# Help with Math for Area Calculations

Guilty of bunking off double maths on monday mornings and now need help. Im trying to set the long edge of a fixed aspect rectangle to = defined area. I have all the photoshop processes run without issue it’s just my maths thats letting me down. This is just the math parts as I have them but its working off area relationship to long edge only. I hope I’ve explained this correctly?

``````property ImageArea : 1000 -- Square Root of Target Image Area in Pixels (1 mega-pixel for test)
--
set docHeight to 6000 -- To be defined by Photoshop at run time
set docWidth to 1500 -- To be defined by Photoshop at run time
--
set ThisImageArea to docHeight * docWidth
set ThisImageArea to SqRoot(ThisImageArea) of me
set AreaPro to (ThisImageArea / ImageArea) -- This is Area
if (docHeight â‰¥ docWidth) then
set AspectRatio to (docHeight / docWidth) -- I think I need to use this some how?
set imageheight to (docHeight / AreaPro) as string -- close but no cigar!!
display dialog imageheight
else
set AspectRatio to (docWidth / docHeight) -- I think I need to use this some how?
set imagewidth to (docWidth / AreaPro) as string
display dialog imagewidth
end if
--
on SqRoot(ThisImageArea)
return ThisImageArea ^ 0.5
end SqRoot
``````

However you’d like to do it, these relationships apply:

Area_oi = H_oi * W_oi [_oi is original image]
AspRatio = H_oi/W_oi
so
H_oi = AspRatio * W_oi
and
Area_oi = AspRatio * (W_oi ^ 2)
thus
W_oi = sqRt(Area_oi / AspRatio)
If we want to reduce the area by a factor of K then
K = Area_oi/Area_ni [_ni is new image]
W_ni = (Area_ni / (AspRatio * K)) ^ 0.5
H_ni = AspRatio * W_ni

I know you can deal with it from there. I know you don’t need help with AppleScript

Adam, thanks for the math lesson I had a feeling this was your bag seem to recall being math teacher or something to that effect? any how I have faith in your formula and will try to implement it in my script. I should then be able to define several image sizes as properties. I reckon with Photoshop’s rounding to the pixel I should be within + or -1 x longest edge which will be more than close enough thanks very much.

Mechanical Engineering Professor at SUNY@B, MIT, then here in Halifax, Head of ME Department, then Dean of Eng, and then Principal of the College, in fact. If you have problems with it, don’t hesitate.

Adam, I’ve had a look at this but appear to be going wrong with the formula some where. What Im getting when I test is the aspect ratio maintained but the long edge is to square root new image area so if say for instance aspect ratio is 2:1 then the new image area is half what I wanted. I dont think I had made myself very clear in the first post. Here is what I was using so you can check if I did something wrong.

``````property ImageArea : 1000000 -- NI Area (No longer as SqRt)
--
set docHeight to 1000 -- OI Height
set docWidth to 2000 -- OI Width
set ThisImageArea to docHeight * docWidth --OI Area
set AspectRatio to (docHeight / docWidth) --OI AR
--
set AreaPro to (ThisImageArea / ImageArea) -- K
--
set imagewidth to ((ImageArea / (AspectRatio * AreaPro)) ^ 0.5) as string
set imageheight to (AspectRatio * imagewidth) as string
display dialog imageheight & " x " & imagewidth
--
``````

Wrong area in formula - you want to reduce the original. This works:

``````
property ImageArea : 1000000 -- NI Area (No longer as SqRt)
--
set docHeight to 1000 -- OI Height
set docWidth to 2000 -- OI Width
set ThisImageArea to docHeight * docWidth -- OI Area
set AspectRatio to (docHeight / docWidth) -- OI AR
--
set AreaPro to (ThisImageArea / ImageArea) -- K
--
set imagewidth to ((ThisImageArea / (AspectRatio * AreaPro)) ^ 0.5) as string
set imageheight to (AspectRatio * imagewidth) as string

display dialog imageheight & " x " & imagewidth & return & return & "New Area Check: = " & imageheight * imagewidth
--

``````

If you don’t need the intermediate variables (I don’t know what you’re trying to achieve), then this is much simpler:

``````
property ImageArea : 1000000 -- New Area
--
set docHeight to 1000 -- OI Height
set docWidth to 2000 -- OI Width
--
set imagewidth to ((docWidth * ImageArea / docHeight) ^ 0.5) as string
set imageheight to (docHeight * imagewidth / docWidth) as string

display dialog imageheight & " x " & imagewidth & return & return & "New Area Check: = " & imageheight * imagewidth
--

