/**
* Compute the angular separation between two vectors.
*
* <p>This method computes the angular separation between two vectors using the dot product for
* well separated vectors and the cross product for almost aligned vectors. This allows to have a
* good accuracy in all cases, even for vectors very close to each other.
*
* @param v1 first vector
* @param v2 second vector
* @return angular separation between v1 and v2
* @exception ArithmeticException if either vector has a null norm
*/
public static double angle(Vector3D v1, Vector3D v2) {
double normProduct = v1.getNorm() * v2.getNorm();
if (normProduct == 0) {
throw MathRuntimeException.createArithmeticException(LocalizedFormats.ZERO_NORM);
}
double dot = dotProduct(v1, v2);
double threshold = normProduct * 0.9999;
if ((dot < -threshold) || (dot > threshold)) {
// the vectors are almost aligned, compute using the sine
Vector3D v3 = crossProduct(v1, v2);
if (dot >= 0) {
return FastMath.asin(v3.getNorm() / normProduct);
}
return FastMath.PI - FastMath.asin(v3.getNorm() / normProduct);
}
// the vectors are sufficiently separated to use the cosine
return FastMath.acos(dot / normProduct);
}
/**
* Get the elevation of the vector.
*
* @return elevation (δ) of the vector, between -π/2 and +π/2
* @see #Vector3D(double, double)
*/
public double getDelta() {
return FastMath.asin(z / getNorm());
}