3465 1800 3465 1800 2250 +2 3 0 1 0 6 60 0 20 0.000 0 0 -1 0 0 6 + 3375 2250 3375 3465 4950 2520 4950 1350 3375 2250 3375 2250 +2 1 1 1 0 7 50 0 -1 4.000 0 0 -1 0 0 2 + 2700 1755 2700 3465 +2 1 0 1 0 7 50 0 -1 4.000 0 0 -1 0 0 2 + 2700 3465 2700 3825 +2 1 0 1 0 7 50 0 -1 4.000 0 0 -1 1 1 2 + 1 1 1.00 60.00 120.00 + 1 1 1.00 60.00 120.00 + 3105 3240 3105 3645 +4 0 0 50 0 16 12 0.0000 4 105 90 1035 3960 x\001 +4 0 0 50 0 16 12 0.0000 4 105 90 2655 855 z\001 +4 0 0 50 0 16 12 0.0000 4 150 105 5715 3015 y\001 +4 0 0 50 0 16 12 0.0000 4 180 1290 3240 3690 reflection plane\001 +4 0 0 50 0 16 12 0.0000 4 135 615 1755 1395 rotation\001 +4 0 0 50 0 16 12 0.0000 4 135 330 1890 1575 axis\001 diff --git a/doc/fig/rotate_reflect.eps b/doc/fig/rotate_reflect.eps new file mode 100644 index 0000000..9f2ce06 --- /dev/null +++ b/doc/fig/rotate_reflect.eps @@ -0,0 +1,340 @@ +%!PS-Adobe-2.0 EPSF-2.0 +%%Title: rotate_reflect.eps +%%Creator: fig2dev Version 3.2 Patchlevel 3d +%%CreationDate: Sat Jun 8 18:20:30 2002 +%%For: dp@nbdell15 (Denis Pollney,,,) +%%BoundingBox: 0 0 524 277 +%%Magnification: 1.0000 +%%EndComments +/$F2psDict 200 dict def +$F2psDict begin +$F2psDict /mtrx matrix put +/col-1 {0 setgray} bind def +/col0 {0.000 0.000 0.000 srgb} bind def +/col1 {0.000 0.000 1.000 srgb} bind def +/col2 {0.000 1.000 0.000 srgb} bind def +/col3 {0.000 1.000 1.000 srgb} bind def +/col4 {1.000 0.000 0.000 srgb} bind def +/col5 {1.000 0.000 1.000 srgb} bind def +/col6 {1.000 1.000 0.000 srgb} bind def +/col7 {1.000 1.000 1.000 srgb} bind def +/col8 {0.000 0.000 0.560 srgb} bind def +/col9 {0.000 0.000 0.690 srgb} bind def +/col10 {0.000 0.000 0.820 srgb} bind def +/col11 {0.530 0.810 1.000 srgb} bind def +/col12 {0.000 0.560 0.000 srgb} bind def +/col13 {0.000 0.690 0.000 srgb} bind def +/col14 {0.000 0.820 0.000 srgb} bind def +/col15 {0.000 0.560 0.560 srgb} bind def +/col16 {0.000 0.690 0.690 srgb} bind def +/col17 {0.000 0.820 0.820 srgb} bind def +/col18 {0.560 0.000 0.000 srgb} bind def +/col19 {0.690 0.000 0.000 srgb} bind def +/col20 {0.820 0.000 0.000 srgb} bind def +/col21 {0.560 0.000 0.560 srgb} bind def +/col22 {0.690 0.000 0.690 srgb} bind def +/col23 {0.820 0.000 0.820 srgb} bind def +/col24 {0.500 0.190 0.000 srgb} bind def +/col25 {0.630 0.250 0.000 srgb} bind def +/col26 {0.750 0.380 0.000 srgb} bind def +/col27 {1.000 0.500 0.500 srgb} bind def +/col28 {1.000 0.630 0.630 srgb} bind def +/col29 {1.000 0.750 0.750 srgb} bind def +/col30 {1.000 0.880 0.880 srgb} bind def +/col31 {1.000 0.840 0.000 srgb} bind def + +end +save +newpath 0 277 moveto 0 0 lineto 524 0 lineto 524 277 lineto closepath clip newpath +-10.6 340.9 translate +1 -1 scale + +/cp {closepath} bind def +/ef {eofill} bind def +/gr {grestore} bind def +/gs {gsave} bind def +/sa {save} bind def +/rs {restore} bind def +/l {lineto} bind def +/m {moveto} bind def +/rm {rmoveto} bind def +/n {newpath} bind def +/s {stroke} bind def +/sh {show} bind def +/slc {setlinecap} bind def +/slj {setlinejoin} bind def +/slw {setlinewidth} bind def +/srgb {setrgbcolor} bind def +/rot {rotate} bind def +/sc {scale} bind def +/sd {setdash} bind def +/ff {findfont} bind def +/sf {setfont} bind def +/scf {scalefont} bind def +/sw {stringwidth} bind def +/tr {translate} bind def +/tnt {dup dup currentrgbcolor + 4 -2 roll dup 1 exch sub 3 -1 roll mul add + 4 -2 roll dup 1 exch sub 3 -1 roll mul add + 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} + bind def +/shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul + 4 -2 roll mul srgb} bind def +/$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def +/$F2psEnd {$F2psEnteredState restore end} def + +$F2psBegin +10 setmiterlimit +0 slj 0 slc + 0.06299 0.06299 sc +% +% Fig objects follow +% +% Polyline +435.000 slw +gs clippath +3300 2580 m 3300 1830 l 3161 1830 l 3281 2205 l 3161 2580 l cp +eoclip +n 2385 2205 m + 3285 2205 l gs col6 s gr gr + +% arrowhead +7.500 slw +n 3161 2580 m 3281 2205 l 3161 1830 l 3161 2580 l cp gs col6 1.00 shd ef gr col6 s +% Polyline +435.000 slw +gs clippath +6225 2580 m 6225 1830 l 6086 1830 l 6206 2205 l 6086 2580 l cp +eoclip +n 5310 2205 m + 6210 2205 l gs col6 s gr gr + +% arrowhead +7.500 slw +n 6086 2580 m 6206 2205 l 6086 1830 l 6086 2580 l cp gs col6 1.00 shd ef gr col6 s +% Polyline +435.000 slw +gs clippath +4965 4830 m 4965 4080 l 4826 4080 l 4946 4455 l 4826 4830 l cp +eoclip +n 3800 4455 m + 4950 4455 l gs col7 1.00 shd ef gr gs col6 s gr gr + +% arrowhead +7.500 slw +n 4826 4830 m 4946 4455 l 4826 4080 l 4826 4830 l cp gs col6 1.00 shd ef gr col6 s +% Polyline +gs clippath +1815 2280 m 1815 2220 l 1664 2220 l 1784 2250 l 1664 2280 l cp +eoclip +n 1125 2250 m + 1800 2250 l gs col0 s gr gr + +% arrowhead +n 1664 2280 m 1784 2250 l 1664 2220 l 1664 2280 l cp gs 0.00 setgray ef gr col0 s +% Polyline +gs clippath +643 2689 m 685 2731 l 792 2625 l 686 2689 l 749 2582 l cp +eoclip +n 1125 2250 m + 675 2700 l gs col0 s gr gr + +% arrowhead +n 749 2582 m 686 2689 l 792 2625 l 749 2582 l cp gs 0.00 setgray ef gr col0 s +% Polyline +gs clippath +1155 1560 m 1095 1560 l 1095 1711 l 1125 1591 l 1155 1711 l cp +eoclip +n 1125 2250 m + 1125 1575 l gs col0 s gr gr + +% arrowhead +n 1155 1711 m 1125 1591 l 1095 1711 l 1155 1711 l cp gs 0.00 setgray ef gr col0 s +/Helvetica ff 180.00 scf sf +630 2835 m +gs 1 -1 sc (x) col0 sh gr +/Helvetica ff 180.00 scf sf +1845 2340 m +gs 1 -1 sc (y) col0 sh gr +/Helvetica ff 180.00 scf sf +1080 1530 m +gs 1 -1 sc (z) col0 sh gr +% Polyline +gs clippath +7365 1560 m 7305 1560 l 7305 1711 l 7335 1591 l 7365 1711 l cp +eoclip +n 7335 2250 m + 7335 1575 l gs col0 s gr gr + +% arrowhead +n 7365 1711 m 7335 1591 l 7305 1711 l 7365 1711 l cp gs 0.00 setgray ef gr col0 s +% Polyline +gs clippath +6645 2220 m 6645 2280 l 6796 2280 l 6676 2250 l 6796 2220 l cp +eoclip +n 7335 2250 m + 6660 2250 l gs col0 s gr gr + +% arrowhead +n 6796 2220 m 6676 2250 l 6796 2280 l 6796 2220 l cp gs 0.00 setgray ef gr col0 s +% Polyline +gs clippath +7816 1810 m 7774 1768 l 7667 1874 l 7774 1811 l 7710 1917 l cp +eoclip +n 7335 2250 m + 7785 1800 l gs col0 