File content as of revision 8:4ee054567b6c:

#ifndef _HELPER_3DMATH_H_
#define _HELPER_3DMATH_H_

class Quaternion {
    public:
        float w;
        float x;
        float y;
        float z;

        Quaternion() {
            w = 1.0f;
            x = 0.0f;
            y = 0.0f;
            z = 0.0f;
        }

        Quaternion(float nw, float nx, float ny, float nz) {
            w = nw;
            x = nx;
            y = ny;
            z = nz;
        }

        Quaternion getProduct(Quaternion q) {
            // Quaternion multiplication is defined by:
            //     (Q1 * Q2).w = (w1w2 - x1x2 - y1y2 - z1z2)
            //     (Q1 * Q2).x = (w1x2 + x1w2 + y1z2 - z1y2)
            //     (Q1 * Q2).y = (w1y2 - x1z2 + y1w2 + z1x2)
            //     (Q1 * Q2).z = (w1z2 + x1y2 - y1x2 + z1w2
            return Quaternion(
                w*q.w - x*q.x - y*q.y - z*q.z,  // new w
                w*q.x + x*q.w + y*q.z - z*q.y,  // new x
                w*q.y - x*q.z + y*q.w + z*q.x,  // new y
                w*q.z + x*q.y - y*q.x + z*q.w); // new z
        }

        Quaternion getConjugate() {
            return Quaternion(w, -x, -y, -z);
        }

        float getMagnitude() {
            return sqrt((float)(w*w + x*x + y*y + z*z));
        }

        void normalize() {
            float m = getMagnitude();
            w /= m;
            x /= m;
            y /= m;
            z /= m;
        }

        Quaternion getNormalized() {
            Quaternion r(w, x, y, z);
            r.normalize();
            return r;
        }
};

class VectorInt16 {
    public:
        int16_t x;
        int16_t y;
        int16_t z;

        VectorInt16() {
            x = 0;
            y = 0;
            z = 0;
        }

        VectorInt16(int16_t nx, int16_t ny, int16_t nz) {
            x = nx;
            y = ny;
            z = nz;
        }

        float getMagnitude() {
            return sqrt((float)(x*x + y*y + z*z));
        }

        void normalize() {
            float m = getMagnitude();
            x /= m;
            y /= m;
            z /= m;
        }

        VectorInt16 getNormalized() {
            VectorInt16 r(x, y, z);
            r.normalize();
            return r;
        }

        void rotate(Quaternion *q) {
            // http://www.cprogramming.com/tutorial/3d/quaternions.html
            // http://www.euclideanspace.com/maths/algebra/realNormedAlgebra/quaternions/transforms/index.htm
            // http://content.gpwiki.org/index.php/OpenGL:Tutorials:Using_Quaternions_to_represent_rotation
            // ^ or: http://webcache.googleusercontent.com/search?q=cache:xgJAp3bDNhQJ:content.gpwiki.org/index.php/OpenGL:Tutorials:Using_Quaternions_to_represent_rotation&hl=en&gl=us&strip=1

            // P_out = q * P_in * conj(q)
            // - P_out is the output vector
            // - q is the orientation quaternion
            // - P_in is the input vector (a*aReal)
            // - conj(q) is the conjugate of the orientation quaternion (q=[w,x,y,z], q*=[w,-x,-y,-z])
            Quaternion p(0, x, y, z);

            // quaternion multiplication: q * p, stored back in p
            p = q -> getProduct(p);

            // quaternion multiplication: p * conj(q), stored back in p
            p = p.getProduct(q -> getConjugate());

            // p quaternion is now [0, x', y', z']
            x = p.x;
            y = p.y;
            z = p.z;
        }

        VectorInt16 getRotated(Quaternion *q) {
            VectorInt16 r(x, y, z);
            r.rotate(q);
            return r;
        }
};

class VectorFloat {
    public:
        float x;
        float y;
        float z;

        VectorFloat() {
            x = 0;
            y = 0;
            z = 0;
        }

        VectorFloat(float nx, float ny, float nz) {
            x = nx;
            y = ny;
            z = nz;
        }

        float getMagnitude() {
            return sqrt((float)(x*x + y*y + z*z));
        }

        void normalize() {
            float m = getMagnitude();
            x /= m;
            y /= m;
            z /= m;
        }

        VectorFloat getNormalized() {
            VectorFloat r(x, y, z);
            r.normalize();
            return r;
        }

        void rotate(Quaternion *q) {
            Quaternion p(0, x, y, z);

            // quaternion multiplication: q * p, stored back in p
            p = q -> getProduct(p);

            // quaternion multiplication: p * conj(q), stored back in p
            p = p.getProduct(q -> getConjugate());

            // p quaternion is now [0, x', y', z']
            x = p.x;
            y = p.y;
            z = p.z;
        }

        VectorFloat getRotated(Quaternion *q) {
            VectorFloat r(x, y, z);
            r.rotate(q);
            return r;
        }
};

#endif /* _HELPER_3DMATH_H_ */