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# Grid data demo.
#
# Copyright (C) 2004 Joao Cardoso
# Copyright (C) 2008 Andrew Ross
#
# This file is part of PLplot.
#
# PLplot is free software; you can redistribute it and/or modify
# it under the terms of the GNU Library General Public License as
# published by the Free Software Foundation; either version 2 of the
# License, or (at your option) any later version.
#
# PLplot is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Library General Public License for more details.
#
# You should have received a copy of the GNU Library General Public
# License along with PLplot; if not, write to the Free Software
# Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
#
# Note:
# This example uses NaNs (not-a-number) and these special "numbers"
# are only properly supported by Tcl 8.5 and later (in the sense
# that a NaN does not stop the program with an error message).
proc x21 {{w loopback}} {
set PI $::PLPLOT::PL_PI
set pts 500
set xp 25
set yp 20
set nl 16
set knn_order 20
set threshold 1.001
set wmin -1e3
set randn 0
set rosen 0
matrix x f $pts
matrix y f $pts
matrix z f $pts
matrix clev f $nl
matrix xg f $xp
matrix yg f $yp
matrix zg f $xp $yp
set title {"-dummy-"
"Cubic Spline Approximation"
"Delaunay Linear Interpolation"
"Natural Neighbors Interpolation"
"KNN Inv. Distance Weighted"
"3NN Linear Interpolation"
"4NN Around Inv. Dist. Weighted"}
matrix opt f 6 = { 0.0 0.0 0.0 0.0 0.0 0.0 }
set xmin -0.2
set ymin -0.2
set xmax 0.6
set ymax 0.6
opt 2 = $wmin
opt 3 = [expr {double($knn_order)}]
opt 4 = $threshold
$w cmd plseed 5489
cmap1_init $w
for {set i 0} {$i < $pts} {incr i} {
set xt [expr {($xmax-$xmin)*[$w cmd plrandd]}]
set yt [expr {($ymax-$ymin)*[$w cmd plrandd]}]
if {$randn == 0} {
x $i = [expr {$xt + $xmin}]
y $i = [expr {$yt + $ymin}]
} else {
x $i = [expr {sqrt(-2.*log($xt)) * cos(2.*$PI*$yt) + $xmin}]
y $i = [expr {sqrt(-2.*log($xt)) * sin(2.*$PI*$yt) + $ymin}]
}
if {$rosen == 0} {
set xx [x $i]
set yy [y $i]
set r [expr {sqrt($xx*$xx + $yy*$yy)}]
z $i = [expr {exp(-$r*$r)*cos(2.*$PI*$r)}]
} else {
set xx [x $i]
set yy [y $i]
z $i = [expr {log(pow(1.-$xx,2)) + 100.*pow($yy-pow($xx,2),2)}]
}
}
set zmin [z 0]
set zmax [z 0]
for {set i 1} {$i < $pts} {incr i} {
set zmax [max $zmax [z $i]]
set zmin [min $zmin [z $i]]
}
for {set i 0} {$i < $xp} {incr i} {
xg $i = [expr {$xmin + ($xmax-$xmin)*$i/double($xp-1.)}]
}
for {set i 0} {$i < $yp} {incr i} {
yg $i = [expr {$ymin + ($ymax-$ymin)*$i/double($yp-1.)}]
}
$w cmd plcol0 1
$w cmd plenv $xmin $xmax $ymin $ymax 2 0
$w cmd plcol0 15
$w cmd pllab "X" "Y" "The original data sampling"
matrix xstr f 1 = {0.0}
matrix ystr f 1 = {0.0}
for {set i 0} {$i < $pts} {incr i} {
$w cmd plcol1 [expr {([z $i] - $zmin ) / ( $zmax - $zmin )}]
# The following plstring call should be the the equivalent of
# plpoin( 1, &x[i], &y[i], 5 ); Use plstring because it is
# not deprecated like plpoin and has much more powerful
# capabilities. N.B. symbol 141 works for Hershey devices
# (e.g., -dev xwin) only if plfontld( 0 ) has been called
# while symbol 727 works only if plfontld( 1 ) has been
# called. The latter is the default which is why we use 727
# here to represent a centred X (multiplication) symbol.
# This dependence on plfontld is one of the limitations of
# the Hershey escapes for PLplot, but the upside is you get
# reasonable results for both Hershey and Unicode devices.
xstr 0 = [x $i]
ystr 0 = [y $i]
$w cmd plstring 1 xstr ystr "#(727)"
}
$w cmd pladv 0
$w cmd plssub 3 2
for {set k 0} {$k < 2} {incr k} {
$w cmd pladv 0
for {set alg 1} {$alg <= 6} {incr alg} {
$w cmd plgriddata x y z xg yg zg $alg [opt [expr {$alg-1}]]
# - CSA can generate NaNs (only interpolates? #).
# - DTLI and NNI can generate NaNs for points outside the convex hull
# of the data points.
# - NNLI can generate NaNs if a sufficiently thick triangle is not found
#
# PLplot should be NaN/Inf aware, but changing it now is quite a job...
# so, instead of not plotting the NaN regions, a weighted average over
# the neighbors is done.
#
if {($alg == $::PLPLOT::GRID_CSA) || ($alg == $::PLPLOT::GRID_DTLI) ||
($alg == $::PLPLOT::GRID_NNLI) || ($alg == $::PLPLOT::GRID_NNI)} {
for {set i 0} {$i < $xp} {incr i} {
for {set j 0} {$j < $yp} {incr j} {
if { [isnan [zg $i $j]] } {
# average (IDW) over the 8 neighbors
zg $i $j = 0.
set dist 0.
set ii [expr {$i-1}]
while {($ii <= $i+1) && ($ii < $xp)} {
set jj [expr {$j-1}]
while {($jj <= $j+1) && ($jj < $yp)} {
if {($ii >= 0) && ($jj >= 0) &&
![isnan [zg $ii $jj]] } {
if {abs($ii-$i) + abs($jj-$j) == 1} {
set d 1.