s gr gr + +% arrowhead +n 7710 1917 m 7774 1811 l 7667 1874 l 7710 1917 l cp gs 0.00 setgray ef gr col0 s +/Helvetica ff 180.00 scf sf +7290 1530 m +gs 1 -1 sc (z) col0 sh gr +/Helvetica ff 180.00 scf sf +6525 2295 m +gs 1 -1 sc (y) col0 sh gr +/Helvetica ff 180.00 scf sf +7785 1800 m +gs 1 -1 sc (x) col0 sh gr +% Polyline +gs clippath +4620 1560 m 4560 1560 l 4560 1711 l 4590 1591 l 4620 1711 l cp +eoclip +n 4590 2250 m + 4590 1575 l gs col0 s gr gr + +% arrowhead +n 4620 1711 m 4590 1591 l 4560 1711 l 4620 1711 l cp gs 0.00 setgray ef gr col0 s +% Polyline +gs clippath +4108 2689 m 4150 2731 l 4257 2625 l 4151 2689 l 4214 2582 l cp +eoclip +n 4590 2250 m + 4140 2700 l gs col0 s gr gr + +% arrowhead +n 4214 2582 m 4151 2689 l 4257 2625 l 4214 2582 l cp gs 0.00 setgray ef gr col0 s +% Polyline +gs clippath +3855 2220 m 3855 2280 l 4006 2280 l 3886 2250 l 4006 2220 l cp +eoclip +n 4545 2250 m + 3870 2250 l gs col0 s gr gr + +% arrowhead +n 4006 2220 m 3886 2250 l 4006 2280 l 4006 2220 l cp gs 0.00 setgray ef gr col0 s +% Polyline +gs clippath +3900 2220 m 3900 2280 l 4051 2280 l 3931 2250 l 4051 2220 l cp +eoclip +n 4590 2250 m + 3915 2250 l gs col0 s gr gr + +% arrowhead +n 4051 2220 m 3931 2250 l 4051 2280 l 4051 2220 l cp gs 0.00 setgray ef gr col0 s +/Helvetica ff 180.00 scf sf +4050 2835 m +gs 1 -1 sc (x) col0 sh gr +/Helvetica ff 180.00 scf sf +3780 2295 m +gs 1 -1 sc (y) col0 sh gr +/Helvetica ff 180.00 scf sf +4545 1530 m +gs 1 -1 sc (z) col0 sh gr +% Polyline +gs clippath +6240 3810 m 6180 3810 l 6180 3961 l 6210 3841 l 6240 3961 l cp +eoclip +n 6210 4500 m + 6210 3825 l gs col0 s gr gr + +% arrowhead +n 6240 3961 m 6210 3841 l 6180 3961 l 6240 3961 l cp gs 0.00 setgray ef gr col0 s +% Polyline +gs clippath +5520 4470 m 5520 4530 l 5671 4530 l 5551 4500 l 5671 4470 l cp +eoclip +n 6210 4500 m + 5535 4500 l gs col0 s gr gr + +% arrowhead +n 5671 4470 m 5551 4500 l 5671 4530 l 5671 4470 l cp gs 0.00 setgray ef gr col0 s +% Polyline +gs clippath +6691 4060 m 6649 4018 l 6542 4124 l 6649 4061 l 6585 4167 l cp +eoclip +n 6210 4500 m + 6660 4050 l gs col0 s gr gr + +% arrowhead +n 6585 4167 m 6649 4061 l 6542 4124 l 6585 4167 l cp gs 0.00 setgray ef gr col0 s +/Helvetica ff 180.00 scf sf +6165 3780 m +gs 1 -1 sc (z) col0 sh gr +/Helvetica ff 180.00 scf sf +5400 4545 m +gs 1 -1 sc (y) col0 sh gr +/Helvetica ff 180.00 scf sf +6660 4050 m +gs 1 -1 sc (x) col0 sh gr +% Polyline +gs clippath +3255 4530 m 3255 4470 l 3104 4470 l 3224 4500 l 3104 4530 l cp +eoclip +n 2565 4500 m + 3240 4500 l gs col0 s gr gr + +% arrowhead +n 3104 4530 m 3224 4500 l 3104 4470 l 3104 4530 l cp gs 0.00 setgray ef gr col0 s +% Polyline +gs clippath +2083 4939 m 2125 4981 l 2232 4875 l 2126 4939 l 2189 4832 l cp +eoclip +n 2565 4500 m + 2115 4950 l gs col0 s gr gr + +% arrowhead +n 2189 4832 m 2126 4939 l 2232 4875 l 2189 4832 l cp gs 0.00 setgray ef gr col0 s +% Polyline +gs clippath +2595 3810 m 2535 3810 l 2535 3961 l 2565 3841 l 2595 3961 l cp +eoclip +n 2565 4500 m + 2565 3825 l gs col0 s gr gr + +% arrowhead +n 2595 3961 m 2565 3841 l 2535 3961 l 2595 3961 l cp gs 0.00 setgray ef gr col0 s +/Helvetica ff 180.00 scf sf +2070 5085 m +gs 1 -1 sc (x) col0 sh gr +/Helvetica ff 180.00 scf sf +3285 4590 m +gs 1 -1 sc (y) col0 sh gr +/Helvetica ff 180.00 scf sf +2520 3780 m +gs 1 -1 sc (z) col0 sh gr +% Polyline +n 180 1035 m 8460 1035 l 8460 3150 l 180 3150 l + cp gs col0 s gr +% Polyline +n 180 3285 m 8460 3285 l 8460 5400 l 180 5400 l + cp gs col0 s gr +/Helvetica ff 180.00 scf sf +2745 2340 m +gs 1 -1 sc (y) col0 sh gr +/Helvetica ff 180.00 scf sf +2565 2160 m +gs 1 -1 sc (reflect) col0 sh gr +/Helvetica ff 180.00 scf sf +3825 4410 m +gs 1 -1 sc (rotate about) col0 sh gr +/Helvetica ff 180.00 scf sf +5490 2205 m +gs 1 -1 sc (reflect) col0 sh gr +/Helvetica ff 180.00 scf sf +5670 2385 m +gs 1 -1 sc (x) col0 sh gr +/Helvetica ff 180.00 scf sf +4230 4590 m +gs 1 -1 sc (z) col0 sh gr +$F2psEnd +rs diff --git a/doc/fig/rotate_reflect.fig b/doc/fig/rotate_reflect.fig new file mode 100644 index 0000000..d5598ba --- /dev/null +++ b/doc/fig/rotate_reflect.fig @@ -0,0 +1,101 @@ +#FIG 3.2 +Landscape +Center +Metric +A4 +100.00 +Single +-2 +1200 2 +6 630 1395 1980 2835 +2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 1 0 2 + 1 1 1.00 60.00 120.00 + 1125 2250 1800 2250 +2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 1 0 2 + 1 1 1.00 60.00 120.00 + 1125 2250 675 2700 +2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 1 0 2 + 1 1 1.00 60.00 120.00 + 1125 2250 1125 1575 +4 0 0 50 0 16 12 0.0000 4 105 90 630 2835 x\001 +4 0 0 50 0 16 12 0.0000 4 150 105 1845 2340 y\001 +4 0 0 50 0 16 12 0.0000 4 105 90 1080 1530 z\001 +-6 +6 6525 1395 7875 2340 +2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 1 0 2 + 1 1 1.00 60.00 120.00 + 7335 2250 7335 1575 +2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 1 0 2 + 1 1 1.00 60.00 120.00 + 7335 2250 6660 2250 +2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 1 0 2 + 1 1 1.00 60.00 120.00 + 7335 2250 7785 1800 +4 0 0 50 0 16 12 0.0000 4 105 90 7290 1530 z\001 +4 0 0 50 0 16 12 0.0000 4 150 105 6525 2295 y\001 +4 0 0 50 0 16 12 0.0000 4 105 90 7785 1800 x\001 +-6 +6 3780 1395 4635 2835 +2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 1 0 2 + 1 1 1.00 60.00 120.00 + 4590 2250 4590 1575 +2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 1 0 2 + 1 1 1.00 60.00 120.00 + 4590 2250 4140 2700 +2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 1 0 2 + 1 1 1.00 60.00 120.00 + 4545 2250 3870 2250 +2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 1 0 2 + 1 1 1.00 60.00 120.00 + 4590 2250 3915 2250 +4 0 0 50 0 16 12 0.0000 4 105 90 4050 2835 x\001 +4 0 0 50 0 16 12 0.0000 4 150 105 3780 2295 y\001 +4 0 0 50 0 16 12 0.0000 4 105 90 4545 1530 z\001 +-6 +6 5400 3645 6750 4590 +2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 1 0 2 + 1 1 1.00 60.00 120.00 + 6210 4500 6210 3825 +2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 1 0 2 + 1 1 1.00 60.00 120.00 + 6210 4500 5535 4500 +2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 1 0 2 + 1 