``````

Adam, what I was trying to achieve was a method of sizing down raw images that are large files from our digital studio to several file sizes for differing uses. Photoshop will not let me save file to a given file size but I can pretty much sort this based on a pixel area calculation if Im making myself clear. The images are all product shots with paths, the image is processed to trim just outside of this path so all the images are of irregular size. The paths for these are now being out-sourced I already have some code to check these, after that what I was hoping to do was specify 3 or so ImageArea properties at the beginning to base the script off. I do not need any of the “intermediate variables” your new formula works exactly as I wanted. Thank you very much

I understand. This is prettier:

``````
property ImageArea : 1000000 -- New Area
--
set docHeight to 1500 -- OI Height
set docWidth to 2500 -- OI Width
--
set imagewidth to ((docWidth * ImageArea / docHeight) ^ 0.5)
set imageheight to (docHeight * imagewidth / docWidth)

display dialog "" & (round imageheight) & " x " & (round imagewidth) & return & return & "New Area Check: = " & ((imageheight * imagewidth) as integer)
--

``````

Adam, its in and running in some small tests and now works exactly as I had wished. It’s going to be run each week to deal with several hundred images and there pretty large files. Thats why I had concerns over my math as an error could produce some monster files. It’s all part of a Photoshop script that requires some piecing together but in short this is how Im using it within some loops.

``````property ImageArea1 : 6000000 -- 6 megaPixel
property ImageArea2 : 3000000 -- 3 megaPixel
property ImageArea3 : 1000000 -- 1 megaPixel
--
set docHeight to 1500 -- To be defined by Photoshop at run time
set docWidth to 2500 -- To be defined by Photoshop at run time
--
set imagewidth to ((docWidth * ImageArea1 / docHeight) ^ 0.5)
set imageheight to (docHeight * imagewidth / docWidth)
--
set imagewidth to ((docWidth * ImageArea2 / docHeight) ^ 0.5)
set imageheight to (docHeight * imagewidth / docWidth)
--
set imagewidth to ((docWidth * ImageArea3 / docHeight) ^ 0.5)
set imageheight to (docHeight * imagewidth / docWidth)
``````

I was thinking too much on wether the image was portrait or landscape when in “math” using the correct formula it does not matter.

Now I can’t paste between the blocks doh

Adam, sorry it was me being a muppet my edit was to correct the fact that my code paste had not gone between the "

``````" & "
``````

