﻿

# Maximum squares and circles

Finding the largest shapes of a given solid colour.

Suppose an image contains some black pixels, or some other specified colour (the "foreground" colour). The black pixels may not be entirely connected. The problem is to find the largest square and largest circle that are entirely black.

On this page, we consider only squares that have sides parallel to the x-axis and y-axis. This doesn't search for rotated squares.

The version of IM does not need to be built with HDRI, and can be Q16 or Q32. It does not need my process modules.

## The method

The scripts maxSquare.bat and maxCircle.bat uses morphology distance to find the size of every square and circle that have only foreground colours, and returns the details of the largest.

The scripts have these steps:

1. Prepare the image, changing the colour of foreground pixels to black, and all other pixels to white. The image is grayscale.
2. Apply a -morphology distance operation, which gives the maximum radius at each pixel.
3. -identify finds the lightest pixel, so this is the location of the maximum radius at all pixels.
4. Adjust the details if the diameters can be extended by one.

The scripts use two variations of -morphology distance: Chebyshev for squares, and Euclidean for circles. These give the "radius", the distance from the centre pixel to the nearest non-foreground pixel. As we want the shape to include the last foreground pixel but not the first non-foreground pixel, we need to subtract one from the radius.

The diameter of the circle (or width and height of the square) are twice the radius plus one. But when the radius and the centre coordinates are integers, the diameter (= 2 * radius + 1) is an odd number, although the gap we are trying to fill may have an even number of pixels.

To fix this problem, we examine the pixels to the east, south-east and south of the found centre. If all four pixels have the same maximum radius, then the square or circle can be extended by one pixel to the east and south.

For the test, we crop to the 4 pixels, then the standard_deviation is zero if the four pixels have the same value.

For the circle: the found radius can be non-integer. Without antialias, IM's -draw "circle cx,cy vx,vy" has an even diameter when the centre coordinates are an integer plus 0.5.

## The scripts

The scripts take the following parameters:

Parameter Description
%1 Input image to be searched. Must be opaque.
%2 Prefix for output environment variables.
Default: msq_ or mci_.
%3 Output image, highlighting the found shape.
Default: no output image.
%4 Input foreground colour.
Default: Black.
Default "0" (no minimum).
Default: no maximum.
%7 IM operations to save the radius map.
Default: map is not saved.
%8 Input mask. White where centre can occur; black where it can't.

Only the first parameter is mandatory. As usual in my scripts, any parameter can be "." (dot aka period) to use the default. Trailing "dot" parameters can be omitted.

The script uses the alpha channel to rearrange colours, so any alpha channel will be destroyed.

The scripts write numbers that describe the found square or circle to environment variables. The prefix for these variables can be specified.

