I need to write a function for DPI screen scaling with parameters

[chubbychub]

i need to write a function for DPI screen scaling,

so the parameters is from 100 (percentage) to 350 (percentage) and increases at 25 (percentage) increase, it will subtract additional 1 DPI
so for example:

100% = 96 DPI which is -4
125% =120 DPI which is -5
150% =144 DPI which is -6
175% = 168 DPI which is -7
200% =192 DPI which is -8
225% = 216 DPI which is -9
250% = 240 DPI which is -10
275% = 264 DPI which is -11
300% = 288 DPI which is -12
325% = 312 DPI which is -13
350% = 336 DPi which is -14

if someone can help me solve this math problem please

 

[anuttarasammyak]

I do not know the abbreviation DPI but it seems
1 per cent = 0.96 DPI

 

[chubbychub]

but how can i write that into a function? that at every 25% increase, it should add 1 to subtract from?

 

[Hill]

Isn't it a homework?

 

[Mark44]

I do not know the abbreviation DPI but it seems.
1 per cent = 0.96 DPI

Pretty standard acronym for dots per inch, as used for printers.

The relationship is close to being linear, but a little bit messy. Each 25% increase corresponds to an increase of 24 DPI. A function's formula might have to do some rounding so as to map the percentage and DPI values onto the integers from 4 to 14.

Isn't it a homework?

Maybe, or maybe not.

 

[chubbychub]

no its not homework, i am trying to simplify a small script for macros, to detect screen size at different resolutions, using a function instead so that the script will work all the different monitor size and at different DPI scale for windows 11, if someone can help me write it please

 

[Hill]

no its not homework, i am trying to simplify a small script for macros, to detect screen size at different resolutions, using a function instead so that the script will work all the different monitor size and at different DPI scale for windows 11, if someone can help me write it please

The straightforward one is $Y=\frac {25} {24} X$, where $Y$ is % and $X$ is DPI.

 

[chubbychub]

what about the limitations of 100 lowest bound and 350 highest bound?

 

[Mark44]

The straightforward one is $Y=\frac {25} {24} X$, where $Y$ is % and $X$ is DPI.

This provides only the relationship between dots per inch and percentages. The function also needs to map the DPI to the integers 4 through 14. This is similar to how Fahrenheit temps in the range 32 to 212 map to Celsius temps in the range 0 to 100.

 

[Hill]

what about the limitations of 100 lowest bound and 350 highest bound?

$Y=max(100,min(350,int(\frac {25} {24} X +.5)))$
or
$X=max(96,min(336,int(\frac {24} {25} Y + .5)))$

 

[chubbychub]

why is the .5 added on either equation? what does this means? its increments of 25% at a time, starting at 100% all the way to 350%

 

[Hill]

why is the .5 added on either equation? what does this means? its increments of 25% at a time, starting at 100% all the way to 350%

It is there for rounding if the input is an arbitrary number.