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I'm Okay with fixed scaling factors but this has got me beat.

I have a page that is 100mm and a logo that is 25mm wide making it 25% of the page width when the logo is scaled at 100%.

As the page size increases I want to enlarge the Logo also - but not proportionately - so that when the page is incrementally enlarged to a maximum of 500% or 500mm the logo is scaled to a maximum of say 75mm (300%) not 125mm (500%). Basically as the page size increases the logo enlargement increase to a lesser extent.

Any help would be gratefully received

Thanks

Toggs
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1 Answers1

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Suppose the page width is $P$ millimetres and the logo width is $L$ millimetres

One of many possible solutions to your objective could be an curve $$L=25\left(\frac{P}{100}\right)^{\frac{\log(75)-\log(25)}{\log(500)-\log(100)}} \approx 1.07827\times P^{0.6826}$$ which grows with $P$ but sublinearly

It would suggest the following logo widths for various page widths:

Page (mm)   Logo (mm)     
  10          5.2
  20          8.3
  50         15.6
 100         25.0
 200         40.1
 300         52.9
 400         64.4
 500         75.0
1000        120.4
Henry
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  • I'm trying to implement this in a javascript function which limits me to multiplication and division (and therefore percentaage). I can set L and P as variables - is there an alternative way to do this without using log? – Toggs May 23 '18 at 14:01
  • Javascript does powers, so try something like var L = 1.07827 * Math.pow(P, 0.6826). It does in fact also do natural logarithms with Math.log() and $e^x$ with Math.exp() – Henry May 23 '18 at 14:40