1 1.00 60.00 120.00 + 6210 4500 6660 4050 +4 0 0 50 0 16 12 0.0000 4 105 90 6165 3780 z\001 +4 0 0 50 0 16 12 0.0000 4 150 105 5400 4545 y\001 +4 0 0 50 0 16 12 0.0000 4 105 90 6660 4050 x\001 +-6 +6 2070 3645 3420 5085 +2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 1 0 2 + 1 1 1.00 60.00 120.00 + 2565 4500 3240 4500 +2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 1 0 2 + 1 1 1.00 60.00 120.00 + 2565 4500 2115 4950 +2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 1 0 2 + 1 1 1.00 60.00 120.00 + 2565 4500 2565 3825 +4 0 0 50 0 16 12 0.0000 4 105 90 2070 5085 x\001 +4 0 0 50 0 16 12 0.0000 4 150 105 3285 4590 y\001 +4 0 0 50 0 16 12 0.0000 4 105 90 2520 3780 z\001 +-6 +2 2 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 5 + 180 1035 8460 1035 8460 3150 180 3150 180 1035 +2 2 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 5 + 180 3285 8460 3285 8460 5400 180 5400 180 3285 +2 1 0 30 6 7 60 0 -1 0.000 0 0 -1 1 0 2 + 1 1 1.00 750.00 120.00 + 2385 2205 3285 2205 +2 1 0 30 6 7 60 0 -1 0.000 0 0 -1 1 0 2 + 1 1 1.00 750.00 120.00 + 5310 2205 6210 2205 +2 1 0 30 6 7 60 0 20 0.000 0 0 -1 1 0 2 + 1 1 1.00 750.00 120.00 + 3800 4455 4950 4455 +4 0 0 50 0 16 12 0.0000 4 150 105 2745 2340 y\001 +4 0 0 50 0 16 12 0.0000 4 135 510 2565 2160 reflect\001 +4 0 0 50 0 16 12 0.0000 4 135 990 3825 4410 rotate about\001 +4 0 0 50 0 16 12 0.0000 4 135 510 5490 2205 reflect\001 +4 0 0 50 0 16 12 0.0000 4 105 90 5670 2385 x\001 +4 0 0 50 0 16 12 0.0000 4 105 90 4230 4590 z\001 diff --git a/doc/rotating_sym.tex b/doc/rotating_sym.tex new file mode 100644 index 0000000..e5ef6b7 --- /dev/null +++ b/doc/rotating_sym.tex @@ -0,0 +1,468 @@ +% /*@@ +% @file rotating_sym.tex +% @date 6 June 2002 +% @author Denis Pollney +% @desc +% Description of the implementation of `rotating' +% symmetry conditions in CartGrid3D. +% @enddesc +% @version $Header$ +% @@*/ + +\documentclass{article} + +\newif\ifpdf +\ifx\pdfoutput\undefined +\pdffalse % we are not running PDFLaTeX +\else +\pdfoutput=1 % we are running PDFLaTeX +\pdftrue +\fi + +\ifpdf +\usepackage[pdftex]{graphicx} +\else +\usepackage{graphicx} +\fi + +\parskip = 0 pt +\parindent = 0pt +\oddsidemargin = 0 cm +\textwidth = 16 cm +\topmargin = -1 cm +\textheight = 24 cm + +\begin{document} + +\title{Rotating symmetry conditions} +\author{Denis Pollney} +\date{June 2002} + +\maketitle + +\begin{abstract} +These notes describe the implentation of rotating symmetry conditions +for \emph{bitant} and \emph{quadrant} domains in \texttt{CartGrid3D}. +For these particular domain types, the condition that fields on the +grid are have a rotational symmetry in a plane along one of the +coordinate axes can be simply implemented with minor extensions to the +already existing symmetry mechanism, which copies the components of +a given field to the required ghost-zones with a possible plus-minus +inversion. +\end{abstract} + +%------------------------------------------------------------------------------ +\section{Introduction} +\label{sec:rs_intro} +%------------------------------------------------------------------------------ + +A number of useful physical models involve situations where a +rotational symmetry is present in all of the relevant fields. By +`rotational symmetry' we mean that there exists a pair of half-planes +extending from one of the coordinate axes and separated by an angle +$\theta$ which have the property that on $A$ and near to $A$ can be +mapped onto $B$ and corresponding points near to $B$ (see Figure +\ref{fig:rs_rotation_examples}). +% +\begin{figure} +\centering +\begin{tabular}{ccc} +\ifpdf +\else +\includegraphics[height=40mm]{fig/rotate_general.eps} +\fi +& +\ifpdf +\else +\includegraphics[height=40mm]{fig/rotate_bitant.eps} +\fi +& +\ifpdf +\else +\includegraphics[height=25mm]{fig/rotate_octant.eps} +\fi +\\ +(a) & (b) & (c) +\end{tabular} +\caption{Rotational symmetries, looking down the $z$-axis. In the +general case (a), the half-planes $A$ and $B$ are separated by an +angle $\theta$. Data at $A$ can be mapped on to points of $B$ via a +rotation through $\theta$. Particular cases of importance are the +rotation through $\theta=\pi$, so that data on the positive $y$-axis +is mapped onto the negative $y$, and vice versa; and the rotation +through $\theta=3\pi/2$ so that data need be specified only in a +single quarter-plane.} +\label{fig:rs_rotation_examples} +\end{figure} +% +In particular, situations for which such conditions can be useful +include +\begin{itemize} + \item rotating axisymmetric bodies -- satisfies the rotational + symmetry for arbitrary $\theta$. + \item pairs of massive bodies separated by distances $\pm + \mathbf{d}$ from the origin and with identical oppositely directed + momenta $\pm \mathbf{p}$ (Figure \ref{fig:rs_bbh}) -- satisfies + the half-plane rotational symmetry ($\theta=\pi$) or, if + $\mathbf{p}=0$ then also the quarter plane symmetry + ($\theta=3\pi/2$). +\end{itemize} +\begin{figure} +\centering +\ifpdf +\else +\includegraphics[height=40mm]{fig/rotate_bbh.eps} +\fi +\caption{A physical system consisting of a pair of identical bodies + separated equal distance along a line through the origin, and moving + with equal but opposite momenta, can be modelled using only the + positive half-plane if the rotating symmetry condition is applied to + the $x=0$ plane.} +\label{fig:rs_bbh} +\end{figure} + +In order to apply the boundary condition exactly on a numerical grid, +it is necessary that grid points to each side of the mapping planes +$A$ and $B$ can be mapped onto each other exactly. In particular, this +means that the rotating symmetry conditions can be applied exactly if +the half-planes are each aligned with one of the coordinate axes. For +general planes $A$ and $B$, however, interpolation would be required +to put data in the neighbourhood of $A$ onto grid points near +$B$. Only the particular cases described by Figures +\ref{fig:rs_rotation_examples} (b) and (c) will be +considered here. + +%------------------------------------------------------------------------------ +\section{Symmetry conditions} +\label{sec:rs_application} +%------------------------------------------------------------------------------ + +For a given field, the boundary condition is applied as follows. For +each ghost-zone point along the symmetry plane, the corresponding +point on the physical grid (under the rotational $\theta$) is +determined. To determine the value of the ghost-zone point, the +value on the physical grid is simply transformed under the given +rotation.