Third Person Camera Splines

Question

I'm having trouble coming up with a formula/method of creating third person camera with a variable distance from the player given a specific camera pitch.

This image shows something close to my desired result:

I basically only have two requirements. The camera has to be directly calculated from a pitch. The camera should roughly follow a smooth curve between the minimum and maximum camera distance and the halfway point is around 50% of the distance (as seen by the graph in the top right of the image).

So, Option A:

I create a function online to convert a pitch directly to a camera distance and use that. http://www.timotheegroleau.com/Flash/experiments/easing_function_generator.htm

I have this working and it ends up looking close but has two distinct problems. It is rigid and doesn't allow me to edit any of the offsets or distances without having to create a whole new function and the camera at 0 degrees pitch ends up being around 15-30% of the maximum distance which doesn't feel as good as if it were closer to 50%.

Option B:

Come up with a spline, perhaps a cubic bezier, between the min and max distances and somehow project the camera on to that spline given a specific pitch. I'm not sure how I would be able to do this. The disadvantages would be that the camera distance curve would not be as smooth without some tweaking and again it would require more work if any of the distances or offsets change.

Option C:

Come up with a specific formula which I have no idea how to find. Given the min and max camera distances, the offsets, and the camera pitch, return a distance that follows a smooth camera distance curve and a mid point of roughly 50% of the max distance.

So my question is can/how do I accomplish Option B or C? Is there a better way?

Answer 1

I would look into using an AnimationCurve for this. Add a curve to the script that controls your camera, then use the inspector to plot camera distance vs. pitch angle. (If the pitch has to go negative, I believe you'll have to offset it. No big deal!)

Now you can evaluate this curve (passing in pitch + offset) to get your camera distance out.

This will be quick to edit, and you should be able to fine-tune the curve while the game is running.

Answer 2

To make sure that I understand, what you're saying is that for option A: when you have the camera "flat" (pitch 0) it feels like it's too close to the player? If so... welcome to every third person game ever!

In all seriousness though, I think that you're maybe overthinking it. Why not take option A and then put a check in place for under/over certain pitch values and modify the distance slightly? What you'd essentially get is the typical 3rd person "bounce" when you go too high or low with the pitch.

I would also say that in the end most players prefer to manually set and adjust the camera distance themselves, making the auto-distance floating camera kind of a moot point. Obviously it needs to be functional, but I wouldn't worry about it being absolutely perfect because a lot of people won't use it.