arcball.h

基于NEHE第48课的程序,改为MFC下运行.运用轨迹球技术,初学者值得参考

      * quaternion argument. 
      * @param q1 the quaternion to be converted 
      */
    //$hack this can be optimized some(if s == 0)
    inline
    static void Matrix3fSetRotationFromQuat4f(Matrix3fT* NewObj, const Quat4fT* q1)
    {
        GLfloat n, s;
        GLfloat xs, ys, zs;
        GLfloat wx, wy, wz;
        GLfloat xx, xy, xz;
        GLfloat yy, yz, zz;

        assert(NewObj && q1);

        n = (q1->s.X * q1->s.X) + (q1->s.Y * q1->s.Y) + (q1->s.Z * q1->s.Z) + (q1->s.W * q1->s.W);
        s = (n > 0.0f) ? (2.0f / n) : 0.0f;

        xs = q1->s.X * s;  ys = q1->s.Y * s;  zs = q1->s.Z * s;
        wx = q1->s.W * xs; wy = q1->s.W * ys; wz = q1->s.W * zs;
        xx = q1->s.X * xs; xy = q1->s.X * ys; xz = q1->s.X * zs;
        yy = q1->s.Y * ys; yz = q1->s.Y * zs; zz = q1->s.Z * zs;

        NewObj->s.XX = 1.0f - (yy + zz); NewObj->s.YX =         xy - wz;  NewObj->s.ZX =         xz + wy;
        NewObj->s.XY =         xy + wz;  NewObj->s.YY = 1.0f - (xx + zz); NewObj->s.ZY =         yz - wx;
        NewObj->s.XZ =         xz - wy;  NewObj->s.YZ =         yz + wx;  NewObj->s.ZZ = 1.0f - (xx + yy);
    }

    /**
     * Sets the value of this matrix to the result of multiplying itself
     * with matrix m1. 
     * @param m1 the other matrix 
     */
    inline
    static void Matrix3fMulMatrix3f(Matrix3fT* NewObj, const Matrix3fT* m1)
    {
        Matrix3fT Result; //safe not to initialize

        assert(NewObj && m1);

        // alias-safe way.
        Result.s.M00 = (NewObj->s.M00 * m1->s.M00) + (NewObj->s.M01 * m1->s.M10) + (NewObj->s.M02 * m1->s.M20);
        Result.s.M01 = (NewObj->s.M00 * m1->s.M01) + (NewObj->s.M01 * m1->s.M11) + (NewObj->s.M02 * m1->s.M21);
        Result.s.M02 = (NewObj->s.M00 * m1->s.M02) + (NewObj->s.M01 * m1->s.M12) + (NewObj->s.M02 * m1->s.M22);

        Result.s.M10 = (NewObj->s.M10 * m1->s.M00) + (NewObj->s.M11 * m1->s.M10) + (NewObj->s.M12 * m1->s.M20);
        Result.s.M11 = (NewObj->s.M10 * m1->s.M01) + (NewObj->s.M11 * m1->s.M11) + (NewObj->s.M12 * m1->s.M21);
        Result.s.M12 = (NewObj->s.M10 * m1->s.M02) + (NewObj->s.M11 * m1->s.M12) + (NewObj->s.M12 * m1->s.M22);

        Result.s.M20 = (NewObj->s.M20 * m1->s.M00) + (NewObj->s.M21 * m1->s.M10) + (NewObj->s.M22 * m1->s.M20);
        Result.s.M21 = (NewObj->s.M20 * m1->s.M01) + (NewObj->s.M21 * m1->s.M11) + (NewObj->s.M22 * m1->s.M21);
        Result.s.M22 = (NewObj->s.M20 * m1->s.M02) + (NewObj->s.M21 * m1->s.M12) + (NewObj->s.M22 * m1->s.M22);

        //copy result back to this
        *NewObj = Result;
    }

    inline
    static void Matrix4fSetRotationScaleFromMatrix4f(Matrix4fT* NewObj, const Matrix4fT* m1)
    {
        assert(NewObj && m1);