\\ + +The first of these issues is not difficult to resolve. As an example, +consider the half-plane rotational symmetry about the $z$-axis applied +in the $x=0$ plane, as depicted in Figure \ref{fig:rs_grid}. The has +$j=0\ldots m$ in the $y$ direction, an arbitrary number of points in the +$x$ and $z$ directions, and some ghostzones whose $j$ coordinates are +labelled $j=-1,-2,\ldots$. Then for the ghost-zone point $(n-i, -j, +k)$, the corresponding physical point under rotation is (1) $(i,j-1,k)$ +if the $x=0$ plane is on the grid, or (2) $(i,j,k)$ if the $x=0$ plane +is staggered between a grid point and the first ghost-zone +point. There is an implicit assumption here that the grid extends +exactly the same distance to each side of the rotation axis. \\ + +\begin{figure} +\centering +\ifpdf +\else +\includegraphics[height=40mm]{fig/rotate_grid.eps} +\fi +\caption{The mapping of physical points onto ghost-zone points for a + half-plane rotation about the $z$-axis, where the $x=0$ plane is + staggered between gridpoints, and two ghost zones have been + allocated.} +\label{fig:rs_grid} +\end{figure} + +The remaining issue is to determine how the fields at a point +$(i,j,k)$ are modified under a rotation of a given angle. A set of +basis vectors $(\mathbf{\hat{x}},\mathbf{\hat{y}},\mathbf{\hat{z}})$ +can be rotated to an arbitrary direction by applying the rotation +matrix +\begin{equation} + \mathbf{P} = + \left[ + \begin{array}{ccc} + \eta_1(\cos\theta_1\cos\theta_3 - \sin\theta_1\cos\theta_2\sin\theta_3) & + \sin\theta_1\cos\theta_3 + \cos\theta_1\cos\theta_2\sin\theta_3 & + \sin\theta_2\sin\theta_3 \\ + -(\cos\theta_1\sin\theta_3 + \sin\theta_1\cos\theta_2\cos\theta3) & + \eta_2(\sin\theta_1\sin\theta_3 + \cos\theta_1\cos\theta_2\cos\theta_3) & + \sin\theta_2\cos\theta_3 \\ + \sin\theta_1\sin\theta_2 & + -\cos\theta_1\sin\theta_2 & + \eta_3\cos\theta_2 + \end{array} + \right], +\end{equation} +which preserves the orthogonality of the basis. The matrix +$\mathbf{P}$ has been written in terms of the Euler angles +$0\leq\theta_1<2\pi$, $0\leq\theta_2<2\pi$, and $0\leq\theta_3<\pi$, +and the factors $\eta_1=\pm 1$, $\eta_2=\pm 1$, $\eta_3=\pm 1$ are +introduced to allow for reflections of individual axes (ie. changes of +handedness of the basis). +The basis is transformed under $\mathbf{P}$ via the matrix multiplication +\begin{equation} + \left[ + \begin{array}{c} + \mathbf{\hat{x}^\prime} \\ + \mathbf{\hat{y}^\prime} \\ + \mathbf{\hat{z}^\prime} + \end{array} + \right] + = + \mathbf{P} + \left[ + \begin{array}{c} + \mathbf{\hat{x}} \\ + \mathbf{\hat{y}} \\ + \mathbf{\hat{z}} + \end{array} + \right]. +\end{equation} + +Vectors and tensor components are transformed under the given rotation +by applying the $\mathbf{P}$ matrix: +\begin{eqnarray} + \mathbf{v} & \rightarrow & \mathbf{P}^T \mathbf{v}, \\ + \mathbf{G} & \rightarrow & \mathbf{P}^T \mathbf{G} \mathbf{P}, +\end{eqnarray} +where $\mathbf{v}$ is a 3-vector, +\begin{equation} + \mathbf{v} = [v_x, v_y, v_z]^T, +\end{equation} +and $\mathbf{G}$ is a two-index tensor treated as a matrix, +\begin{equation} + \mathbf{G} = + \left[ + \begin{array}{ccc} + g_{xx} & g_{xy} & g_{xz} \\ + g_{yx} & g_{yy} & g_{yz} \\ + g_{zx} & g_{zy} & g_{zz} + \end{array} + \right]. +\end{equation} + +\emph{Example 1.} The special case of a reflection in the $x=0$ plane +corresponds to an inversion of the $x$-axis, so that +$\theta_1=\theta_2=\theta_3=0$ and $\eta_1=-1$, +\begin{equation} + \mathbf{P}_{x-\mathrm{reflect}} = \left[ + \begin{array}{ccc} + -1 & 0 & 0 \\ + 0 & 1 & 0 \\ + 0 & 0 & 1 + \end{array} + \right]. +\end{equation} + +\emph{Example 2.} For a rotation about the $z$ axis by an angle of +$\theta=\pi$ (corresponding to Figure \ref{fig:rs_grid}), the only +non-zero rotation angle is $\theta_1=\pi$, so that +\begin{equation} + \mathbf{P}_{z-\mathrm{rotate}} = \left[ + \begin{array}{ccc} + -1 & 0 & 0 \\ + 0 & -1 & 0 \\ + 0 & 0 & 1 + \end{array} + \right]. +\end{equation} + +\emph{Example 3.} A quarter-plane grid with positive $y$-axis values +mapped onto the positive $x$-axis (as in Figure\nobreak~ +\ref{fig:rs_rotation_examples}) corresponds non-zero angle +$\theta_1=3\pi/2$, with the resulting rotation matrix +\begin{equation} + \mathbf{P}_{z-\mathrm{rotate(3/2)}} = \left[ + \begin{array}{ccc} + 0 & -1 & 0 \\ + 1 & 0 & 0 \\ + 0 & 0 & 1 + \end{array} + \right]. +\end{equation} + +%------------------------------------------------------------------------------ +\section{Implementation} +\label{sec:rs_implementation} +%------------------------------------------------------------------------------ + +In order to implement the bitant, quadrant and octant +\emph{reflection} symmetries which already exist in +\texttt{CartGrid3D}, it was necessary to attach to each grid function +information corresponding to how the field transforms under +reflections in each of the $x$, $y$, and $z$ axes. These are +specified as an array of three integers, each taking the value $+1$ or +$-1$, which is passed to the symmetry registration function. For +example, +\begin{verbatim} + static int one=1; + int sym[3]; + sym[0] = -one; + sym[1] = -one; + sym[2] = one; + SetCartSymVN(cctkGH, sym,"einstein::gxy"); +\end{verbatim} +specifies that the grid function \texttt{einstein::gxy} should be +negated under reflections in $x=0$ and $y=0$, but keeps the same value +under reflections in the $z=0$ plane.