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# Contour plot demo.
proc x09 {{w loopback}} {
set xpts 35
set ypts 46
matrix clevel f 11 = {-1., -.8, -.6, -.4, -.2, 0, .2, .4, .6, .8, 1.}
matrix mark i 1 = { 1500 }
matrix space i 1 = { 1500 }
matrix none i 0
matrix zz f $xpts $ypts
matrix ww f $xpts $ypts
# Calculate the data matrices.
for {set i 0} {$i < $xpts} {incr i} {
set xx [expr {($i - ($xpts / 2)) / double($xpts / 2)} ]
for {set j 0} {$j < $ypts} {incr j} {
set yy [expr {($j - ($ypts / 2)) / double($ypts / 2) - 1.0} ]
zz $i $j = [expr {$xx * $xx - $yy * $yy} ]
ww $i $j = [expr {2. * $xx * $yy} ]
}
}
matrix xg0 f $xpts
matrix yg0 f $ypts
matrix xg1 f $xpts
matrix yg1 f $ypts
matrix xg2 f $xpts $ypts
matrix yg2 f $xpts $ypts
set distort .4
# Build the 1-d coord arrays.
for {set i 0} {$i < $xpts} {incr i} {
set xx [expr {-1. + $i * ( 2. / ($xpts-1.) )}]
xg0 $i = [expr {$xx}]
xg1 $i = [expr {$xx + $distort * cos( .5 * $::PLPLOT::PL_PI * $xx )} ]
}
for {set j 0} {$j < $ypts} {incr j} {
set yy [expr {-1. + $j * ( 2. / ($ypts-1.) )}]
yg0 $j = [expr {$yy}]
yg1 $j = [expr {$yy - $distort * cos( .5 * $::PLPLOT::PL_PI * $yy )} ]
}
# Build the 2-d coord arrays.
for {set i 0} {$i < $xpts} {incr i} {
set xx [expr {-1. + $i * ( 2. / ($xpts-1.) )}]
for {set j 0} {$j < $ypts} {incr j} {
set yy [expr {-1. + $j * ( 2. / ($ypts-1.) )}]
set argx [expr .5 * $::PLPLOT::PL_PI * $xx]
set argy [expr .5 * $::PLPLOT::PL_PI * $yy]
xg2 $i $j = [expr {$xx + $distort * cos($argx) * cos($argy)} ]
yg2 $i $j = [expr {$yy - $distort * cos($argx) * cos($argy)} ]
}
}
# Plot using scaled identity transformation used to create
# xg0 and yg0. The implementation is different, but this gives
# the same results as the mypltr transformation for the first
# plots in x09c.
# $w cmd pl_setcontlabelparam 0.006 0.3 0.1 0
# $w cmd plenv -1.0 1.0 -1.0 1.0 0 0
# $w cmd plcol0 2
# $w cmd plcont zz clevel pltr1 xg0 yg0
# $w cmd plstyl 1 mark space
# $w cmd plcol0 3
# $w cmd plcont ww clevel pltr1 xg0 yg0
# $w cmd plstyl 0 mark space
# $w cmd plcol0 1
# $w cmd pllab "X Coordinate" "Y Coordinate" "Streamlines of flow"
$w cmd pl_setcontlabelformat 4 3
$w cmd pl_setcontlabelparam 0.006 0.3 0.1 1
$w cmd plenv -1.0 1.0 -1.0 1.0 0 0
$w cmd plcol0 2
$w cmd plcont zz clevel pltr1 xg0 yg0
$w cmd plstyl mark space
$w cmd plcol0 3
$w cmd plcont ww clevel pltr1 xg0 yg0
$w cmd plstyl none none
$w cmd plcol0 1
$w cmd pllab "X Coordinate" "Y Coordinate" "Streamlines of flow"
# Plot using 1d coordinate transform
$w cmd pl_setcontlabelparam 0.006 0.3 0.1 0
$w cmd plenv -1.0 1.0 -1.0 1.0 0 0
$w cmd plcol0 2
$w cmd plcont zz clevel pltr1 xg1 yg1
$w cmd plstyl mark space
$w cmd plcol0 3
$w cmd plcont ww clevel pltr1 xg1 yg1
$w cmd plstyl none none
$w cmd plcol0 1
$w cmd pllab "X Coordinate" "Y Coordinate" "Streamlines of flow"
# $w cmd pl_setcontlabelparam 0.006 0.3 0.1 1
# $w cmd plenv -1.0 1.0 -1.0 1.0 0 0
# $w cmd plcol0 2
# $w cmd plcont zz clevel pltr1 xg1 yg1
# $w cmd plstyl 1 mark space
# $w cmd plcol0 3
# $w cmd plcont ww clevel pltr1 xg1 yg1
# $w cmd plstyl 0 mark space
# $w cmd plcol0 1
# $w cmd pllab "X Coordinate" "Y Coordinate" "Streamlines of flow"
# Plot using 2d coordinate transform
# $w cmd pl_setcontlabelparam 0.006 0.3 0.1 0
$w cmd plenv -1.0 1.0 -1.0 1.0 0 0
$w cmd plcol0 2
$w cmd plcont zz clevel pltr2 xg2 yg2
$w cmd plstyl mark space
$w cmd plcol0 3
$w cmd plcont ww clevel pltr2 xg2 yg2
$w cmd plstyl none none
$w cmd plcol0 1
$w cmd pllab "X Coordinate" "Y Coordinate" "Streamlines of flow"
# $w cmd pl_setcontlabelparam 0.006 0.3 0.1 1
# $w cmd plenv -1.0 1.0 -1.0 1.0 0 0
# $w cmd plcol0 2
# $w cmd plcont zz clevel pltr2 xg2 yg2
# $w cmd plstyl 1 mark space
# $w cmd plcol0 3
# $w cmd plcont ww clevel pltr2 xg2 yg2
# $w cmd plstyl 0 mark space
# $w cmd plcol0 1
# $w cmd pllab "X Coordinate" "Y Coordinate" "Streamlines of flow"
#polar contour example.
