Quaternion Comparison?

Question

Is quaternion comparison possible? I'm writing a Java class of Quaternions and I want to implement the Comparable interface to use the Collections.sort(List<Quaternion>) facility. I'm not expert at math, I really don't understand the things I read about Quaternions. So, can anyone tell me can I override the compareTo method for Quaternions and how?

My class declarition:

public class Quaternion implements Serializable, Comparable<Quaternion> {

    private double s; // scalar part
    private double i, j, k; // vectorel part


    public Quaternion() {
        super();
    }

    public Quaternion(double s, double i, double j, double k) {
        super();
        this.s = s;
        this.i = i;
        this.j = j;
        this.k = k;
    }

Answer 1

There is no reason why you can't compare two quaternions. Assuming that you want to compare magnitudes, compute and compare the Quaternion Norms. Your Quaternion class should have a norm (magnitude) method allowing a toCompare to be something like the following:

int compareTo(Quaternion o){
  return (int)(this.norm() - o.norm());
}

A better version would be:

int compareTo(Quaternion o){
  // return (int)(this.norm() - o.norm());
  double tNorm = this.norm;
  double oNorm = o.norm;
  int retVal = 0;

  if (tNorm < oNorm){
    retVal = -1;
  } else if (tNorm > oNorm){
    retVal = 1;
  }

  return retVal;
}