## Examples

In the following examples, we make an image and find the largest square and largest circle that are entirely black. We show the input image, and versions marked up with the found square and circle.

 ```%IMG7%magick ^ -size 200x200 xc:White ^ -fill Black ^ +antialias ^ -draw "ellipse 100,100 80,40 0,360" ^ msc_ex_ellip.png call %PICTBAT%maxSquare ^ msc_ex_ellip.png ex_ellip_ msc_ex_ellip_out.png set ex_ellip_ ``` ```ex_ellip__area=5329 ex_ellip__Rad=36 ex_ellip__X0=64 ex_ellip__X1=136 ex_ellip__XC=100 ex_ellip__Y0=64 ex_ellip__Y1=136 ex_ellip__YC=100``` ```call %PICTBAT%maxCircle ^ msc_ex_ellip.png ex_ellip_c_ msc_ex_ellip_c_out.png set ex_ellip_c_ ``` ```ex_ellip_c__Rad=40 ex_ellip_c__XC=95 ex_ellip_c__YC=100``` ```%IMG7%magick ^ -size 200x200 xc:Black ^ -bordercolor White ^ -border 5 ^ msc_ex_black2.png call %PICTBAT%maxSquare ^ msc_ex_black2.png ex_black2_ msc_ex_black2_out.png set ex_black2_ ``` ```ex_black2__area=40000 ex_black2__Rad=99.5 ex_black2__X0=5 ex_black2__X1=204 ex_black2__XC=104 ex_black2__Y0=5 ex_black2__Y1=204 ex_black2__YC=104``` ```call %PICTBAT%maxCircle ^ msc_ex_black2.png ex_black2_c_ msc_ex_black2_c_out.png set ex_black2_c_ ``` ```ex_black2_c__Rad=100 ex_black2_c__XC=104.5 ex_black2_c__YC=104.5``` Special case: all pixels are black. ```%IMG7%magick ^ -size 200x200 xc:Black ^ msc_ex_black.png call %PICTBAT%maxSquare ^ msc_ex_black.png ex_black_ msc_ex_black_out.png set ex_black_ ``` ```ex_black__area=40000 ex_black__Rad=99.5 ex_black__X0=0 ex_black__X1=199 ex_black__XC=99 ex_black__Y0=0 ex_black__Y1=199 ex_black__YC=99``` ```call %PICTBAT%maxCircle ^ msc_ex_black.png ex_black_c_ msc_ex_black_c_out.png set ex_black_c_ ``` ```ex_black_c__Rad=100 ex_black_c__XC=99.5 ex_black_c__YC=99.5``` Special case: exactly one pixel is black. ```%IMG7%magick ^ -size 1x1 xc:Black ^ -bordercolor White ^ -border 100 ^ msc_ex_black3.png call %PICTBAT%maxSquare ^ msc_ex_black3.png ex_black3_ msc_ex_black3_out.png set ex_black3_ ``` ```ex_black3__area=1 ex_black3__Rad=0 ex_black3__X0=100 ex_black3__X1=100 ex_black3__XC=100 ex_black3__Y0=100 ex_black3__Y1=100 ex_black3__YC=100``` ```call %PICTBAT%maxCircle ^ msc_ex_black3.png ex_black3_c_ msc_ex_black3_c_out.png set ex_black3_c_ ``` ```ex_black3_c__Rad=0 ex_black3_c__XC=100 ex_black3_c__YC=100``` Special case: no black pixels. ```%IMG7%magick ^ -size 200x200 xc:White ^ msc_ex_white.png call %PICTBAT%maxSquare ^ msc_ex_white.png ex_white_ msc_ex_white_out.png set ex_white_ ``` ```ex_white__area=1 ex_white__Rad=-1 ex_white__X0=1 ex_white__X1=-1 ex_white__XC=0 ex_white__Y0=1 ex_white__Y1=-1 ex_white__YC=0``` A negative radius means no square was possible. ```call %PICTBAT%maxCircle ^ msc_ex_white.png ex_white_c_ msc_ex_white_c_out.png set ex_white_c_ ``` ```ex_white_c__Rad=-1 ex_white_c__XC=0 ex_white_c__YC=0``` A negative radius means no circle was possible.

The foreground colour can reach the edge of the image:

