One of the things I’m happiest to have learned in the past few months is a great use for Log + Exp in games when zooming in and out.
You may have already know that linear speeds work horribly for zooming, e.g.:
void Update() {
scale = scale + speed * Time.deltaTime;
}
…slowing down horribly as you zoom out and speeds up way too fast when you zoom in.
Instead, a better way is to do something like:
scale = scale * (1 + speed * Time.deltaTime);
…where speed is positive or negative depending on whether you want to zoom in or out.
However, I found recently that the best method of all is to use a linear scale for “number of times you’ve zoomed in or out”, and then use Exp to turn it into a scale:
// Similar to first example - it’s linear
zoomLevels = zoomLevels + speed * Time.deltaTime;
scale = originalScale * Mathf.Exp(zoomLevels);
So, say your originalScale is 1.0. If your zoomLevel is zero, then e^0 = 1, so we stay at the original zoom level. When you “zoom in once”, i.e. when zoomLevels == 1, then the scale is e^1 = e. And if you zoom in 3 times, then the scale is e^3, or e * e * e, since you’ve zoomed in “by e”, three times. It works when zoomLevels goes negative too.
And the best thing of all, is that if you’re internally using the linear zoomLevels scale, then it works great with functions like Unity’s Mathf.SmoothDamp, or simple Mathf.Lerp - it’ll zoom in out totally smoothly without having weird accelerations or decelerations at the start or end.