        NewObj->s.XX = m1->s.XX; NewObj->s.YX = m1->s.YX; NewObj->s.ZX = m1->s.ZX;
        NewObj->s.XY = m1->s.XY; NewObj->s.YY = m1->s.YY; NewObj->s.ZY = m1->s.ZY;
        NewObj->s.XZ = m1->s.XZ; NewObj->s.YZ = m1->s.YZ; NewObj->s.ZZ = m1->s.ZZ;
    }

    /**
      * Performs SVD on this matrix and gets scale and rotation.
      * Rotation is placed into rot3, and rot4.
      * @param rot3 the rotation factor(Matrix3d). if null, ignored
      * @param rot4 the rotation factor(Matrix4) only upper 3x3 elements are changed. if null, ignored
      * @return scale factor
      */
    inline
    static GLfloat Matrix4fSVD(const Matrix4fT* NewObj, Matrix3fT* rot3, Matrix4fT* rot4)
    {
        GLfloat s, n;

        assert(NewObj);

        // this is a simple svd.
        // Not complete but fast and reasonable.
        // See comment in Matrix3d.

        s = FuncSqrt(
                ( (NewObj->s.XX * NewObj->s.XX) + (NewObj->s.XY * NewObj->s.XY) + (NewObj->s.XZ * NewObj->s.XZ) + 
                  (NewObj->s.YX * NewObj->s.YX) + (NewObj->s.YY * NewObj->s.YY) + (NewObj->s.YZ * NewObj->s.YZ) +
                  (NewObj->s.ZX * NewObj->s.ZX) + (NewObj->s.ZY * NewObj->s.ZY) + (NewObj->s.ZZ * NewObj->s.ZZ) ) / 3.0f );

        if (rot3)   //if pointer not null
        {
            //this->getRotationScale(rot3);
            rot3->s.XX = NewObj->s.XX; rot3->s.XY = NewObj->s.XY; rot3->s.XZ = NewObj->s.XZ;
            rot3->s.YX = NewObj->s.YX; rot3->s.YY = NewObj->s.YY; rot3->s.YZ = NewObj->s.YZ;
            rot3->s.ZX = NewObj->s.ZX; rot3->s.ZY = NewObj->s.ZY; rot3->s.ZZ = NewObj->s.ZZ;

            // zero-div may occur.

            n = 1.0f / FuncSqrt( (NewObj->s.XX * NewObj->s.XX) +
                                      (NewObj->s.XY * NewObj->s.XY) +
                                      (NewObj->s.XZ * NewObj->s.XZ) );
            rot3->s.XX *= n;
            rot3->s.XY *= n;
            rot3->s.XZ *= n;

            n = 1.0f / FuncSqrt( (NewObj->s.YX * NewObj->s.YX) +
                                      (NewObj->s.YY * NewObj->s.YY) +
                                      (NewObj->s.YZ * NewObj->s.YZ) );
            rot3->s.YX *= n;
            rot3->s.YY *= n;
            rot3->s.YZ *= n;

            n = 1.0f / FuncSqrt( (NewObj->s.ZX * NewObj->s.ZX) +
                                      (NewObj->s.ZY * NewObj->s.ZY) +
                                      (NewObj->s.ZZ * NewObj->s.ZZ) );
            rot3->s.ZX *= n;
            rot3->s.ZY *= n;
            rot3->s.ZZ *= n;
        }

        if (rot4)   //if pointer not null
        {
            if (rot4 != NewObj)
            {
                Matrix4fSetRotationScaleFromMatrix4f(rot4, NewObj);  // private method
            }

            // zero-div may occur.

