#ifndef POI_MATH
#define POI_MATH
#ifndef pi
    #define pi float(3.14159265359)
#endif
float4 quaternion_conjugate(float4 v)
{
    return float4(
        v.x, -v.yzw
    );
}
float4 quaternion_mul(float4 v1, float4 v2)
{
    float4 result1 = (v1.x * v2 + v1 * v2.x);
    float4 result2 = float4(
        - dot(v1.yzw, v2.yzw),
        cross(v1.yzw, v2.yzw)
    );
    return float4(result1 + result2);
}
float4 get_quaternion_from_angle(float3 axis, float angle)
{
    return float4(
        cos(angle / 2.0),
        normalize(axis) * sin(angle / 2.0)
    );
}
float4 quaternion_from_vector(float3 inVec)
{
    return float4(0.0, inVec);
}
float degree_to_radius(float degree)
{
    return(
        degree / 180.0 * pi
    );
}
float3 rotate_with_quaternion(float3 inVec, float3 rotation)
{
    float4 qx = get_quaternion_from_angle(float3(1, 0, 0), degree_to_radius(rotation.x));
    float4 qy = get_quaternion_from_angle(float3(0, 1, 0), degree_to_radius(rotation.y));
    float4 qz = get_quaternion_from_angle(float3(0, 0, 1), degree_to_radius(rotation.z));
    #define MUL3(A, B, C) quaternion_mul(quaternion_mul((A), (B)), (C))
    float4 quaternion = normalize(MUL3(qx, qy, qz));
    float4 conjugate = quaternion_conjugate(quaternion);
    float4 inVecQ = quaternion_from_vector(inVec);
    float3 rotated = (
        MUL3(quaternion, inVecQ, conjugate)
    ).yzw;
    return rotated;
}
float4 transform(float4 input, float4 pos, float4 rotation, float4 scale)
{
    input.rgb *= (scale.xyz * scale.w);
    input = float4(rotate_with_quaternion(input.xyz, rotation.xyz/* * rotation.w*/) + (pos.xyz/* * pos.w*/), input.w);
    return input;
}
#endif