#!/bin/bash # # Developed by Fred Weinhaus 6/29/2015 .......... revised 1/17/2022 # # ------------------------------------------------------------------------------ # # Licensing: # # Copyright © Fred Weinhaus # # My scripts are available free of charge for non-commercial use, ONLY. # # For use of my scripts in commercial (for-profit) environments or # non-free applications, please contact me (Fred Weinhaus) for # licensing arrangements. My email address is fmw at alink dot net. # # If you: 1) redistribute, 2) incorporate any of these scripts into other # free applications or 3) reprogram them in another scripting language, # then you must contact me for permission, especially if the result might # be used in a commercial or for-profit environment. # # My scripts are also subject, in a subordinate manner, to the ImageMagick # license, which can be found at: http://www.imagemagick.org/script/license.php # # ------------------------------------------------------------------------------ # #### # # USAGE: conformal [-d dimensions] [-f formula] [-g gain] [-v vp] [-b bcolor] # [-z zcolor] [-m monitor] infile outfile # # USAGE: conformal [-h|help] # # OPTIONS: # # -d dimension output dimensions WxH; "x" separated pair of integers>0; # default=input dimension # -f formula flag for the complex expression; integer between # 1 and 8; default=1 # -g gain effect gain factor (zoom); pair of comma separate # floats>0; xgain,ygain; default="1,1" # -v vp virtual-pixel method; default=tile # -b bcolor background color for virtual-pixel method; any valid # IM color is allowed; default=black # -z zcolor zero color; color for where the formula has a divide # by zero; default=black # -m monitor monitor enables the progress monitor; choices are: # on or off; default=off # ### # # NAME: CONFORMAL # # PURPOSE: To apply a conformal mapping to an image. # # DESCRIPTION: CONFORMAL applies a conformal mapping to an image. The user may # select from on of 8 complex expressions. The virtual pixel method may also # be selected. # # OPTIONS: # # -d dimension ... DIMENSIONS specify the output image dimensions WxH. The # value is an "x" separated pair of integers>0. The default=input dimensions # # -f formula ... FORMULA is a flag for the complex expression. Value are # integer between 1 and 6. 1=-1/z, 2=(z+1/z)/2, 3=z^2, 4=sin(z), 5=cos(z), # 6=ln(z), 7=(z+1)/(z-1), 8=1/(4*z^2-1), where z=x+i*y is a complex value. # The default=1. # # -g gain ... GAIN is a gain factor (zoom) that controls the look of the # conformal mapping. Values are a pair of comma separate floats>0 as # "xgain,ygain". If only one value is provided it will be used for both. The # default="1,1". # # -v vp ... VP is the virtual-pixel method. Any virtual-pixel method is # allowed. The default=tile. # # -b bcolor ... BCOLOR is the background color for the virtual-pixel method # that is a color. Any valid IM color is allowed. The default=black. # # -z zcolor ... ZCOLOR is the zero color, which is the color for where the # formula has a divide by zero. Relevant only to formula 1, 2 and 6. The # default=black. # # -m monitor ... MONITOR enables the progress monitor. Choices are: on or off. # The default=off # # NOTE: This script will be slow due to the use of -fx. On my Mac Mini with # two cores, it took about 10-15 sec for a 500x500 image. # # REFERENCES: # https://www.youtube.com/watch?v=CMMrEDIFPZY # http://www.dimensions-math.org/Dim_CH5_E.htm # http://www.mathworks.com/help/images/examples/exploring-a-conformal-mapping.html?requestedDomain=www.mathworks.com # # CAVEAT: No guarantee that this script will work on all platforms, # nor that trapping of inconsistent parameters is complete and # foolproof. Use At Your Own Risk. # ###### # # set default values dimensions="" # output dimensions WxH; default=input dimension formula="1" # 1=-1/z, 2=(z+1/z)/2, 3=z^2, 