BLIT, Limits, and zero denominators...oh my....
Good evening...I am trying to bash out a BLIT function so I can peek~ it into a wavetable and make magical sounding things...Just gotta dig around under the hood...
Anyway, I am running into a little problem with the function. Running it through grapher (app in mac) works great, the app seems to just know what it's supposed to draw with all the limits and such. However, the max implementation I wrote does that whole positive negative infinity thing.
You can see it happening in this screen shot. The BLIT is in red, and the green is the cosine which shows where the limit should land. I'm not good with this type of math, and looking for a way to approximate it easily for table values.
I've found that the equation graphs fine in grapher (for mac OSX). However, I can't seem to export a table of values, which would be nice.
I'm even open to other software options...wouldn't mind hacking this out in excel and pasting it into a coll. However, I want to get around the limit problem.
you are dividing by zero in the expression on the left. Try doing all of your math between +1 and -1. instead of using division multiply by a decimal.
Update: Please pardon me answering my own question. I figured it be good to document it here.
I worked around a solution by using the cosine function. In order to make it fit better, I widened the cosine formula, and then designated a range near the zero denominator part of the function, mapped a cosine to "crossfade" the formulas over to the cosine function, and then convert back. This is probably just an approximation, and can be improved upon.
Now that only value that is completely out is 255 input, which is the zero denominator. I overrode that value in the input to explicitly return the known limit, 1.0. So if you're using this pasted patch, and want to change the input resolution, or scale the output, make sure to change these corrections. I'll leave it to ya'll to look at the pasted patch to figure out any super-specific values.
It's also a pretty slow running function, not optimized. The purpose of it is to render a wavetable for later lookup.