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POAlgorithm to calculate a diminishing value, approaching a limit
 

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    <p>I've been trying to find a Javascript version of a handy method I'd used (not written) a while ago in LPC, it was called dimval(), and it took this form:</p> <pre><code>NAME dimval() - returns values with a reduced increase in output as input values grow larger. SYNOPSIS float dimval(float input, float max_input, float max_output, float min_input, float min_output, float rate); DESCRIPTION Returns (as a float) a value between min_output and max_output, with values increasing at a reduced rate as they move from min_input toward max_output. Input is the input value. Max_input is the maximum acceptable input. Any higher input value will be capped to this. Max_output is the maximum value returned. Min_input is the (optional) minimum input. Default is zero. Min_output is the (optional) minimum output. Default is zero. Rate determines how quickly the cost increases to achieve greater return values. Higher numbers are faster, lower numbers are slower. </code></pre> <p>I <a href="http://lostsouls.org/grimoire_diminishing_returns" rel="nofollow noreferrer">read this article</a>, but it doesn't seem to capture what I want (it looks much simpler for a start). I also <a href="https://stackoverflow.com/questions/2813621/how-do-you-create-a-formula-that-has-diminishing-returns">read this SO question</a> and... well I think this could work... but the Math is beyond me, to be honest. I understand the description above and how the parameters work together to produce the kind of result I want.</p> <p>I'd greatly appreciate it if someone could provide a method which has the above constraints, in Javascript.</p> <p>cheers!</p> <h2>EDIT: Sample outputs from original method.</h2> <ul> <li>eval return dimval(5.0, 100.0, 100.0, 0.0, 0.0, 1.0) => 22.360680</li> <li>eval return dimval(10.0, 100.0, 100.0, 0.0, 0.0, 1.0) => 31.622776</li> <li><p>eval return dimval(50.0, 100.0, 100.0, 0.0, 0.0, 1.0) => 70.710678</p></li> <li><p>eval return dimval(10.0, 100.0, 100.0, 0.0, 0.0, 2.0) => 15.811388</p></li> <li><p>eval return dimval(10.0, 100.0, 100.0, 0.0, 0.0, 10.0) => 3.162278</p></li> <li><p>eval return dimval(200.0, 100.0, 100.0, 0.0, 0.0, 10.0) => 10.000000</p></li> <li><p>eval return dimval(200.0, 100.0, 100.0, 0.0, 0.0, 1.0) => 100.000000</p></li> <li><p>eval return dimval(1.0, 100.0, 100.0, 10.0, 0.0, 10.0) => 0.000000</p></li> </ul> <hr> <p>Let me know if you want me to run any more samples.</p>
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    1. COYou know, I'm not even sure if the title of this question is quite accurate, I'm basing it on the name of the method I once used, and the research done so far. Please correct it if it's wrong.
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    2. CO"they move from min_input toward max_output" is that really right? Not from `min_input` towards `max_input`?
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    3. COI'll do an edit in a sec with some sample values, I can actually still run the old LPC method, but don't have the code.
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