 ```%IMG7%magick ^ -size 200x200 xc:White ^ -fill Black ^ +antialias ^ -draw "ellipse 10,100 80,40 0,360" ^ msc_ex_edge.png call %PICTBAT%maxSquare ^ msc_ex_edge.png ex_edge_ msc_ex_edge_out.png set ex_edge_ ``` ```ex_edge__area=3844 ex_edge__Rad=30.5 ex_edge__X0=0 ex_edge__X1=61 ex_edge__XC=30 ex_edge__Y0=69 ex_edge__Y1=130 ex_edge__YC=99``` ```call %PICTBAT%maxCircle ^ msc_ex_edge.png ex_edge_c_ msc_ex_edge_c_out.png set ex_edge_c_ ``` ```ex_edge_c__Rad=36 ex_edge_c__XC=36 ex_edge_c__YC=100``` ```%IMG7%magick ^ -size 200x200 xc:White ^ -fill Black ^ +antialias ^ -draw "ellipse 100,10 80,40 0,360" ^ msc_ex_edge2.png call %PICTBAT%maxSquare ^ msc_ex_edge2.png ex_edge2_ msc_ex_edge2_out.png set ex_edge2_ ``` ```ex_edge2__area=2401 ex_edge2__Rad=24 ex_edge2__X0=73 ex_edge2__X1=121 ex_edge2__XC=97 ex_edge2__Y0=0 ex_edge2__Y1=48 ex_edge2__YC=24``` ```call %PICTBAT%maxCircle ^ msc_ex_edge2.png ex_edge2_c_ msc_ex_edge2_c_out.png set ex_edge2_c_ ``` ```ex_edge2_c__Rad=25 ex_edge2_c__XC=94 ex_edge2_c__YC=25```

There may be multiple non-connected areas of foreground colour:

 ```%IMG7%magick ^ -size 200x200 xc:White ^ -fill Black ^ +antialias ^ -draw "ellipse 60,60 40,20 0,360" ^ -draw "ellipse 110,140 20,60 0,360" ^ -draw "rectangle 140,30 160,90" ^ msc_ex_multi.png call %PICTBAT%maxSquare ^ msc_ex_multi.png ex_multi_ msc_ex_multi_out.png set ex_multi_ ``` ```ex_multi__area=1521 ex_multi__Rad=19 ex_multi__X0=91 ex_multi__X1=129 ex_multi__XC=110 ex_multi__Y0=118 ex_multi__Y1=156 ex_multi__YC=137``` ```call %PICTBAT%maxCircle ^ msc_ex_multi.png ex_multi_c_ msc_ex_multi_c_out.png set ex_multi_c_ ``` ```ex_multi_c__Rad=20 ex_multi_c__XC=56 ex_multi_c__YC=60```

If two or more centre locations have equally largest squares or circles, the scripts will find only one:

 ```%IMG7%magick ^ -size 200x200 xc:White ^ -fill Black ^ +antialias ^ -draw "ellipse 60,50 40,20 0,360" ^ -draw "ellipse 150,90 40,20 0,360" ^ -draw "ellipse 120,150 40,20 0,360" ^ msc_ex_equi.png call %PICTBAT%maxSquare ^ msc_ex_equi.png ex_equi_ msc_ex_equi_out.png set ex_equi_ ``` ```Channel maximum locations: Gray: 65535 (1) 59,50 60,50 61,50 149,90 150,90 151,90 119,150 120,150 121,150``` ```call %PICTBAT%maxCircle ^ msc_ex_equi.png ex_equi_c_ msc_ex_equi_c_out.png set ex_equi_c_ ``` ```ex_equi_c__Rad=20 ex_equi_c__XC=56 ex_equi_c__YC=50```

If the foreground colour is not black, it must be specified as a parameter to the script.

 ```%IMG7%magick ^ xc:Lime xc:Red ^ +append +repage -write mpr:MAP ^ +delete ^ toes.png +dither -remap mpr:MAP ^ msc_ex_toes.png call %PICTBAT%maxSquare ^ msc_ex_toes.png ex_toes_ ^ msc_ex_toes_out.png red set ex_toes_ ``` ```ex_toes__area=8649 ex_toes__Rad=46 ex_toes__X0=94 ex_toes__X1=186 ex_toes__XC=140 ex_toes__Y0=38 ex_toes__Y1=130 ex_toes__YC=84``` ```call %PICTBAT%maxCircle ^ msc_ex_toes.png ex_toes_c_ ^ msc_ex_toes_c_out.png red set ex_toes_c_ ``` ```ex_equi_c__Rad=20 ex_equi_c__XC=56 ex_equi_c__YC=50```

For squares, the script easily calculates the area. For circles, the approximate area is pi*rad2. I haven't reverse-engineered the rasterizing code to derive a general formula for the exact area. We can find the area from the debugging image:

```%IMG7%magick ^
msc_ex_equi_c_out.png ^
-fill Black -opaque White ^
-fill White +opaque Black ^
-format "area=%%[fx:floor(mean*w*h+0.5)]\n" ^
info: ```
`area=1313`

We can specify the minimum and maximum radius of the shapes. If either or both of these are set, the script will ignore pixels where the maximum radius at that pixel is outside the limits.