\\ + +This is the only information required for the reflection symmetry +since the value of the field at the new (reflected) point does not +require information from any other fields. For example, for a vector +$v = (v_x, v_y, v_z)^T$ reflected in $x=0$, we have +\begin{equation} + v_x \rightarrow -v_x, \qquad v_y \rightarrow v_y, \qquad + v_z \rightarrow v_z. +\end{equation} +That is, the transformation of $v_x$ only needs to know the values of +$v_x$, and does not need to know anything about the values of $v_y$ or +$v_z$. On the other hand, for the $3\pi/2$-rotation corresponding to +Example 3, above, the vector would transform as: +\begin{equation} + v_x \rightarrow -v_y, \qquad v_y \rightarrow v_x, \qquad + v_z \rightarrow v_z. +\end{equation} +In this case, to determine the rotated $v_x$ component it is necessary +to know the value of $v_y$. However, there is no concept of vector or +tensor within Cactus, so that given a grid function corresponding to +$v_x$, it is not generally possible to know which grid function +corresponds to $v_y$ which should be used to determine the rotated +values.\\ + +As a result, the only symmetries which can easily be implemented +within the current mechanism are those which require only the grid +function itself in order to determine the ghost zone points. This +includes the $\pi$-rotation symmetries (`half-plane', Figure +\ref{fig:rs_rotation_examples} (b)) but not the $3\pi/2$-rotation +symmetries (`quarter-plane', Figure \ref{fig:rs_rotation_examples} +(c)).\\ + +Table \ref{tbl:rs_xform} lists the transformations of the components +of an arbitrary scalar, vector and two-index tensor under reflections +in each plane, and rotations about each axis. +\begin{table} +\centering +\begin{tabular}{r|rrr|rrr}\hline\hline + & \multicolumn{3}{c|}{reflection in} + & \multicolumn{3}{c}{rotation about} \\ + & $x$ & $y$ & $z$ & $x$ & $y$ & $z$ \\ \hline +$\phi$ & 1 & 1 & 1 & 1 & 1 & 1 \\ \hline +$v_x$ & -1 & 1 & 1 & 1 & -1 & -1 \\ +$v_y$ & 1 & -1 & 1 & -1 & 1 & -1 \\ +$v_z$ & 1 & 1 & -1 & -1 & -1 & 1 \\ \hline +$g_{xx}$ & 1 & 1 & 1 & 1 & 1 & 1 \\ +$g_{xy}$ & -1 & -1 & 1 & -1 & -1 & 1 \\ +$g_{xz}$ & -1 & 1 & -1 & -1 & 1 & -1 \\ +$g_{yy}$ & 1 & 1 & 1 & 1 & 1 & 1 \\ +$g_{yz}$ & 1 & -1 & -1 & 1 & -1 & -1 \\ +$g_{zz}$ & 1 & 1 & 1 & 1 & 1 & 1 \\ \hline\hline +\end{tabular} +\caption{Transformation factors for reflection and half-plane rotation +symmetries.} +\label{tbl:rs_xform} +\end{table} +We note the following useful fact: The transformation factor $s_i$ for +a rotation about the axis $i$ is given by $s_j \times s_k$ where +$i\neq j\neq k$. For example, for a rotation about the $z$-axis, the +transformation factor for the is given by +\begin{equation} + s_x \times s_y = -1 \times -1 = 1. +\end{equation} +Intuitively, this is clear since the rotation of the axes by $\pi$ +radians about $z$ is equivalent to a reflection in $y$ followed by +a reflection in $x$ (Figure \ref{fig:rs_rotate_reflect}).\\ + +\begin{figure} +\centering +\ifpdf +\else +\includegraphics[height=40mm]{fig/rotate_reflect.eps} +\fi +\caption{A rotation by $\pi$ radians about the $z$-axis is equivalent + to successive reflections about the $y$- and $x$-axes.} +\label{fig:rs_rotate_reflect} +\end{figure} + +Since the transformation values for reflection symmetries are +already specified for each Cactus grid function, we can use this +information to unambiguously determine the $\pi$-rotation +transformation coefficients, without requiring that any new +information be added if the reflection symmetries have already +been defined (as is the case for any Cactus GFs which are able to +use the current \texttt{bitant}, \texttt{quadrant} and \texttt{octant} +domains). + +%------------------------------------------------------------------------------ +\section{\texttt{CartGrid3D} Notes} +\label{sec:rs_cartgrid3d} +%------------------------------------------------------------------------------ + +Two types of rotating symmetry conditions have been implemented in +\texttt{CartGrid3D} as extensions to the \texttt{grid::domain} +parameter.\\ + +The first, \texttt{bitant\_rotate}, defines a grid which is half-sized +along one axis, and assumes a field that is rotating about a +perpendicular axis. The half-axis is chosen using the +\texttt{bitant\_plane} parameter, which specifies the plane at which +the grid is to be cut as either ``\texttt{xy}'', ``\texttt{xz}'' or +``\texttt{yz}''. The rotation axis is chosen using the +\texttt{rotation\_axis} parameter, which takes values of +``\texttt{x}'', ``\texttt{y}'' or ``\texttt{z}''. For example, to +specify a bitant domain along the positive $y$-axis, on which fields +are rotating about the $z$-axis, the following parameters would do the +job: +\begin{verbatim} + grid::domain = "bitant_rotate" + grid::bitant_plane = "xz" + grid::rotation_axis = "z" +\end{verbatim} +This setup is illustrated in Figure \ref{fig:rs_bitant_example} (a).\\ + +\begin{figure} +\centering +\begin{tabular}{cc} +\ifpdf +\else +\includegraphics[height=40mm]{fig/rotate_bitant_example.eps} +\fi +& +\ifpdf +\else +\includegraphics[height=30mm]{fig/rotate_quadrant_example.eps} +\fi +\\ +(a) & (b) +\end{tabular} +\caption{Active grids for the \texttt{bitant\_rotate} and + \texttt{quadrant\_reflect\_rotate} domains for the examples given in + the text. (a) The given \texttt{bitant\_rotate} domain corresponds + to the $y>0$ half-grid, with fields rotating about the $z$-axis. (b) + The \texttt{quadrant\_reflect\_rotate} example is similar, except + the active grid is only along the positive $z$-axis and a reflection + symmetry is assumed in the $z=0$ plane.} +\label{fig:rs_bitant_example} +\end{figure} + +The \texttt{quadrant\_reflect\_rotate} symmetry cuts two of the axes +in half so that only a quadrant of the full domain is active. A +standard reflection symmetry is applied to one of the half-planes, +while the physical fields are assumed to rotate in the other plane. To +set up such a grid which rotates about the $z$-axis and which is +reflection symmetric in the $z=0$ plane, the following parameters +could be used: +\begin{verbatim} + grid::domain = "quadrant_rotate_reflect" + grid::quadrant_direction = "x" + grid::rotation_axis = "z" +\end{verbatim} +Note that the \texttt{quadrant\_direction} parameter follows the +current \texttt{CartGrid3D} standard, which defines the domain on the +\emph{positive} quadrant with the long edge aligned with the specified +axis. It is currently not possible to choose the negative quadrant.