Optimaze for: sin(atan()) and cost(atan()) on Android

OpenGL
1

optimaze for: sin(atan()) and cost(atan()) on Android.
float YX = uv.y / uv.x;
float ATAN = atan(YX);
float SIN = sin(ATAN);
float COS = cos(ATAN);

what’s the best way to replace this functions, thanks!

2

SIN = uv.y/length(uv.xy);
COS = uv.x/length(uv.xy);
watch for division by zero

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3

according to :
sin(atan(T)) = T / sqrt(1 + T * T);
cos(atan(T)) = 1 / sqrt(1 + T * T);
Thanks!

5

If length(uv.xy) is zero, the angle is undefined and so are sin/cos/tan. Even the two-argument form atan(uv.y,uv.x) (and atan2() in C or C++) is undefined in that case.

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6

if use atan(uv.y, uv.x), also must check if(uv.x != 0.0), right?

7

No. The two-argument form will return ±π/2 if the first argument is non-zero and the second argument is zero. It will also get the quadrant correct, i.e. atan(-x,-y) isn’t the same as atan(x,y) (the two will differ by ±π).

According to the GLSL spec, atan(0,0) is undefined (the C and C++ standards actually define this case according to the signs of the arguments; -0.0 and +0.0 are distinct in those languages).

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