If the minimum radius is set, for example to 20, then any pixels where the maximum available radius is less than 20 will be ignored.

If the maximum radius is set, for example to 30, then any pixels where the maximum available radius is more than 30 will be ignored.

For example, if the minimum is set to 20 and the maximum to 30, then the script will find pixels where the maximum radius is between 20 and 30, inclusive, and will return the first of these.

Setting these limits will slightly increase the time taken.

If no pixels are found where the maximum radius is between the limits, the script returns a negative radius.

If we set the minimum and maximum to the same value, the script will find only pixels where the maximum radius is that value.

 ```call %PICTBAT%maxSquare ^ msc_ex_toes.png ex_toesmin_ ^ msc_ex_toesmin_out.png red ^ "20" "30" set ex_toesmin_ ``` ```ex_toesmin__area=1681 ex_toesmin__Rad=20 ex_toesmin__X0=163 ex_toesmin__X1=203 ex_toesmin__XC=183 ex_toesmin__Y0=32 ex_toesmin__Y1=72 ex_toesmin__YC=52``` ```call %PICTBAT%maxCircle ^ msc_ex_toes.png ex_toesmin_c_ ^ msc_ex_toesmin_c_out.png red ^ "20" "30" set ex_toesmin_c_ ``` ```ex_toesmin_c__Rad=20 ex_toesmin_c__XC=106 ex_toesmin_c__YC=52```

The script returns the first location that has its maximum square or circle within the limits set by the script parameters. Internally to the script, it finds the maximum square or circle at all locations, then eliminates those with radius outside the limits.

A parameter to the script enables us to save the radius map. The parameter should be one or more complete IM operations, such as "-write x.png" or "-auto-level -write x.png".

The map records, at each pixel, the radius of the largest square or circle centred on that pixel. These are the values returned by morphology distance, without adustment for the problem that these always yield odd-sized diameters. Values are integers on a nominal scale of 0 to QuantumRange. For example, if the radius map pixel has a value of 100, the maximal radius square at that location has a radius of 99 or 99.5 pixels. If Q16 is used, a value of 100 is 0.0015259 of QuantumRange, or 0.15259%. Radii can be large, eg 1 million pixels, so QuantumRange can be exceeded. For this reason, we should save as floating-point, or -auto-level if saving to an integer format such as PNG.

These examples don't make a debug image, but do make map images:

 ```call %PICTBAT%maxSquare ^ msc_ex_toes.png . . red ^ . . ^ "-auto-level -write msc_ex_ram.png"``` ```call %PICTBAT%maxCircle ^ msc_ex_toes.png . . red ^ . . ^ "-auto-level -write msc_ex_ram_c.png"```

The map images for squares and circles are similar, but not identical.

In the map image, lighter pixels show the centres of larger squares or circles. The lightest pixel(s) show the centres of global maximum(s). Because we have done a -auto-level, the lightest pixels are white.

