ericlengyel / terathon-math-library Goto Github PK

Hi,

We (Masterbrain Bytes/Cattle and Crops) have camera code that uses polar coordinates to handle input, and we also want the camera to move (and turn) with the vehicle the player is currently driving.
So we're using code like

float zrot = Arctan( vehicleTransform.m10, vehicleTransform.m00 );
azimuth += zrot;

This generally works, but we noticed that when just driving in a circle, at certain angles the camera stuttered.
When replacing Arctan() with atan2f() those problems went away.

This could've been it, but this issue somehow nerdsniped me so I started investigating and found out that Arctan(float x) has errors of up to 0.004459 (compared to atan(x) in double precision).

When looking up how a fast atan() can be implemented, I stumbled upon the idea of just doing a linear interpolation between values of a lookup table.
So I implemented it (with the existing lookup-table), just interpolating between table[i] and table[i+1], using b - i as the lerp factor, and to my big surprise this works really well - the maximal error seems to be below 0.000020, i.e. over 200 times lower.
In addition to that, it even seems to be about twice as fast, and it works with our camera code.

I tested this extensively both with values between +/- 10'000 (in steps of 0.00001) and values between +/- 1.5 (in steps of 0.00000001) and it indeed seems to work quite well.

Here's my test program (tested on both Linux and Windows), including both your and my Arctan(float) implementation: atantest-upd.cpp.txt (Github doesn't allow attaching .cpp files so I had to append .txt).
UPDATE: Replaced the file with an updated one with one more element in table; also added function with 130 element lookup table.
Feel free to use it (also in your commercial code).

Here's my test results from both Linux (on a AMD Ryzen 2700X) and Win10 (on an Intel Haswell i7-4771): atanresults.txt

Cheers,
Daniel

the TSMath.h header seems to be missing, it's being called from TSAlgebra.h , Thank you

Looks like TSBasic.h is missing (included in TSMatrix3D.cpp)

I think the formula in the documentation is wrong.

It should not be (a - a.b)b, but rather a - (a.b)b

The actual code seems fine, though:

I suggest adding topics such as geometric-algebra, quaternion in the About section

Any plans on adding unit tests to the library? I think it could prevent issues like these:

#5