package robotrace;

/**
 * Represents a 3D vector (immutable).
 */
public class Vector {

    // Origin and axis vectors.
    public final static Vector O = new Vector(0, 0, 0);
    public final static Vector X = new Vector(1, 0, 0);
    public final static Vector Y = new Vector(0, 1, 0);
    public final static Vector Z = new Vector(0, 0, 1);

    // Components.
    protected double x, y, z;
    
    /**
     * Construct from components.
     */
    public Vector(double x, double y, double z) {
        this.x = x;
        this.y = y;
        this.z = z;
    }

    /**
     * Get X component.
     */
    public double x() {
        return x;
    }

    /**
     * Get Y component.
     */
    public double y() {
        return y;
    }
    
    /**
     * Get Z component.
     */
    public double z() {
        return z;
    }

    /**
     * Euclidian length squared.
     */
    public double lengthSqr() {
        return x * x + y * y + z * z;
    }

    /**
     * Euclidian length.
     */
    public double length() {
        return Math.sqrt(x * x + y * y + z * z);
    }

    /**
     * Normalized vector, which is not defined for
     * a vector of zero length.
     */
    public Vector normalized() {
        double length = length();

        return new Vector(x / length, y / length, z / length);
    }

    /**
     * Dot product with the given vector.
     */
    public double dot(Vector that) {
        return this.x * that.x +
               this.y * that.y +
               this.z * that.z;
    }
    
    /**
     * Cross product with the given vector.
     */
    public Vector cross(Vector that) {
        return new Vector(this.y * that.z - this.z * that.y,
                          this.z * that.x - this.x * that.z,
                          this.x * that.y - this.y * that.x);
    }

    /**
     * Add with the given vector.
     */
    public Vector add(Vector that) {
        return new Vector(this.x + that.x,
                          this.y + that.y,
                          this.z + that.z);
    }

    /**
     * Subtract by the given vector.
     */
    public Vector subtract(Vector that) {
        return new Vector(this.x - that.x,
                          this.y - that.y,
                          this.z - that.z);
    }

    /**
     * Multiply with the given scalar.
     */
    public Vector scale(double scalar) {
        return new Vector(scalar * this.x,
                          scalar * this.y,
                          scalar * this.z);
    }
    
    /**
     * String representation.
     */
    @Override
    public String toString() {
        return "(" + x + "," + y + "," + z + ")";
    }

}