When two or more locations have equally largest squares or circles, the map helps us to retrieve all the shapes. For example, using the image of three equal ellipses created above:

 ```call %PICTBAT%maxSquare ^ msc_ex_equi.png ex_equi2_ msc_ex_equi2_out.png ^ . . . ^ "-auto-level -write msc_ex_equi_map.png"```

We can find the maximum pixels:

```%IMG7%magick ^
msc_ex_equi_map.png ^
-define identify:locate=maximum ^
-identify NULL: ```
```Channel maximum locations:
Gray: 65535 (1) 59,50 60,50 61,50 149,90 150,90 151,90 119,150 120,150 121,150```

As expected, we have found pairs of coordinates in three areas. However, each area has three adjacent pixels of the maximum lightness. We can reduce the adjacent pixels to isolated pixels like this:

```%IMG7%magick ^
msc_ex_equi_map.png ^
-fill Black +opaque White ^
-morphology Thinning:-1 "Skeleton;LineEnds:1^>" ^
-define identify:locate=maximum ^
-identify NULL: ```
```Channel maximum locations:
Gray: 65535 (1) 60,50 150,90 120,150```

The map records the maximum radii of the found shapes, but not all possible shapes may have been found. If increment and maximum have not been set, then the map will include the global maximum. But if either has been set, the global maximum may not have been found.

A mask can limit the pixels that are considered for the centre of shapes. The mask should be the same size as the input image, and should contain black and white pixels only. Where the mask is black, that location will not be considered for a centre, Where it is white, the location will be a candidate centre.

A mask has no effect on performance.

For a simple example, we constrain the centre to be within a small central circle.

 Make a mask, white where we want the centre. ```%IMG7%magick ^ msc_ex_toes.png ^ -fill Black -colorize 100 ^ -fill White -draw ^ "translate %%[fx:w/2],%%[fx:h/2] circle 0,0,20,0" ^ msc_mask.png``` ```call %PICTBAT%maxSquare ^ msc_ex_toes.png ex_mask_ ^ msc_ex_mask_out.png red ^ . . . msc_mask.png set ex_mask_ ``` ```ex_mask__area=4489 ex_mask__Rad=33 ex_mask__X0=97 ex_mask__X1=163 ex_mask__XC=130 ex_mask__Y0=64 ex_mask__Y1=130 ex_mask__YC=97``` ```call %PICTBAT%maxCircle ^ msc_ex_toes.png ex_mask_c_ ^ msc_ex_mask_c_out.png red ^ . . . msc_mask.png set ex_mask_c_ ``` ```ex_mask_c__Rad=35 ex_mask_c__XC=130 ex_mask_c__YC=97```

For a more complex example, we loop through the centre locations found in the example above:

```set ImgNum=0
for /F "usebackq skip=8 tokens=1,2 delims=," %%A in (`%IMG7%magick ^
msc_ex_equi_map.png ^
-fill Black +opaque White ^
-morphology Thinning:-1 "Skeleton;LineEnds:1^>" ^
-define "identify:locate=maximum" ^
-identify NULL: ^| tr " " "\n" `) do (
echo !ImgNum! [%%A,%%B]

%IMG7%magick ^
msc_ex_equi.png ^
-fill Black -colorize 100 ^
-fill White -draw "point %%A,%%B" ^

call %PICTBAT%maxSquare msc_ex_equi.png . msc_ex_equi_pr!ImgNum!_out.png ^

set /A ImgNum+=1
)```

This has created three images:

## Performance

Elapsed time is proportional to the number of pixels in the image, and is not a problem: maxSquare.bat takes about 0.4 seconds for a 1000x1000 pixel input and maxCircle.bat takes about 0.8 seconds.

## Future

A script for maximum ellipse could be useful.

The scripts find shapes that are exactly the foreground colour; it has no "fuzz" facility. This could be added, as an extra step in the pre-processing.

## Scripts

For convenience, .bat scripts are also available in a single zip file. See Zipped BAT files.