\\ + +Octant rotation symmetries, or the alternate quadrant symmetry (for +which the data on one half-plane is rotated onto the other), are more +difficult to implement without some generalisation of the existing +\texttt{CartGrid3D} specification of symmetry boundaries for the +reasons mentioned in the previous section. + +%------------------------------------------------------------------------------ +\end{document} @@ -118,10 +118,12 @@ KEYWORD type "Grid type" KEYWORD domain "Domain type" { - "octant" :: "Use an octant about the origin" - "quadrant" :: "Use a quadrant in x-y plane" - "bitant" :: "Use a bitant about the x-y plane" - "full" :: "Use the full domain" + "octant" :: "Use an octant about the origin" + "quadrant" :: "Use a quadrant in x-y plane" + "quadrant_reflect_rotate" :: "Use a quadrant with rotation symmetry about an axis" + "bitant" :: "Use a bitant about the x-y plane" + "bitant_rotate" :: "Use a bitant with rotation symmetry about an axis" + "full" :: "Use the full domain" } "full" KEYWORD bitant_plane "Plane defining bitant domain" @@ -138,6 +140,14 @@ KEYWORD quadrant_direction "Direction defining quadrant domain" "z" :: "z-direction" } "z" +KEYWORD rotation_axis "Axis about which the rotation symmetry is to be applied" +{ + "x" :: "x-axis" + "y" :: "y-axis" + "z" :: "z-axis" +} "z" + + BOOLEAN symmetry_xmin "Symmetry boundary condition on lower x boundary" { : :: "Logical" diff --git a/src/CartGrid3D.c b/src/CartGrid3D.c index 64792f5..c4674aa 100644 --- a/src/CartGrid3D.c +++ b/src/CartGrid3D.c @@ -16,6 +16,7 @@ #include "cctk.h" #include "cctk_Arguments.h" #include "cctk_Parameters.h" +#include "Symmetry.h" static const char *rcsid = "$Header$"; @@ -425,6 +426,19 @@ void CartGrid3D(CCTK_ARGUMENTS) } /* if (coarsest refinement level) */ + if ((domainsym[0]==GFSYM_ROTATION_Y || domainsym[2]==GFSYM_ROTATION_X) + && (lowerz != -upperz)) + CCTK_WARN(0, "minimum z must equal maximum z for rotation symmetry"); + + if ((domainsym[0]==GFSYM_ROTATION_Z || domainsym[4]==GFSYM_ROTATION_X) + && (lowery != -uppery)) + CCTK_WARN(0, "minimum y must equal maximum y for rotation symmetry"); + + if ((domainsym[2]==GFSYM_ROTATION_Z || domainsym[4]==GFSYM_ROTATION_Y) + && (lowerx != -upperx)) + CCTK_WARN(0, "minimum x must equal maximum x for rotation symmetry"); + + #ifdef CCTK_DEBUG printf("\n"); printf("CartGrid3D\n"); diff --git a/src/DecodeSymParameters.c b/src/DecodeSymParameters.c index df8d581..88b12b5 100644 --- a/src/DecodeSymParameters.c +++ b/src/DecodeSymParameters.c @@ -1,3 +1,4 @@ + /*@@ @file DecodeSymParameters.c @date Wed May 10 18:58:00 EST 2000 @@ -11,6 +12,7 @@ #include "cctk.h" #include "cctk_Arguments.h" #include "cctk_Parameters.h" +#include "Symmetry.h" static const char *rcsid = "$Header$"; @@ -55,39 +57,105 @@ void DecodeSymParameters3D(int sym[6]) { if (CCTK_Equals(bitant_plane, "xy")) { - sym[4] = 1; + sym[4] = GFSYM_REFLECTION; + } + else if (CCTK_Equals(bitant_plane, "xz")) + { + sym[2] = GFSYM_REFLECTION; + } + else if (CCTK_Equals(bitant_plane, "yz")) + { + sym[0] = GFSYM_REFLECTION; + } + } + else if (CCTK_Equals(domain, "bitant_rotate")) + { + if (CCTK_Equals(bitant_plane, "xy")) + { + if (CCTK_Equals(rotation_axis, "y")) + sym[4] = GFSYM_ROTATION_Y; + else if (CCTK_Equals(rotation_axis, "x")) + sym[4] = GFSYM_ROTATION_X; } else if (CCTK_Equals(bitant_plane, "xz")) { - sym[2] = 1; + if (CCTK_Equals(rotation_axis, "x")) + sym[2] = GFSYM_ROTATION_X; + else if (CCTK_Equals(rotation_axis, "z")) + sym[2] = GFSYM_ROTATION_Z; } else if (CCTK_Equals(bitant_plane, "yz")) { - sym[0] = 1; + if (CCTK_Equals(rotation_axis, "y")) + sym[0] = GFSYM_ROTATION_Y; + else if (CCTK_Equals(rotation_axis, "z")) + sym[0] = GFSYM_ROTATION_Z; } } else if (CCTK_Equals(domain, "quadrant")) { if (CCTK_Equals(quadrant_direction, "x")) { - sym[2] = 1; - sym[4] = 1; + sym[2] = GFSYM_REFLECTION; + sym[4] = GFSYM_REFLECTION; + } + else if (CCTK_Equals(quadrant_direction, "y")) + { + sym[0] = GFSYM_REFLECTION; + sym[4] = GFSYM_REFLECTION; + } + else if (CCTK_Equals(quadrant_direction, "z")) + { + sym[0] = GFSYM_REFLECTION; + sym[2] = GFSYM_REFLECTION; + } + } + else if (CCTK_Equals(domain, "quadrant_reflect_rotate")) + { + if (CCTK_Equals(quadrant_direction, "x")) + { + if (CCTK_Equals(rotation_axis, "y")) + { + sym[2] = GFSYM_REFLECTION; + sym[4] = GFSYM_ROTATION_Y; + } + else if (CCTK_Equals(rotation_axis, "z")) + { + sym[2] = GFSYM_ROTATION_Z; + sym[4] = GFSYM_REFLECTION; + } } else if (CCTK_Equals(quadrant_direction, "y")) { - sym[0] = 1; - sym[4] = 1; + if (CCTK_Equals(rotation_axis, "x")) + { + sym[0] = GFSYM_REFLECTION; + sym[4] = GFSYM_ROTATION_X; + } + if (CCTK_Equals(rotation_axis, "z")) + { + sym[0] = GFSYM_ROTATION_Z; + sym[4] = GFSYM_REFLECTION; + } } else if (CCTK_Equals(quadrant_direction, "z")) { - sym[0] = 1; - sym[2] = 1; + if (CCTK_Equals(rotation_axis, "x")) + { + sym[0] = GFSYM_REFLECTION; + sym[2] = GFSYM_ROTATION_X; + } + if (CCTK_Equals(rotation_axis, "y")) + { + sym[0] = GFSYM_ROTATION_Y; + sym[2] = GFSYM_REFLECTION; + } } } else if (CCTK_Equals(domain, "octant")) { - sym[0] = 1; - sym[2] = 1; - sym[4] = 1; + sym[0] = GFSYM_REFLECTION; + sym[2] = GFSYM_REFLECTION; + sym[4] = GFSYM_REFLECTION; } } diff --git a/src/ParamCheck.c b/src/ParamCheck.c index 71a8ab2..35d7a42 100644 --- a/src/ParamCheck.c +++ b/src/ParamCheck.c @@ -51,10 +51,18 @@ void ParamCheck_CartGrid3D(CCTK_ARGUMENTS) { iflag++; } + else if (CCTK_Equals(domain,"quadrant_reflect_rotate")) + { + iflag++; + } else if (CCTK_Equals(domain,"bitant")) { iflag++; } + else if (CCTK_Equals(domain,"bitant_rotate")) + { + iflag++; + } else if (CCTK_Equals(domain,"full")) { iflag++; @@ -67,10 +75,19 @@ void ParamCheck_CartGrid3D(CCTK_ARGUMENTS) { iflag++; } + if (CCTK_Equals(domain,"bitant_rotate")) + { + iflag++; + } else if (CCTK_Equals(domain,"quadrant")) { iflag++; - } else if (CCTK_Equals(domain,"octant")) + } + else