Quaternion Math Library

// --- Quaternions
function Quaternion() {
    this.x = 0;
    this.y = 0;
    this.z = 0;
    this.w = 1;
}

Quaternion.prototype = {
    makeIdentity: function() {
        return this.make(0, 0, 0, 1);
    },

    make: function(x, y, z, w) {
        this.x = x;
        this.y = y;
        this.z = z;
        this.w = w;

        return this;
    },

    copy: function(quat) {
        this.x = quat.x;
        this.y = quat.y;
        this.z = quat.z;
        this.w = quat.w;

        return this;
    },

    add: function(quat) {
        this.x += quat.x;
        this.y += quat.y;
        this.z += quat.z;
        this.w += quat.w;

        return this;
    },

    sub: function(quat) {
        this.x -= quat.x;
        this.y -= quat.y;
        this.z -= quat.z;
        this.w -= quat.w;

        return this;
    },

    length: function() {
        return Math.sqrt(this.x * this.x + this.y * this.y + this.z * this.z + this.w * this.w);
    },

    length2: function() {
        return this.x * this.x + this.y * this.y + this.z * this.z + this.w * this.w;
    },

    conjugate: function() {
        this.x = -this.x;
        this.y = -this.y;
        this.z = -this.z;

        this.normalize();

        return this;
    },

    normalize: function() {
        var quatLenght = this.length();

        if (quatLenght === 0) {
            this.x = 0;
            this.y = 0;
            this.z = 0;
            this.w = 0;
        }
        else {
            this.x /= quatLenght;
            this.y /= quatLenght;
            this.z /= quatLenght;
            this.w /= quatLenght;
        }

        return this;
    },

    multiply: function(quat) {
        this.x = this.x*quat.w + this.w*quat.x + this.y*quat.z - this.z*quat.y;
        this.y = this.y*quat.w + this.z*quat.x + this.w*quat.y - this.x*quat.z;
        this.z = this.z*quat.w + this.x*quat.y + this.w*quat.z - this.y*quat.x;
        this.w = this.w*quat.w - this.x*quat.x - this.y*quat.y - this.z*quat.z;

        return this;
    },

    quaternionToMatrix: function() {
        var aMatrix = new Matrix4x3();

        aMatrix.element[0] = 1 - 2 * (this.y * this.y - this.z * this.z);
        aMatrix.element[1] = 2 * (this.x * this.y + this.w * this.z);
        aMatrix.element[2] = 2 * (this.x * this.z - this.w * this.y);

        aMatrix.element[4] = 2 * (this.x * this.y - this.w * this.z);
        aMatrix.element[5] = 1 - 2 * (this.x * this.x - this.z * this.z);
        aMatrix.element[6] = 2 * (this.y * this.z + this.w * this.x);

        aMatrix.element[8] = 2 * (this.x * this.z + this.w * this.y);
        aMatrix.element[9] = 2 * (this.y * this.z - this.w * this.x);
        aMatrix.element[10] = 1 - 2 * (this.x * this.x - this.y * this.y);

        return aMatrix;
    },

    axisToQuaternion: function(angle, x, y, z) {
        var quatRotation = new Quaternion();
        var sinA = Math.sin(angle/2);
        var length = Math.sqrt(x*x + y*y + z*z);

        x = x/length;
        y = y/length;
        z = z/length;

        quatRotation.x = (x * sinA);
        quatRotation.y = (y * sinA);
        quatRotation.z = (z * sinA);
        quatRotation.w = Math.cos(angle/2);

        return quatRotation;
    },

    matrixToQuaternion: function(m) {
        function copySign(a, b) {
            return b < 0 ? -Math.abs(a) : Math.abs(a);
        }
        var absQ = Math.pow(m.determinant(), 1.0 / 3.0);

        this.w = Math.sqrt(Math.max(0, absQ + m.element[0] + m.element[5] + m.element[10])) / 2;
        this.x = Math.sqrt(Math.max(0, absQ + m.element[0] - m.element[5] - m.element[10])) / 2;
        this.y = Math.sqrt(Math.max(0, absQ - m.element[0] + m.element[5] - m.element[10])) / 2;
        this.z = Math.sqrt(Math.max(0, absQ - m.element[0] - m.element[5] + m.element[10])) / 2;
        this.x = copySign(this.x, (m.element[9] - m.element[6]));
        this.y = copySign(this.y, (m.element[2] - m.element[8]));
        this.z = copySign(this.z, (m.element[4] - m.element[1]));
        this.normalize();

        return this;
    },
};