$w cmd pl_setcontlabelparam 0.006 0.3 0.1 0
x09_polar $w
# $w cmd pl_setcontlabelparam 0.006 0.3 0.1 1
# x09_polar $w
#potential contour example.
$w cmd pl_setcontlabelparam 0.006 0.3 0.1 0
x09_potential $w
# $w cmd pl_setcontlabelparam 0.006 0.3 0.1 1
# x09_potential $w
# Restore defaults
# $w cmd plcol0 1
# $w cmd pl_setcontlabelparam 0.006 0.3 0.1 0
$w cmd pllsty 1
}
# Demonstrate plotting of wrapped data. What is significant to
# understand about this example is that for the common case of
# plotting polar data (or other forms of coordinates that wrap on
# themselves) you can do it from Tcl /without/ having to go to the
# trouble to construct a special data plotting matrix with an extra
# row or column and then copy the data into it, replicating the first
# row/col into the extra row/col.
proc x09_polar {{w loopback}} {
$w cmd plenv -1 1 -1 1 0 -2
$w cmd plcol0 1
# Hold perimeter
matrix px f 100; matrix py f 100
for {set i 0} {$i < 100} {incr i} {
set t [expr {2. * $::PLPLOT::PL_PI * $i / 99.}]
px $i = [expr {cos($t)}]
py $i = [expr {sin($t)}]
}
$w cmd plline px py
set xpts 40; set ypts 40; set ylim [expr {$ypts - 1}]; set wrap 2
matrix xg f $xpts $ylim
matrix yg f $xpts $ylim
matrix z f $xpts $ylim
for {set i 0} {$i < $xpts} {incr i} {
set r [expr {$i / ($xpts - 1.)}]
for {set j 0} {$j < $ylim} {incr j} {
set t [expr {2. * $::PLPLOT::PL_PI * $j / ($ypts - 1.)}]
xg $i $j = [expr {$r * cos($t)}]
yg $i $j = [expr {$r * sin($t)}]
z $i $j = $r
}
}
matrix lev f 10 = { .05, .15, .25, .35, .45, .55, .65, .75, .85, .95 }
$w cmd plcol0 2
$w cmd plcont z lev pltr2 xg yg $wrap
$w cmd plcol0 1
$w cmd pllab "" "" "Polar Contour Plot"
}
proc x09_potential {{w loopback}} {
# Shielded potential contour plot example
set xpts 40; set ypts 64; set ylim [expr {$ypts - 1}]; set wrap 2;
set perimeterpts 100; set nlevel 20
# Create data to be contoured.
matrix xg f $xpts $ylim
matrix yg f $xpts $ylim
matrix z f $xpts $ylim
for {set i 0} {$i < $xpts} {incr i} {
set r [expr {0.5 + $i}]
for {set j 0} {$j < $ylim} {incr j} {
set theta [expr {(2. * $::PLPLOT::PL_PI / ($ypts - 1.))*(0.5 + $j)}]
xg $i $j = [expr {$r * cos($theta)}]
yg $i $j = [expr {$r * sin($theta)}]
}
}
set rmax $r
set xmin [xg 0 0]
set xmax $xmin
set ymin [yg 0 0]
set ymax $ymin
for {set i 0} {$i < $xpts} {incr i} {
for {set j 0} {$j < $ylim} {incr j} {
if {[xg $i $j] < $xmin} { set xmin [xg $i $j] }
if {[xg $i $j] > $xmax} { set xmax [xg $i $j] }
if {[yg $i $j] < $ymin} { set ymin [yg $i $j] }
if {[yg $i $j] > $ymax} { set ymax [yg $i $j] }
}
}
set x0 [expr {($xmin + $xmax)/2.}]
set y0 [expr {($ymin + $ymax)/2.}]
# Expanded limits.
set peps 0.05
set xpmin [expr {$xmin - abs($xmin)*$peps}]
set xpmax [expr {$xmax + abs($xmax)*$peps}]
set ypmin [expr {$ymin - abs($ymin)*$peps}]
set ypmax [expr {$ymax + abs($ymax)*$peps}]