4=sin(z), 5=cos(z), 6=log(z) gain="1" # input scale factor; float>0; default="1,1" (no change) vp="tile" # virtual-pixel method; default=tile bcolor="black" # background color for virtual-pixel; default=black zcolor="black" # zero divide color default=black monitor="off" # progress monitor; on or off; default=off # set directory for temporary files tmpdir="." # suggestions are tmpdir="." or tmpdir="/tmp" # set up functions to report Usage and Usage with Description PROGNAME=`type $0 | awk '{print $3}'` # search for executable on path PROGDIR=`dirname $PROGNAME` # extract directory of program PROGNAME=`basename $PROGNAME` # base name of program usage1() { echo >&2 "" echo >&2 "$PROGNAME:" "$@" sed >&2 -e '1,/^####/d; /^###/g; /^#/!q; s/^#//; s/^ //; 4,$p' "$PROGDIR/$PROGNAME" } usage2() { echo >&2 "" echo >&2 "$PROGNAME:" "$@" sed >&2 -e '1,/^####/d; /^######/g; /^#/!q; s/^#*//; s/^ //; 4,$p' "$PROGDIR/$PROGNAME" } # function to report error messages errMsg() { echo "" echo $1 echo "" usage1 exit 1 } # function to test for minus at start of value of second part of option 1 or 2 checkMinus() { test=`echo "$1" | grep -c '^-.*$'` # returns 1 if match; 0 otherwise [ $test -eq 1 ] && errMsg "$errorMsg" } # test for correct number of arguments and get values if [ $# -eq 0 ] then # help information echo "" usage2 exit 0 elif [ $# -gt 16 ] then errMsg "--- TOO MANY ARGUMENTS WERE PROVIDED ---" else while [ $# -gt 0 ] do # get parameter values case "$1" in -h|-help) # help information echo "" usage2 exit 0 ;; -d) # get dimensions shift # to get the next parameter # test if parameter starts with minus sign errorMsg="--- INVALID DIMENSIONS SPECIFICATION ---" checkMinus "$1" dimensions=`expr "$1" : '\([0-9]*x[0-9]*\)'` [ "$dimensions" = "" ] && errMsg "--- DIMENSIONS=$dimensions MUST BE A PAIR OF X SEPARATED INTEGERS ---" ;; -f) # get formula shift # to get the next parameter # test if parameter starts with minus sign errorMsg="--- INVALID FORMULA SPECIFICATION ---" checkMinus "$1" formula=`expr "$1" : '\([1-8]\)'` [ "$formula" = "" ] && errMsg "--- FORMULA=$formula MUST BE AN INTEGER BETWEEN 1 AND 8 ---" ;; -g) # get gain shift # to get the next parameter # test if parameter starts with minus sign errorMsg="--- INVALID GAIN SPECIFICATION ---" checkMinus "$1" gain=`expr "$1" : '\([,.0-9]*\)'` [ "$gain" = "" ] && errMsg "--- GAIN=$gain MUST BE A PAIR OF COMMA SEPARATED FLOATS ---" ;; -v) # get vp shift # to get the next parameter # test if parameter starts with minus sign errorMsg="--- INVALID VP SPECIFICATION ---" checkMinus "$1" vp="$1" ;; -b) # get bcolor shift # to get the next parameter # test if parameter starts with minus sign errorMsg="--- INVALID BCOLOR SPECIFICATION ---" checkMinus "$1" bcolor="$1" ;; -z) # get zcolor shift # to get the next parameter # test if parameter starts with minus sign errorMsg="--- INVALID ZCOLOR SPECIFICATION ---" checkMinus "$1" zcolor="$1" ;; -m) # get monitor shift # to get the next parameter # test if parameter starts with minus sign errorMsg="--- INVALID MONITOR SPECIFICATION ---" checkMinus "$1" monitor=`echo "$1" | tr '[A-Z]' '[a-z]'` case "$monitor" in on) monitor="on";; off) monitor="off";; *) errMsg "--- MONITOR=$monitor IS AN INVALID VALUE ---" esac ;; -) # STDIN and end of arguments break ;; -*) # any other - argument errMsg "--- UNKNOWN OPTION ---" ;; *) # end of arguments break ;; esac shift # next option done # # get infile and outfile infile="$1" outfile="$2" fi # test that infile provided [ "$infile" = "" ] && errMsg "NO INPUT FILE SPECIFIED" # test that outfile provided [ "$outfile" = "" ] && errMsg "NO OUTPUT FILE SPECIFIED" # set directory for temporary files # tmpdir="/tmp" tmpdir="." dir="$tmpdir/CONFORMAL.