### maxSquare.bat

```rem From an opaque image, finds maximal square where all pixels are a given foreground colour.
rem
rem %1 Input image.
rem %2 Prefix for output environment variables.
rem %3 Output image, highlighting the found square. Default: no output image.
rem %4 Input foreground colour. Default: Black.
rem %5 Minimum radius. Default "0".
rem %6 Maximum radius. Default: no maximum.
rem %7 IM operations to save the radius map. Default: map is not saved.
@rem    Example operations:
@rem      -write ramap.png
@rem      -auto-level -write ramap.png
@rem      -define quantum:format=floating-point -write ramap.miff
rem %8 Input mask. White where centre can occur; black where it can't. Default: no mask.
@rem
@rem Reference: http://im.snibgo.com/maxrect.htm
@rem

@if "%1"=="" findstr /B "rem @rem" %~f0 & exit /B 1

@setlocal enabledelayedexpansion

@call echoOffSave

call %PICTBAT%setInOut %1 msq

set EnvPref=%2
if "%EnvPref%"=="." set EnvPref=
if "%EnvPref%"=="" set EnvPref=msq_

set OUTFILE=%3
if "%OUTFILE%"=="." set OUTFILE=

set FgndCol=%~4
if "%FgndCol%"=="." set FgndCol=
if "%FgndCol%"=="" set FgndCol=Black

set SaveRam=%~7
if "%SaveRam%"=="." set SaveRam=

if "%SaveRam%"=="" (
set sRAM=
) else (
set sRAM="(" +clone %SaveRam% +delete ")"
)

) else (
)

set TmpFile=%TEMP%\msq_tmp.miff

for /F "usebackq skip=1 tokens=2,4,5 delims=:(), " %%A in (`%IMG7%magick ^
%INFILE% ^
-precision 15 ^
+transparent %FgndCol% ^
-fill White -colorize 100 ^
-background Black -layers Flatten ^
-colorspace Gray ^
-alpha off ^
-virtual-pixel Black ^
-morphology Distance "Chebyshev:1,1" ^
-write ftxt:f.txt ^
+depth ^
^( +clone ^
-define "quantum:format=floating-point" ^
-write %TmpFile% ^
+delete ^
^) ^
%sRAM% ^
-colorspace Gray ^
-write ftxt:f2.txt ^
-define "identify:locate=maximum" ^
-define "identify:limit=1" ^
-identify ^
NULL:`) do (
set XC=%%B
set YC=%%C
)

if ERRORLEVEL 1 exit /B 1

rem FIXME: if central 4 pixels are equal, increment X1 and Y1.

if not %Rad% LSS 0 (
for /F "usebackq" %%L in (`%IMG7%magick ^
%TmpFile% ^
-crop 2x2+%XC%+%YC% +repage ^
-format "SD4=%%[fx:standard_deviation]\n" ^
info:`) do set %%L

if "!SD4!"=="0" (
set /A X1+=1
set /A Y1+=1
)
)

set /A Area=(%X1%-%X0%+1)*(%Y1%-%Y0%+1)

if not "%OUTFILE%"=="" %IMG7%magick ^
%INFILE% ^
-fill sRGBA(100%%,100%%,0,0.75) ^
+antialias ^
-draw "rectangle %X0%,%Y0% %X1%,%Y1%" ^
%OUTFILE%

call echoRestore

endlocal & set msqOUTFILE=%OUTFILE%& ^
set %EnvPref%_area=%Area%& ^
set %EnvPref%_XC=%XC%& ^
set %EnvPref%_YC=%YC%& ^
set %EnvPref%_X0=%X0%& ^
set %EnvPref%_X1=%X1%& ^
set %EnvPref%_Y0=%Y0%& ^
set %EnvPref%_Y1=%Y1%```

### maxCircle.bat

```rem From an opaque image, finds maximal circle where all pixels are a given foreground colour.
rem
rem %1 Input image.
rem %2 Prefix for output environment variables.
rem %3 Output image, highlighting the found circle. Default: no output image.
rem %4 Input foreground colour. Default: Black.
rem %5 Minimum radius. Default "0".
rem %6 Maximum radius. Default: no maximum.
rem %7 IM operations to save the radius map. Default: map is not saved.
@rem    Example operations:
@rem      -write ramap.png
@rem      -auto-level -write ramap.png
@rem      -define quantum:format=floating-point -write ramap.miff
rem %8 Input mask. White where centre can occur; black where it can't. Default: no mask.
@rem
@rem Reference: http://im.snibgo.com/maxrect.htm
@rem
@rem

