package fr.alnotz.quaternion;

/**
 * Classe du quaternion, une combinaison de quatre nombres réels.
 * $q = a + bi + cj + dk$
 */
public class Quaternion implements IsQuaternion{
    private double s;
    private double i;
    private double j;
    private double k;
    public Quaternion(){
        this.s = 0;
        this.i = 0;
        this.j = 0;
        this.k = 0;
    }
    public Quaternion(double s, double i, double j, double k){
        this.s = s;
        this.i = i;
        this.j = j;
        this.k = k;
    }
    public static Quaternion plus(IsQuaternion quaternion0, IsQuaternion quaternion1){
        return new Quaternion(quaternion0.getS() + quaternion1.getS(),
                quaternion0.getI() + quaternion1.getI(),
                quaternion0.getJ() + quaternion1.getJ(),
                quaternion0.getK() + quaternion1.getK());
    }
    public static Quaternion times(IsQuaternion quaternion0, IsQuaternion quaternion1){
        /*
         * (a0 + b0i + c0j + d0k)(a1 + b1i + c1j + d1k)
         * (a0a1 - b0b1 - c0c1 - d0d1) +
         *   (a0b1 + b0a1 + c0d1 - d0c1)i +
         *   (a0c1 - b0d1 + c0a1 + d0b1)j +
         *   (a0d1 + b0c1 - c0b1 + d0a1)k
         */
        double newS = quaternion0.getS() * quaternion1.getS() -
                quaternion1.getI() * quaternion1.getI() -
                quaternion0.getJ() * quaternion1.getJ() -
                quaternion0.getK() * quaternion1.getK();
        double newI = quaternion0.getS() * quaternion1.getI() +
                quaternion0.getI() * quaternion1.getK() +
                quaternion0.getJ() * quaternion1.getS() -
                quaternion0.getK() * quaternion1.getJ();
        double newJ = quaternion0.getS() * quaternion1.getJ() -
                quaternion0.getI() * quaternion1.getK() +
                quaternion0.getJ() * quaternion1.getS() +
                quaternion0.getK() * quaternion1.getI();
        double newK = quaternion0.getS() * quaternion1.getK() +
                quaternion0.getI() * quaternion1.getJ() -
                quaternion0.getJ() * quaternion1.getI() +
                quaternion0.getK() * quaternion1.getS();
        return new Quaternion(newS, newI, newJ, newK);
    }
    public static Quaternion conjugate(IsQuaternion quaternion) {
        return new Quaternion(quaternion.getS(),
                -1 * quaternion.getI(),
                -1 * quaternion.getJ(),
                -1 * quaternion.getK());
    }
    @Override
    public double getS() {
        return this.s;
    }
    @Override
    public double getI() {
        return this.i;
    }
    @Override
    public double getJ() {
        return this.j;
    }
    @Override
    public double getK() {
        return this.k;
    }
    @Override
    public void setS(double s) {
        this.s = s;
    }
    @Override
    public void setI(double i) {
        this.i = i;
    }
    @Override
    public void setJ(double j) {
        this.j = j;
    }
    @Override
    public void setK(double k) {
        this.k = k;
    }
    @Override
    public Quaternion plus(IsQuaternion quaternion) {
        return new Quaternion(this.s + quaternion.getS(),
                this.i + quaternion.getI(),
                this.j + quaternion.getJ(),
                this.k + quaternion.getK());
    }
    @Override
    public Quaternion times(IsQuaternion quaternion) {
        /*
         * (a0 + b0i + c0j + d0k)(a1 + b1i + c1j + d1k)
         * (a0a1 - b0b1 - c0c1 - d0d1) +
         *   (a0b1 + b0a1 + c0d1 - d0c1)i +
         *   (a0c1 - b0d1 + c0a1 + d0b1)j +
         *   (a0d1 + b0c1 - c0b1 + d0a1)k
         */
        double newS = this.s * quaternion.getS() -
                this.i * quaternion.getI() -
                this.j * quaternion.getJ() -
                this.k * quaternion.getK();
        double newI = this.s * quaternion.getI() +
                this.i * quaternion.getK() +
                this.j * quaternion.getS() -
                this.k * quaternion.getJ();
        double newJ = this.s * quaternion.getJ() -
                this.i * quaternion.getK() +
                this.j * quaternion.getS() +
                this.k * quaternion.getI();
        double newK = this.s * quaternion.getK() +
                this.i * quaternion.getJ() -
                this.j * quaternion.getI() +
                this.k * quaternion.getS();
        return new Quaternion(newS, newI, newJ, newK);
    }
    @Override
    public Quaternion conjugate() {
        return new Quaternion(this.s, -1 * this.i, -1 * this.j, -1 * this.k);
    }
    @Override
    public boolean equals(IsQuaternion quaternion) {
        return false;
    }
    @Override
    public String toString(){
        return String.format("%+f %+fi %+fj %+fk\n", this.s, this.i, this.j, this.k);
    }
}