            n = 1.0f / FuncSqrt( (NewObj->s.XX * NewObj->s.XX) +
                                      (NewObj->s.XY * NewObj->s.XY) +
                                      (NewObj->s.XZ * NewObj->s.XZ) );
            rot4->s.XX *= n;
            rot4->s.XY *= n;
            rot4->s.XZ *= n;

            n = 1.0f / FuncSqrt( (NewObj->s.YX * NewObj->s.YX) +
                                      (NewObj->s.YY * NewObj->s.YY) +
                                      (NewObj->s.YZ * NewObj->s.YZ) );
            rot4->s.YX *= n;
            rot4->s.YY *= n;
            rot4->s.YZ *= n;

            n = 1.0f / FuncSqrt( (NewObj->s.ZX * NewObj->s.ZX) +
                                      (NewObj->s.ZY * NewObj->s.ZY) +
                                      (NewObj->s.ZZ * NewObj->s.ZZ) );
            rot4->s.ZX *= n;
            rot4->s.ZY *= n;
            rot4->s.ZZ *= n;
        }

        return s;
    }

    inline
    static void Matrix4fSetRotationScaleFromMatrix3f(Matrix4fT* NewObj, const Matrix3fT* m1)
    {
        assert(NewObj && m1);

        NewObj->s.XX = m1->s.XX; NewObj->s.YX = m1->s.YX; NewObj->s.ZX = m1->s.ZX;
        NewObj->s.XY = m1->s.XY; NewObj->s.YY = m1->s.YY; NewObj->s.ZY = m1->s.ZY;
        NewObj->s.XZ = m1->s.XZ; NewObj->s.YZ = m1->s.YZ; NewObj->s.ZZ = m1->s.ZZ;
    }

    inline
    static void Matrix4fMulRotationScale(Matrix4fT* NewObj, GLfloat scale)
    {
        assert(NewObj);

        NewObj->s.XX *= scale; NewObj->s.YX *= scale; NewObj->s.ZX *= scale;
        NewObj->s.XY *= scale; NewObj->s.YY *= scale; NewObj->s.ZY *= scale;
        NewObj->s.XZ *= scale; NewObj->s.YZ *= scale; NewObj->s.ZZ *= scale;
    }

    /**
      * Sets the rotational component (upper 3x3) of this matrix to the matrix
      * values in the T precision Matrix3d argument; the other elements of
      * this matrix are unchanged; a singular value decomposition is performed
      * on this object's upper 3x3 matrix to factor out the scale, then this
      * object's upper 3x3 matrix components are replaced by the passed rotation
      * components, and then the scale is reapplied to the rotational
      * components.
      * @param m1 T precision 3x3 matrix
      */
    inline
    static void Matrix4fSetRotationFromMatrix3f(Matrix4fT* NewObj, const Matrix3fT* m1)
    {
        GLfloat scale;

        assert(NewObj && m1);

        scale = Matrix4fSVD(NewObj, NULL, NULL);

        Matrix4fSetRotationScaleFromMatrix3f(NewObj, m1);
        Matrix4fMulRotationScale(NewObj, scale);
    }

// 8<--Snip here if you have your own math types/funcs-->8 

    typedef class ArcBall_t
    {
        protected:
            inline
            void _mapToSphere(const Point2fT* NewPt, Vector3fT* NewVec) const;

        public:
            //Create/Destroy
                    ArcBall_t(GLfloat NewWidth, GLfloat NewHeight);
                   ~ArcBall_t() { /* nothing to do */ };

            //Set new bounds
            inline
            void    setBounds(GLfloat NewWidth, GLfloat NewHeight)
            {
                //assert((NewWidth > 1.0f) && (NewHeight > 1.0f));

                //Set adjustment factor for width/height
                this->AdjustWidth  = 1.0f / ((NewWidth  - 1.0f) * 0.5f);
                this->AdjustHeight = 1.0f / ((NewHeight - 1.0f) * 0.5f);
            }

            //Mouse down
            void    click(const Point2fT* NewPt);

            //Mouse drag, calculate rotation
            void    drag(const Point2fT* NewPt, Quat4fT* NewRot);

        protected:
            Vector3fT   StVec;          //Saved click vector
            Vector3fT   EnVec;          //Saved drag vector
		public:
            GLfloat     AdjustWidth;    //Mouse bounds width
            GLfloat     AdjustHeight;   //Mouse bounds height

    } ArcBallT;

#endif