@if "%1"=="" findstr /B "rem @rem" %~f0 & exit /B 1

@setlocal enabledelayedexpansion

@call echoOffSave

call %PICTBAT%setInOut %1 mci

set EnvPref=%2
if "%EnvPref%"=="." set EnvPref=
if "%EnvPref%"=="" set EnvPref=mci_

set OUTFILE=%3
if "%OUTFILE%"=="." set OUTFILE=

set FgndCol=%~4
if "%FgndCol%"=="." set FgndCol=
if "%FgndCol%"=="" set FgndCol=Black

set SaveRam=%~7
if "%SaveRam%"=="." set SaveRam=

if "%SaveRam%"=="" (
set sRAM=
) else (
set sRAM="(" +clone %SaveRam% +delete ")"
)

) else (
)

set TmpFile=%TEMP%\mci_tmp.miff

for /F "usebackq skip=1 tokens=2,4,5 delims=:(), " %%A in (`%IMG7%magick ^
%INFILE% ^
-precision 15 ^
+transparent %FgndCol% ^
-fill White -colorize 100 ^
-background Black -layers Flatten ^
-colorspace Gray ^
-alpha off ^
-virtual-pixel Black ^
-morphology Distance "Euclidean:7,1" ^
+depth ^
^( +clone ^
-define "quantum:format=floating-point" ^
-write %TmpFile% ^
+delete ^
^) ^
%sRAM% ^
-define "identify:locate=maximum" ^
-define "identify:limit=1" ^
-identify ^
NULL:`) do (
set XC=%%B
set YC=%%C
)

if ERRORLEVEL 1 exit /B 1

rem Note: Rad may not be integer.

for /F "usebackq" %%L in (`%IMG7%magick ^
xc: ^
info:`) do set %%L

rem If radius is not negative and central 4 pixels are equal, increment XC and YC by 0.5.

if not %Rad% LSS 0 (
for /F "usebackq" %%L in (`%IMG7%magick ^
%TmpFile% ^
-crop 2x2+%XC%+%YC% +repage ^
-format "SD4=%%[fx:standard_deviation]\n" ^
info:`) do set %%L

if "!SD4!"=="0" (
set XC=%XC%.5
set YC=%YC%.5
)
)

if not "%OUTFILE%"=="" (

set sDRAW=point %XC%,%YC%
) else (
)

%IMG7%magick ^
%INFILE% ^
-fill "sRGBA^(100%%,100%%,0,0.75^)" ^
+antialias ^
-draw "!sDRAW!" ^
%OUTFILE%
)

call echoRestore

endlocal & set mciOUTFILE=%OUTFILE%& ^
set %EnvPref%_XC=%XC%& ^
set %EnvPref%_YC=%YC%& ^

All images on this page were created by the commands shown, using:

`%IMG7%magick -version`
```Version: ImageMagick 7.1.1-20 Q16-HDRI x86 98bb1d4:20231008 https://imagemagick.org
Copyright: (C) 1999 ImageMagick Studio LLC
Features: Cipher DPC HDRI OpenCL OpenMP(2.0)
Delegates (built-in): bzlib cairo freetype gslib heic jng jp2 jpeg jxl lcms lqr lzma openexr pangocairo png ps raqm raw rsvg tiff webp xml zip zlib
Compiler: Visual Studio 2022 (193532217)```

To improve internet download speeds, some images may have been automatically converted (by ImageMagick, of course) from PNG or TIFF or MIFF to JPG.

Source file for this web page is maxsqc.h1. To re-create this web page, run "procH1 maxsqc".

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Anyone is permitted to re-publish this page, but only for non-commercial use.