# Potential inside a conducting cylinder (or sphere) by method of images.
# Charge 1 is placed at (d1, d1), with image charge at (d2, d2).
# Charge 2 is placed at (d1, -d1), with image charge at (d2, -d2).
# Also put in smoothing term at small distances.
set eps 2.
set q1 1.
set d1 [expr {$rmax/4.}]
set q1i [expr {- $q1*$rmax/$d1}]
set d1i [expr {pow($rmax,2)/$d1}]
set q2 -1.
set d2 [expr {$rmax/4.}]
set q2i [expr {- $q2*$rmax/$d2}]
set d2i [expr {pow($rmax,2)/$d2}]
for {set i 0} {$i < $xpts} {incr i} {
for {set j 0} {$j < $ylim} {incr j} {
set div1 [expr {sqrt(pow([xg $i $j]-$d1,2) + pow([yg $i $j]-$d1,2) + pow($eps,2))}]
set div1i [expr {sqrt(pow([xg $i $j]-$d1i,2) + pow([yg $i $j]-$d1i,2) + pow($eps,2))}]
set div2 [expr {sqrt(pow([xg $i $j]-$d2,2) + pow([yg $i $j]+$d2,2) + pow($eps,2))}]
set div2i [expr {sqrt(pow([xg $i $j]-$d2i,2) + pow([yg $i $j]+$d2i,2) + pow($eps,2))}]
z $i $j = [expr {$q1/$div1 + $q1i/$div1i + $q2/$div2 + $q2i/$div2i}]
}
}
set zmin [z 0 0]
set zmax $zmin
for {set i 0} {$i < $xpts} {incr i} {
for {set j 0} {$j < $ylim} {incr j} {
if {[z $i $j] < $zmin} { set zmin [z $i $j] }
if {[z $i $j] > $zmax} { set zmax [z $i $j] }
}
}
# Positive and negative contour levels.
set dz [expr {($zmax-$zmin)/$nlevel}]
set nlevelneg 0
set nlevelpos 0
matrix clevelneg f $nlevel
matrix clevelpos f $nlevel
for {set i 0} {$i < $nlevel} {incr i} {
set clevel [expr {$zmin + ($i + 0.5)*$dz}]
if {$clevel <= 0.} {
clevelneg $nlevelneg = $clevel; incr nlevelneg
} else {
clevelpos $nlevelpos = $clevel; incr nlevelpos
}
}
# Colours!
set ncollin 11
set ncolbox 1
set ncollab 2
# Finally start plotting this page!
$w cmd pladv 0
$w cmd plcol0 $ncolbox
$w cmd plvpas 0.1 0.9 0.1 0.9 1.0
$w cmd plwind $xpmin $xpmax $ypmin $ypmax
$w cmd plbox "" 0. 0 "" 0. 0
$w cmd plcol0 $ncollin
if {$nlevelneg >0} {
# Negative contours
# copy partially full clevelneg to full levneg required by plcont
matrix levneg f $nlevelneg
for {set i 0} {$i < $nlevelneg} {incr i} {
levneg $i = [clevelneg $i]
}
$w cmd pllsty 2
$w cmd plcont z levneg pltr2 xg yg $wrap
}
if {$nlevelpos >0} {
# Positive contours
# copy partially full clevelpos to full levpos required by plcont
matrix levpos f $nlevelpos
for {set i 0} {$i < $nlevelpos} {incr i} {
levpos $i = [clevelpos $i]
}
$w cmd pllsty 1
$w cmd plcont z levpos pltr2 xg yg $wrap
}
#Draw outer boundary
matrix px f $perimeterpts
matrix py f $perimeterpts
for {set i 0} {$i < $perimeterpts} {incr i} {
set t [expr {(2.*$::PLPLOT::PL_PI/($perimeterpts-1))*$i}]
px $i = [expr {$x0 + $rmax*cos($t)}]
py $i = [expr {$y0 + $rmax*sin($t)}]
}
$w cmd plcol0 $ncolbox
$w cmd plline px py
$w cmd plcol0 $ncollab
$w cmd pllab "" "" "Shielded potential of charges in a conducting sphere"
}
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