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So losing precision is generally unavoidable if you using limited precision numbers like float or double. However, there is still hope. One strategy to help prevent the repeated inversions getting worse and worse is to re-normalize the quaternion after each inversion (or after a few of them if you can tolerate more error).

So losing precision is generally unavoidable if you're using limited precision numbers like float or double. However, there is still hope. One strategy to help prevent the repeated inversions getting worse and worse is to re-normalize the quaternion after each inversion (or after a few of them if you can tolerate more error).

This keeps the precision loss from growing out of control. See also this StackOverflow question.

This keeps the precision loss from growing out of control. See also this StackOverflow question.

Quaternion Normalize(Quaternion q) { Quaternion result; float sq = q.x * q.x; sq += q.y * q.y; sq += q.z * q.z; sq += q.w * q.w; //detect badness assert(sq > 0.1f); float inv = 1.0f / sqrt(sq); result.x = q.x * inv; result.y = q.y * inv; result.z = q.z * inv; result.w = q.w * inv; return result; } 

public static class QuaternionExtensions { public static Quaternion Normalize(this Quaternion q)  {   Quaternion result;   float sq = q.x * q.x;   sq += q.y * q.y;   sq += q.z * q.z;   sq += q.w * q.w;   //detect badness   assert(sq > 0.1f);   float inv = 1.0f / sqrt(sq);   result.x = q.x * inv;   result.y = q.y * inv;   result.z = q.z * inv;   result.w = q.w * inv;   return result; } }