$$" mkdir "$dir" || errMsg "--- FAILED TO CREATE TEMPORARY FILE DIRECTORY ---" trap "rm -rf $dir; exit 0" 0 trap "rm -rf $dir; exit 1" 1 2 3 15 # read the input image into the temporary cached image and test if valid convert -quiet "$infile" +repage $dir/tmpI.mpc || errMsg "--- FILE $infile DOES NOT EXIST OR IS NOT AN ORDINARY FILE, NOT READABLE OR HAS ZERO size ---" # get image dimensions and corner coords wxh=`convert -ping $dir/tmpI.mpc -format "%wx%h" info:` ww=`echo "$wxh" | cut -dx -f1` hh=`echo "$wxh" | cut -dx -f2` ww2=`convert xc: -format "%[fx:$ww/2]" info:` hh2=`convert xc: -format "%[fx:$hh/2]" info:` ww4=`convert xc: -format "%[fx:$ww/4]" info:` hh4=`convert xc: -format "%[fx:$hh/4]" info:` #echo "ww=$ww; hh=$hh; ww2=$ww2; hh2=$hh2; ww4=$ww4; hh4=$hh4;" # get output dimensions if [ "$dimensions" = "" ]; then wd=$ww ht=$hh else wd=`echo "$dimensions" | cut -dx -f1` ht=`echo "$dimensions" | cut -dx -f2` fi [ $wd -eq 0 -o $ht -eq 0 ] && errMsg "--- OUTPUT DIMENSIONS MAY NOT BE ZERO ---" wd2=`convert xc: -format "%[fx:$wd/2]" info:` ht2=`convert xc: -format "%[fx:$ht/2]" info:` wd4=`convert xc: -format "%[fx:$wd/4]" info:` ht4=`convert xc: -format "%[fx:$ht/4]" info:` #echo "wd=$wd; ht=$ht; wd2=$wd2; ht2=$ht2; wd4=$wd4; ht4=$ht4;" # split gains and biases and offsets gx=`echo "$gain" | cut -d, -f1` gy=`echo "$gain" | cut -d, -f2` test=`convert xc: -format "%[fx:( ($gx==0) || ($gy==0) )?1:0]" info:` [ $test -eq 1 ] && errMsg "--- OUTPUT DIMENSIONS MAY NOT BE ZERO ---" #echo "gx=$gx; gy=$gy;" # set up monitor if [ "$monitor" = "on" ]; then monitoring1="-monitor" monitoring2="+monitor" else monitoring1="" monitoring2="" fi if [ $formula -eq 1 ]; then convert -size ${wd}x${ht} xc: $dir/tmpI.mpc \ -background "$bcolor" -virtual-pixel $vp $monitoring1 -fx \ "xx=(i-$wd2)/$wd2; yy=(j-$ht2)/$ht2; rr=(xx*xx+yy*yy); \ (xx==0 && yy==0)?$zcolor:v.p{-$gx*$ww4*xx/rr+$ww2,$gy*$hh4*yy/rr+$hh2}" \ $monitoring2 "$outfile" elif [ $formula -eq 2 ]; then convert -size ${wd}x${ht} xc: $dir/tmpI.mpc \ -background "$bcolor" -virtual-pixel $vp $monitoring1 -fx \ "xx=(i-$wd2)/$wd2; yy=(j-$ht2)/$ht2; rr=(xx*xx+yy*yy); \ (xx==0 && yy==0)?$zcolor:v.p{$gx*$ww4*(xx*rr-xx)/rr+$ww2,$gy*$hh4*(yy*rr-yy)/rr+$hh2}" \ $monitoring2 "$outfile" elif [ $formula -eq 3 ]; then convert -size ${wd}x${ht} xc: $dir/tmpI.mpc \ -background "$bcolor" -virtual-pixel $vp $monitoring1 -fx \ "xx=(i-$wd2)/$wd2; yy=(j-$ht2)/$ht2; \ v.p{$gx*$ww4*(xx*xx-yy*yy)+$ww2,$gy*$hh2*2*xx*yy+$hh2}" \ $monitoring2 "$outfile" elif [ $formula -eq 4 ]; then convert -size ${wd}x${ht} xc: $dir/tmpI.mpc \ -background "$bcolor" -virtual-pixel $vp $monitoring1 -fx \ "xx=(i-$wd2)/$wd2; yy=(j-$ht2)/$ht2; \ v.p{$gx*$ww4*sin(pi*xx)*cosh(yy)+$ww2,$gy*$hh2*cos(pi*xx)*sinh(yy)+$hh2}" \ $monitoring2 "$outfile" elif [ $formula -eq 5 ]; then convert -size ${wd}x${ht} xc: $dir/tmpI.mpc \ -background "$bcolor" -virtual-pixel $vp $monitoring1 -fx \ "xx=(i-$wd2)/$wd2; yy=(j-$ht2)/$ht2; \ v.p{$gx*$ww4*cos(pi*xx)*cosh(yy)+$ww2,-$gy*$hh2*sin(pi*xx)*sinh(yy)+$hh2}" \ $monitoring2 "$outfile" elif [ $formula -eq 6 ]; then convert -size ${wd}x${ht} xc: $dir/tmpI.mpc \ -background "$bcolor" -virtual-pixel $vp $monitoring1 -fx \ "xx=(i-$wd2)/$wd2; yy=(j-$ht2)/$ht2; rr=(xx*xx+yy*yy); \ ( (rr==0) || (xx==0) )?$zcolor:v.p{$gx*$ww4*ln(sqrt(rr))+$ww2,$gy*$hh2*atan(yy/xx)+$hh2}" \ $monitoring2 "$outfile" elif [ $formula -eq 7 ]; then convert -size ${wd}x${ht} xc: $dir/tmpI.mpc \ -background "$bcolor" -virtual-pixel $vp $monitoring1 -fx \ "xx=(i-$wd2)/$wd2; yy=(j-$ht2)/$ht2; rr=xx*xx+yy*yy; dd=(rr-2*xx+1); \ (dd==0)?$zcolor:v.p{$gx*$ww4*(rr+1)+$ww2,$gy*$hh2*2*yy+$hh2}" \ $monitoring2 "$outfile" elif [ $formula -eq 8 ]; then convert -size ${wd}x${ht} xc: $dir/tmpI.mpc \ -background "$bcolor" -virtual-pixel $vp $monitoring1 -fx \ "xx=(i-$wd2)/$wd2; yy=(j-$ht2)/$ht2; \ aa=4*(xx*xx-yy*yy)-1; bb=8*xx*yy; cc=(aa*aa+bb*bb); \ (cc==0)?$zcolor:v.p{$gx*$ww4*(aa/cc)+$ww2,-$gy*$hh2*(bb/cc)+$hh2}" \ $monitoring2 "$outfile" fi exit 0