Math functions

[Xrayez]

I created this discussion to track and consider what kind of functions are worth to be implemented in GoostMath singleton (including implementation).

List

• Interpolation functions:
  • Bezier: Add GoostMath singleton #153
  • Catmull-Rom: Add GoostMath singleton #153
• Combinatorics (for procedural generation)
• Statistics (for economy games)
• Probability (perhaps some of the stuff could be implemented in Random singleton instead).

Misc

• Add is_between() method #154

Note that I'm not sure what functions might be actually worthless or not that useful in gamedev, as I'm learning myself as well. The list above is obviously not complete and I'll be updating this list, feel free to suggest more!

[Xrayez]

I created a new GoostMath singleton: #153.

[sairam4123]

Please do Statistics, would be so helpful for OpenSkyCity!

[ghost]

There is a useful repo with many additional math functions but is from 2017. Math doesn't change but perhaps some have already been implemented. This is the repo https://github.com/SaracenOne/godot_math_extension.

[Xrayez]

Some functions seem to be quite specific there, and some are already implemented in Godot, including:

• ease_in/out() is already implemented in Godot, but there are a variety of other easing functions... https://easings.net/, and for the most part these are available via Godot's Tween class anyways, so not really worth to bloat the API with those I guess.
• smooth_step() is already implemented in Godot, but not smoother_step().
• Inverse_lerp() is already implemented in Godot.
• base_log() - I don't really know what it's used for...

[ghost]

Based on the implementation is meant to be a log in any base. Godot has one log and is in base e (I think) because is more useful. There is no way to specify any other base but the math formula log(n)/log(base) used by the function creates any log in any base. Log 2 is also useful. I have used log 10 for dB power conversions to turn a log volume slider linear. I actually implemented it in my game. Their dB conversions don't give the right linearity.

[Xrayez]

Makes sense, I think we should go for Python approach: add log(x, base), where base will be e by default.
log2() and log10() could also be added since those will be more efficient to compute.

I certainly need to refresh/learn fundamental math! 😃

Update: added in #155.

[ghost]

The other ones that are interesting 2d_position_from_3d_position pretty common to use mouse pos to pick 3d objects. This is not as easy to implement. Your 2d mouse uses screen width x height where as 3D space uses well viewport size. Usually is done by creating an arbitrary z depth and converting screen xy to viewport xy then casting a ray from 0,0,0 center of camera to x,y,z and picking the first object hit.

Also clamp_angle quite common for example in 3D looking up and down you need to clamp angles to +90 and -90 i think is pitch x coordinate maybe. Usually angle clamping is done per axis so you only need a min, max clamp. Clamp angle is kinda like a regular clamp except since is an angle it spins around so your values > 360 become 0and < 0become 360 again .

Also adjust_facing which is like look_at but has additional adjusting parameters so you can rotate something in relation to the target you're looking at. I think not sure. You can also do this using look_at then rotate

Finally the other interesting one is camera_position_distance which gives you a distance from camera to a specific vector position.