It's so handy to have functions that evaluate to either the derivative or the integral for a particular (version of a) shaping function like smoothstep.
Analytic integration has yielded some of the most stunning optimizations in graphics rendering! Replacing sample-the-hell-out-of-signal-and-integrate-the-samples with instead direct evaluation of an integral (or good-enough-standin-integral) function (where that itself can be known or derived) can yield many speedups and cool tricks!
Analytic integration has yielded some of the most stunning optimizations in graphics rendering! Replacing sample-the-hell-out-of-signal-and-integrate-the-samples with instead direct evaluation of an integral (or good-enough-standin-integral) function (where that itself can be known or derived) can yield many speedups and cool tricks!