if (CCTK_Equals(domain,"quadrant_reflect_rotate")) + { + iflag++; + } + else if (CCTK_Equals(domain,"octant")) { iflag++; } @@ -94,6 +111,39 @@ void ParamCheck_CartGrid3D(CCTK_ARGUMENTS) CCTK_PARAMWARN("No grid set up in CartGrid3D"); } + if (CCTK_Equals(domain, "bitant_rotate")) + { + if (CCTK_Equals(bitant_plane, "xy") && CCTK_Equals(rotation_axis, "z")) + CCTK_PARAMWARN( + "rotation_axis=\"z\" is incompatible with bitant_plane=\"xy\""); + + if (CCTK_Equals(bitant_plane, "xz") && CCTK_Equals(rotation_axis, "y")) + CCTK_PARAMWARN( + "rotation_axis=\"y\" is incompatible with bitant_plane=\"xz\""); + + if (CCTK_Equals(bitant_plane, "yz") && CCTK_Equals(rotation_axis, "x")) + CCTK_PARAMWARN( + "rotation_axis=\"x\" is incompatible with bitant_plane=\"yz\""); + } + + if (CCTK_Equals(domain, "quadrant_reflect_rotate")) + { + if (CCTK_Equals(quadrant_direction, "x") && + CCTK_Equals(rotation_axis, "x")) + CCTK_PARAMWARN( + "rotation_axis=\"x\" is incompatible with quadrant_direction=\"x\""); + + if (CCTK_Equals(quadrant_direction, "y") && + CCTK_Equals(rotation_axis, "y")) + CCTK_PARAMWARN( + "rotation_axis=\"y\" is incompatible with quadrant_direction=\"y\""); + + if (CCTK_Equals(quadrant_direction, "z") && + CCTK_Equals(rotation_axis, "z")) + CCTK_PARAMWARN( + "rotation_axis=\"z\" is incompatible with quadrant_direction=\"z\""); + } + return; } diff --git a/src/SetSymmetry.c b/src/SetSymmetry.c index 092dafb..afefea2 100644 --- a/src/SetSymmetry.c +++ b/src/SetSymmetry.c @@ -20,10 +20,6 @@ static const char *rcsid = "$Header$"; CCTK_FILEVERSION(CactusBase_CartGrid3D_SetSymmetry_c) -#define MAX_DIM 3 -#define MAX_FACE 6 - - /******************************************************************** ********************* Local Data Types *********************** ********************************************************************/ @@ -94,10 +90,22 @@ int SetCartSymVI(cGH *GH, int *sym, int vi) DecodeSymParameters3D(domainsym); for (dir=0; dir<MAX_FACE; ++dir) { - if (domainsym[dir]) + if (domainsym[dir] == GFSYM_REFLECTION) { sGHex->GFSym[vi][dir] = sym[dir/2]; - } + } + else if (domainsym[dir] == GFSYM_ROTATION_X) + { + sGHex->GFSym[vi][dir] = sym[1]*sym[2]; + } + else if (domainsym[dir] == GFSYM_ROTATION_Y) + { + sGHex->GFSym[vi][dir] = sym[0]*sym[2]; + } + else if (domainsym[dir] == GFSYM_ROTATION_Z) + { + sGHex->GFSym[vi][dir] = sym[0]*sym[1]; + } else { sGHex->GFSym[vi][dir] = GFSYM_NOSYM; @@ -105,7 +113,7 @@ int SetCartSymVI(cGH *GH, int *sym, int vi) } #ifdef SYM_DEBUG - printf("SetSymmetry: %s [%d,%d,%d]\n\n",imp_gf, + printf("SetSymmetry: %s [%d,%d,%d]\n\n", CCTK_VarName(vi), sGHex->GFSym[vi][0], sGHex->GFSym[vi][2], sGHex->GFSym[vi][4]); @@ -217,10 +225,22 @@ int SetCartSymGI(cGH *GH, int *sym, int gi) DecodeSymParameters3D (domainsym); for (dir=0; dir<MAX_FACE; dir++) { - if (domainsym[dir]) + if (domainsym[dir] == GFSYM_REFLECTION) { sGHex->GFSym[vi][dir] = sym[dir/2]; } + else if (domainsym[dir] == GFSYM_ROTATION_X) + { + sGHex->GFSym[vi][dir] = sym[1]*sym[2]; + } + else if (domainsym[dir] == GFSYM_ROTATION_Y) + { + sGHex->GFSym[vi][dir] = sym[0]*sym[2]; + } + else if (domainsym[dir] == GFSYM_ROTATION_Z) + { + sGHex->GFSym[vi][dir] = sym[0]*sym[1]; + } else { sGHex->GFSym[vi][dir] = GFSYM_NOSYM; @@ -228,7 +248,7 @@ int SetCartSymGI(cGH *GH, int *sym, int gi) } #ifdef SYM_DEBUG - printf("SetSymmetry: %s [%d,%d,%d]\n\n",imp_gf, + printf("SetSymmetry: %s [%d,%d,%d]\n\n", CCTK_VarName(vi), sGHex->GFSym[vi][0], sGHex->GFSym[vi][2], sGHex->GFSym[vi][4]); diff --git a/src/Symmetry.c b/src/Symmetry.c index 7b65592..f245600 100644 --- a/src/Symmetry.c +++ b/src/Symmetry.c @@ -15,6 +15,7 @@ #include <string.h> #include "cctk.h" +#include "Symmetry.h" static const char *rcsid = "$Header$"; @@ -66,7 +67,7 @@ int CartApplySym3Di(cGH *GH, int *doSym, int *cntstag, int *lssh, int *ghostz, int *sym, CCTK_REAL *var) { - int i,j,k; + int i, j, k; #ifdef SYM_DEBUG printf(" doSym: %d %d / %d %d / %d %d \n", @@ -79,7 +80,10 @@ int CartApplySym3Di(cGH *GH, int *doSym, int *cntstag, printf(" cntstag: %d %d %d\n",cntstag[0],cntstag[1],cntstag[2]); #endif - if (doSym[0] == 1) + /* + * Apply symmetry to the lower x face. + */ + if (doSym[0] == GFSYM_REFLECTION) { for(k=0; k < lssh[2]; k++) { @@ -87,40 +91,157 @@ int CartApplySym3Di(cGH *GH, int *doSym, int *cntstag, { for(i=0; i < ghostz[0]; i++) { - var[CCTK_GFINDEX3D(GH,i,j,k)] = - sym[0]*var[CCTK_GFINDEX3D(GH,2*ghostz[0]-cntstag[0]-i,j,k)]; + var[CCTK_GFINDEX3D(GH,i,j,k)] = sym[0] * + var[CCTK_GFINDEX3D(GH, 2*ghostz[0]-cntstag[0]-i, j, k)]; } } } } - if (doSym[2] == 1) + else if (doSym[0] == GFSYM_ROTATION_Y) + { + /* + * FIXME: The following loop is local, but global indices are + * FIXME: needed for this to work on multiple processors. + */ + for(k=0; k < lssh[2]; k++) + { + for(j=0; j < lssh[1]; j++) + { + for(i=0; i < ghostz[0]; i++) + { + var[CCTK_GFINDEX3D(GH,i,j,k)] = sym[0] * + var[CCTK_GFINDEX3D(GH, 2*ghostz[0]-cntstag[0]-i, j, lssh[2]-k-1)]; + } + } + } + } + else if (doSym[0] == GFSYM_ROTATION_Z) + { + /* + * FIXME: The following loop is local, but global indices are + * FIXME: needed for this to work on multiple processors. + */ + for(k=0; k < lssh[2]; k++) + { + for(j=0; j < lssh[1]; j++) + { + for(i=0; i < ghostz[0]; i++) + { + var[CCTK_GFINDEX3D(GH,i,j,k)] = sym[0] * + var[CCTK_GFINDEX3D(GH, 2*ghostz[0]-cntstag[0]-i, lssh[1]-j-1, k)]; + } + } + } + } + + /* + * Apply symmetry to the lower y face. + */ + if (doSym[2] == GFSYM_REFLECTION) + { + for(i=0; i < lssh[0]; i++) + { + for(k=0; k < lssh[2]; k++) + { + for(j=0; j < ghostz[1]; j++) + { + var[CCTK_GFINDEX3D(GH,i,j,k)] = sym[2] * + var[CCTK_GFINDEX3D(GH, i, 2*ghostz[1]-cntstag[1]-j, k)]; + } + } + } + } + else if (doSym[2] == GFSYM_ROTATION_X) + { + /* + * FIXME: The following loop is local, but global indices are + * FIXME: needed for this to work on multiple processors. + */ + for(i=0; i < lssh[0]; i++) + { + for(k=0; k < lssh[2]; k++) + { + for(j=0; j < ghostz[1]; j++) + { + var[CCTK_GFINDEX3D(GH,i,j,k)] = sym[2] * + var[CCTK_GFINDEX3D(GH, i, 2*ghostz[1]-cntstag[1]-j, lssh[2]-k-1)]; + } + } + } + } + else