} else {
set d 1.4142
}
zg $i $j = [expr {[zg $i $j] + [zg $ii $jj]/($d*$d)}]
set dist [expr {$dist + $d}]
}
incr jj
}
incr ii
}
if {$dist != 0.} {
zg $i $j = [expr {[zg $i $j] / $dist}]
} else {
zg $i $j = $zmin
}
}
}
}
}
a2mnmx zg $xp $yp lzmin lzmax
set lzmin [min $lzmin $zmin]
set lzmax [max $lzmax $zmax]
set lzmin [expr {$lzmin - 0.01}]
set lzmax [expr {$lzmax + 0.01}]
$w cmd plcol0 1
$w cmd pladv $alg
if {$k == 0} {
for {set i 0} {$i < $nl} {incr i} {
clev $i = [expr {$lzmin + ($lzmax-$lzmin)/double($nl-1.)*$i}]
}
$w cmd plenv0 $xmin $xmax $ymin $ymax 2 0
$w cmd plcol0 15
$w cmd pllab "X" "Y" [lindex $title $alg]
$w cmd plshades zg $xmin $xmax $ymin $ymax clev 1. 0 1. 1 "NULL"
$w cmd plcol0 2
} else {
for {set i 0} {$i < $nl} {incr i} {
clev $i = [expr {$lzmin + ($lzmax-$lzmin)/double($nl-1.)*$i}]
}
$w cmd plvpor 0. 1. 0. 0.9
$w cmd plwind -1.1 0.75 -0.65 1.20
#
# For the comparison to be fair, all plots should have the
# same z values, but to get the max/min of the data generated
# by all algorithms would imply two passes. Keep it simple.
#
# plw3d(1., 1., 1., xmin, xmax, ymin, ymax, zmin, zmax, 30, -60);
#
$w cmd plw3d 1. 1. 1. $xmin $xmax $ymin $ymax \
$lzmin $lzmax 30. -40.
$w cmd plbox3 "bntu" "X" 0. 0 \
"bntu" "Y" 0. 0 \
"bcdfntu" "Z" 0.5 0
$w cmd plcol0 15
$w cmd pllab "" "" [lindex $title $alg]
$w cmd plot3dc xg yg zg $xp $yp \
[expr {$::PLPLOT::DRAW_LINEXY|$::PLPLOT::MAG_COLOR|$::PLPLOT::BASE_CONT}] clev $nl
}
}
}
$w cmd plflush
#$w cmd plend
$w cmd plssub 1 1
}
#----------------------------------------------------------------------------
# isnan
#
# Note: the current string interface exposes the string representation
# of NaNs to the Tcl side. As there is a very wide variety of such
# represetations (NAN, nan, "-1.#IND", "1.#QNAN" being but a few
# - see also: http://wiki.apache.org/stdcxx/FloatingPoint)
# we take a shortcut:
# - x is supposed to be a valid number, finite or NaN
# - if it is not recognised as a double precision number, it is assumed
# to be NaN
# - if it is not equal to itself, it definitely is a NaN, as that is
# the distinguishing property of NaNs.
#
#
proc isnan {x} {
if {![string is double $x] || $x != $x} {
return 1
} else {
return 0
}
}
#----------------------------------------------------------------------------
# proc max and min
proc min {args} {
set x [lindex $args 0]
foreach i $args {
if {$i<$x} {set x $i}
}
return $x
}
proc max {args} {
set x [lindex $args 0]
foreach i $args {
if {$i>$x} {set x $i}
}
return $x
}
#----------------------------------------------------------------------------
# proc cmap1_init
# Set up the colour map
proc cmap1_init {w} {
matrix i f 2
matrix h f 2
matrix l f 2
matrix s f 2
matrix r i 2
i 0 = 0.
i 1 = 1.
h 0 = 240.
h 1 = 0.
l 0 = 0.6
l 1 = 0.6
s 0 = 0.8
s 1 = 0.8
r 0 = 0
r 1 = 0
$w cmd plscmap1n 256
$w cmd plscmap1l 0 2 i h l s r
}
#----------------------------------------------------------------------------
# proc a2mnmx
# Minimum and the maximum elements of a 2-d array.
proc a2mnmx {f nx ny fmin fmax} {
upvar 1 $fmin vmin
upvar 1 $fmax vmax
set vmax [$f 0 0]
set vmin $vmax
for {set j 0} {$j < $ny} {incr j} {
for {set i 0} {$i < $nx} {incr i} {
set vmax [max $vmax [$f $i $j]]
set vmin [min $vmin [$f $i $j]]
}
}
}
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