" things. Here is what I have so far needs some more work but Im pretty pleased with this so far.

``````property ImageArea1 : 6000000 -- 6 megaPixel
property ImageArea2 : 3000000 -- 3 megaPixel
property ImageArea3 : 1000000 -- 1 megaPixel
--
set inputFolder to choose folder with prompt "Where are the Images?" without invisibles
set TodaysDate to do shell script "date \"+%d-%m-%y\""
--
tell application "Finder"
set filesList to files in inputFolder
set ResizedImages to make new folder at desktop with properties ¬
{name:"Resized Images " & TodaysDate}
set LargeImages to make new folder at ResizedImages with properties ¬
{name:"Large Images"}
set MediumImages to make new folder at ResizedImages with properties ¬
{name:"Medium Images"}
set SmallImages to make new folder at ResizedImages with properties ¬
{name:"Small Images"}
set MediumGrayImages to make new folder at ResizedImages with properties ¬
{name:"Medium GrayScale Images"}
set SmallGrayImages to make new folder at ResizedImages with properties ¬
{name:"Small GrayScale Images"}
end tell
--
set display dialogs to never
set UserPrefs to properties of settings
set ruler units of settings to pixel units
end tell
--
repeat with aFile in filesList
set fileIndex to 0
tell application "Finder"
set theFile to aFile as alias
set theFileName to name of theFile
end tell
activate
open theFile
set docRef to the current document
tell docRef
set docName to name of docRef
set docBaseName to getBaseName(docName) of me
if (bits per channel of docRef is sixteen) then
set bits per channel of docRef to eight
end if
if (mode of docRef is not CMYK) then
change mode docRef to CMYK
end if
delete (every channel whose kind is not component channel)
if (count of art layers) > 1 or (count of layer sets) > 0 or ((count of art layers) is 1 and not background layer of layer 1) then flatten
if exists (path item 1) then
set thepath to name of path item 1
set subpaths to count of sub path items of path item 1
set openPaths to (count of (sub path items whose closed is false) of path item 1) as string
set thepoints to 0
repeat with x from 0 to (subpaths - 1) -- Java's index starts at "0" Zero
do javascript "activeDocument.pathItems[0].subPathItems[" & x & "].pathPoints.length" show debugger on runtime error
set pathpoints to the result as string
set thepoints to thepoints + pathpoints as string
end repeat
make clipping path path item 1 flatness 0.3
create selection path item 1 feather amount 0 with antialiasing
expand selection by 10
invert selection
fill selection with contents {class:RGB color, red:255, green:255, blue:255}
deselect
trim basing trim on top left pixel
else
set thepath to "No Clipping Path"
set thepoints to "0"
set openPaths to "0"
end if
writelog(docName, thepath, openPaths, thepoints) of me
--
set docHeight to height of docRef
set docWidth to width of docRef
set savedState to current history state of docRef
--
set imagewidth to ((docWidth * ImageArea1 / docHeight) ^ 0.5) as string
set imageheight to (docHeight * imagewidth / docWidth) as string
resize image height imageheight width imagewidth resolution 300
set newFileName to (LargeImages as string) & docBaseName
save docRef in file newFileName as Photoshop EPS with options ¬
{class:EPS save options, embed color profile:true, encoding:binary, preview type:eight bit TIFF} ¬
appending lowercase extension with copying
set current history state of docRef to savedState
--
set imagewidth to ((docWidth * ImageArea2 / docHeight) ^ 0.5) as string
set imageheight to (docHeight * imagewidth / docWidth) as string
resize image height imageheight width imagewidth resolution 300
set newFileName to (MediumImages as string) & docBaseName
save docRef in file newFileName as Photoshop EPS with options ¬
{class:EPS save options, embed color profile:true, encoding:binary, preview type:eight bit TIFF} ¬
appending lowercase extension with copying
--
change mode docRef to grayscale
set newFileName to (MediumGrayImages as string) & docBaseName
save docRef in file newFileName as Photoshop EPS with options ¬
{class:EPS save options, embed color profile:true, encoding:binary, preview type:eight bit TIFF} ¬
appending lowercase extension with copying
set current history state of docRef to savedState
--
set imagewidth to ((docWidth * ImageArea3 / docHeight) ^ 0.5) as string
set imageheight to (docHeight * imagewidth / docWidth) as string
resize image height imageheight width imagewidth resolution 200
set newFileName to (SmallImages as string) & docBaseName
save docRef in file newFileName as Photoshop EPS with options ¬
{class:EPS save options, embed color profile:true, encoding:binary, preview type:eight bit TIFF} ¬
appending lowercase extension with copying
--
change mode docRef to grayscale
set newFileName to (SmallGrayImages as string) & docBaseName
save docRef in file newFileName as Photoshop EPS with options ¬
{class:EPS save options, embed color profile:true, encoding:binary, preview type:eight bit TIFF} ¬
appending lowercase extension with copying
end tell
close current document without saving
end tell
end repeat
--
set ruler units of settings to ruler units of UserPrefs
end tell
--
set ReadFile to ((path to desktop folder) as text) & "Path Point Log.txt" as alias
tell application "TextEdit"
activate
end tell
--
on getBaseName(fName)
set baseName to fName
repeat with idx from 1 to (length of fName)
if (item idx of fName = ".") then
set baseName to (items 1 thru (idx - 1) of fName) as string
exit repeat
end if
end repeat
return baseName
end getBaseName
--
on writelog(docName, thepath, openPaths, thepoints)
set theLog to ((path to desktop folder) as text) & "Path Point Log.txt"
try
open for access file the theLog with write permission
write (return & docName & " - " & thepath & " - " & thepoints & " Points - Open Sub Paths " & openPaths) to file the theLog starting at eof
close access file the theLog
on error
try
close access file the theLog
end try
end try
end writelog
--
``````

What I mean’t to say was the things when you press the “Applescript” button. I tried to quote them and it buggered up oh I have a long way to go yet!!! Have a good weekend. where do I send the cigar? I was close ish but you were on the money!