if (doSym[2] == GFSYM_ROTATION_Z) + { + /* + * FIXME: The following loop is local, but global indices are + * FIXME: needed for this to work on multiple processors. + */ + for(i=0; i < lssh[0]; i++) + { + for(k=0; k < lssh[2]; k++) + { + for(j=0; j < ghostz[1]; j++) + { + var[CCTK_GFINDEX3D(GH,i,j,k)] = sym[2] * + var[CCTK_GFINDEX3D(GH, lssh[0]-i-1, 2*ghostz[1]-cntstag[1]-j, k)]; + } + } + } + } + + /* + * Apply symmetry to the lower z face. + */ + if (doSym[4] == GFSYM_REFLECTION) { for(i=0; i < lssh[0]; i++) + { + for(j=0; j < lssh[1]; j++) { - for(k=0; k < lssh[2]; k++) - { - for(j=0; j < ghostz[1]; j++) - { - var[CCTK_GFINDEX3D(GH,i,j,k)] = - sym[2]*var[CCTK_GFINDEX3D(GH,i,2*ghostz[1]-cntstag[1]-j,k)]; - } - } + for(k=0; k < ghostz[2]; k++) + { + var[CCTK_GFINDEX3D(GH,i,j,k)] = sym[4] * + var[CCTK_GFINDEX3D(GH, i, j, 2*ghostz[2]-cntstag[2]-k)]; + } } + } } - if (doSym[4] == 1) + else if (doSym[4] == GFSYM_ROTATION_X) { + /* + * FIXME: The following loop is local, but global indices are + * FIXME: needed for this to work on multiple processors. + */ for(i=0; i < lssh[0]; i++) + { + for(j=0; j < lssh[1]; j++) { - for(j=0; j < lssh[1]; j++) - { - for(k=0; k < ghostz[2]; k++) - { - var[CCTK_GFINDEX3D(GH,i,j,k)] = - sym[4]*var[CCTK_GFINDEX3D(GH,i,j,2*ghostz[2]-cntstag[2]-k)]; - } - } + for(k=0; k < ghostz[2]; k++) + { + var[CCTK_GFINDEX3D(GH,i,j,k)] = sym[4] * + var[CCTK_GFINDEX3D(GH, i, lssh[1]-j-1, 2*ghostz[2]-cntstag[2]-k)]; + } } + } } + else if (doSym[4] == GFSYM_ROTATION_Y) + { + /* + * FIXME: The following loop is local, but global indices are + * FIXME: needed for this to work on multiple processors. + */ + for(i=0; i < lssh[0]; i++) + { + for(j=0; j < lssh[1]; j++) + { + for(k=0; k < ghostz[2]; k++) + { + var[CCTK_GFINDEX3D(GH,i,j,k)] = sym[4] * + var[CCTK_GFINDEX3D(GH, lssh[0]-i-1, j, 2*ghostz[2]-cntstag[2]-k)]; + } + } + } + } + return(0); } @@ -149,28 +270,58 @@ int CartApplySym3Di(cGH *GH, int *doSym, int *cntstag, int CartApplySym2Di(cGH *GH, int *doSym, int *cntstag, int *lssh, int *ghostz, int *sym, CCTK_REAL *var) { - int i,j; + int i, j; - if (doSym[0] == 1) + if (doSym[0] == GFSYM_REFLECTION) + { + for(j=0; j < lssh[1]; j++) + { + for(i=0; i < ghostz[0]; i++) + { + var[CCTK_GFINDEX2D(GH,i,j)] = sym[0] * + var[CCTK_GFINDEX2D(GH, 2*ghostz[0]-cntstag[0]-i, j)]; + } + } + } + else if (doSym[0] == GFSYM_ROTATION_Z) { + /* + * FIXME: The following loop is local, but global indices are + * FIXME: needed for this to work on multiple processors. + */ for(j=0; j < lssh[1]; j++) { for(i=0; i < ghostz[0]; i++) { - var[CCTK_GFINDEX2D(GH,i,j)] = - sym[0]*var[CCTK_GFINDEX2D(GH,2*ghostz[0]-cntstag[0]-i,j)]; + var[CCTK_GFINDEX2D(GH,i,j)] = sym[0] * + var[CCTK_GFINDEX2D(GH, 2*ghostz[0]-cntstag[0]-i, lssh[1]-j-1)]; } } } - if (doSym[2] == 1) + if (doSym[2] == GFSYM_REFLECTION) + { + for(i=0; i < lssh[0]; i++) + { + for(j=0; j < ghostz[1]; j++) + { + var[CCTK_GFINDEX2D(GH,i,j)] = sym[2] * + var[CCTK_GFINDEX2D(GH, i, 2*ghostz[1]-cntstag[1]-j)]; + } + } + } + else if (doSym[2] == GFSYM_ROTATION_Z) { + /* + * FIXME: The following loop is local, but global indices are + * FIXME: needed for this to work on multiple processors. + */ for(i=0; i < lssh[0]; i++) { for(j=0; j < ghostz[1]; j++) { - var[CCTK_GFINDEX2D(GH,i,j)] = - sym[2]*var[CCTK_GFINDEX2D(GH,i,2*ghostz[1]-cntstag[1]-j)]; + var[CCTK_GFINDEX2D(GH,i,j)] = sym[2] * + var[CCTK_GFINDEX2D(GH, lssh[0]-i-1, 2*ghostz[1]-cntstag[1]-j)]; } } } @@ -210,7 +361,7 @@ int CartApplySym1Di(cGH *GH, int *doSym, int *cntstag, GH = GH; lssh = lssh; - if (doSym[0] == 1) + if (doSym[0] == GFSYM_REFLECTION) { for(i=0; i < ghostz[0]; i++) { diff --git a/src/Symmetry.h b/src/Symmetry.h index e0b496a..4d23baf 100644 --- a/src/Symmetry.h +++ b/src/Symmetry.h @@ -19,8 +19,16 @@ #ifndef _SYMMETRY_H_ #define _SYMMETRY_H_ -#define GFSYM_UNSET -42 -#define GFSYM_NOSYM -41 +#define GFSYM_UNSET -41 +#define GFSYM_NOSYM -42 + +#define GFSYM_REFLECTION 1 +#define GFSYM_ROTATION_X 2 +#define GFSYM_ROTATION_Y 3 +#define GFSYM_ROTATION_Z 4 + +#define MAX_DIM 3 +#define MAX_FACE 6 typedef struct Symmetry { diff --git a/src/SymmetryWrappers.c b/src/SymmetryWrappers.c index 19386fb..548c149 100644 --- a/src/SymmetryWrappers.c +++ b/src/SymmetryWrappers.c @@ -14,6 +14,8 @@ #include "cctk_FortranString.h" #include "Symmetry.h" +void DecodeSymParameters3D(int sym[6]); + void CCTK_FCALL CCTK_FNAME(CartSymGI)(int *ierr, cGH *GH, int *gi); void CCTK_FCALL CCTK_FNAME(CartSymGN) (int *ierr, cGH *GH, ONE_FORTSTRING_ARG); @@ -50,7 +52,7 @@ static const char *rcsid = "$Header$"; CCTK_FILEVERSION(CactusBase_CartGrid3D_SymmetryWrappers_c) -/*$#define SYM_DEBUG$*/ +/*#define SYM_DEBUG*/ /*@@ @@ -77,6 +79,7 @@ int CartSymGI(cGH *GH, int gi) int berr=-1,ierr=-1; int time; int *doSym, *dstag, *lssh, *cntstag; + int domainsym[MAX_FACE]; SymmetryGHex *sGHex; /* Get out if we are sure no symmetries should be applied */ @@ -118,6 +121,8 @@ int CartSymGI(cGH *GH, int gi) time = 0; }*/ + DecodeSymParameters3D(domainsym); + for (vi=first_vi; vi<first_vi+numvars; vi++) { /* Apply Symmetries to lower sides [0,2,4,...] if: @@ -139,16 +144,24 @@ int CartSymGI(cGH *GH, int gi) } lssh[idim] = GH->cctk_lssh[CCTK_LSSH_IDX(dstag[idim],idim)]; - - doSym[idim*2] = (((sGHex->GFSym[vi][idim*2]!=GFSYM_NOSYM) && - (sGHex->GFSym[vi][idim*2]!=GFSYM_UNSET)) && - lssh[idim]>1 && GH->cctk_bbox[idim*2]==1); + + if (((sGHex->GFSym[vi][idim*2] != GFSYM_NOSYM) && + (sGHex->GFSym[vi][idim*2] != GFSYM_UNSET)) && + lssh[idim]>1 && GH->cctk_bbox[idim*2]==1) + { + doSym[idim*2] = domainsym[idim*2]; + } + else + { + doSym[idim*2] = 0; + } + doSym[idim*2+1] = 0; } #ifdef SYM_DEBUG - printf(" DOSYM: %s [%d,%d] [%d,%d] [%d,%d] --- %d %d %d \n", + printf(" DOSYM: %s [%d,%d] [%d,%d] [%d,%d] --- %d %d %d\n", CCTK_VarName(vi), doSym[0],doSym[1], doSym[2],doSym[3], @@ -335,7 +348,7 @@ int CartSymVI(cGH *GH, int vi) } #ifdef SYM_DEBUG - printf(" DOSYM: %s [%d,%d] [%d,%d] [%d,%d] --- %d %d %d \n", + printf(" DOSYM: %s [%d,%d] [%d,%d] [%d,%d] --- %d %d %d\n", CCTK_VarName(vi), doSym[0],doSym[1], doSym[2],doSym[3], |