Quaternion Quaternion::operator* (const Quaternion& other) const // quaternion multiplication
{
return Quaternion( w * other.x + x * other.w + y * other.z - z * other.y,
w * other.y - x * other.z + y * other.w + z * other.x,
w * other.z + x * other.y - y * other.x + z * other.w,
w * other.w - x * other.x - y * other.y - z * other.z);
}
Quaternion Quaternion::unitpow(float exponent) const // power of unit quaternion, use with caution
{
assert(std::abs(x*x + y*y + z*z + w*w-1)<0.01);
float thetadiv2 = acos(w);
float vec_factor = sin(exponent*thetadiv2)/sin(thetadiv2);
return Quaternion( vec_factor * x,
vec_factor * y,
vec_factor * z,
cos(exponent*thetadiv2));
}
Quaternion Quaternion::quatpow(float exponent) const // power
{
float vmagnitude_squared = x*x + y*y + z*z;
float magnitudepow = pow(sqrt(w*w + vmagnitude_squared),exponent);
float vmagnitude = sqrt(vmagnitude_squared);
float thetadiv2 = atan2(w, vmagnitude);
float vec_factor = magnitudepow * sin(exponent*thetadiv2)/vmagnitude;
return Quaternion( vec_factor * x,
vec_factor * y,
vec_factor * z,
magnitudepow * cos(exponent*thetadiv2));
}
Quaternion Quaternion::unit() const // unit quaternion
{
float magnitude = sqrt(w*w + x*x + y*y + z*z);
return Quaternion(x/magnitude, y/magnitude, z/magnitude, w/magnitude);
}
Quaternion Quaternion::inverse() const // inverse/conjugate quaternion
{
return Quaternion(-x,-y,-z,w);
}
