agg_trans_affine.h

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        // Calculate the determinant of matrix
        double determinant() const
        {
            return sx * sy - shy * shx;
        }

        // Calculate the reciprocal of the determinant
        double determinant_reciprocal() const
        {
            return 1.0 / (sx * sy - shy * shx);
        }

        // Get the average scale (by X and Y). 
        // Basically used to calculate the approximation_scale when
        // decomposinting curves into line segments.
        double scale() const;

        // Check to see if the matrix is not degenerate
        bool is_valid(double epsilon = affine_epsilon) const;

        // Check to see if it's an identity matrix
        bool is_identity(double epsilon = affine_epsilon) const;

        // Check to see if two matrices are equal
        bool is_equal(const trans_affine& m, double epsilon = affine_epsilon) const;

        // Determine the major parameters. Use with caution considering 
        // possible degenerate cases.
        double rotation() const;
        void   translation(double* dx, double* dy) const;
        void   scaling(double* x, double* y) const;
        void   scaling_abs(double* x, double* y) const;
    };

    //------------------------------------------------------------------------
    inline void trans_affine::transform(double* x, double* y) const
    {
        register double tmp = *x;
        *x = tmp * sx  + *y * shx + tx;
        *y = tmp * shy + *y * sy  + ty;
    }

    //------------------------------------------------------------------------
    inline void trans_affine::transform_2x2(double* x, double* y) const
    {
        register double tmp = *x;
        *x = tmp * sx  + *y * shx;
        *y = tmp * shy + *y * sy;
    }

    //------------------------------------------------------------------------
    inline void trans_affine::inverse_transform(double* x, double* y) const
    {
        register double d = determinant_reciprocal();
        register double a = (*x - tx) * d;
        register double b = (*y - ty) * d;
        *x = a * sy - b * shx;
        *y = b * sx - a * shy;
    }

    //------------------------------------------------------------------------
    inline double trans_affine::scale() const
    {
        double x = 0.707106781 * sx  + 0.707106781 * shx;
        double y = 0.707106781 * shy + 0.707106781 * sy;
        return sqrt(x*x + y*y);
    }

    //------------------------------------------------------------------------
    inline const trans_affine& trans_affine::translate(double x, double y) 
    { 
        tx += x;
        ty += y; 
        return *this;
    }

    //------------------------------------------------------------------------
    inline const trans_affine& trans_affine::rotate(double a) 
    {
        double ca = cos(a); 
        double sa = sin(a);
        double t0 = sx  * ca - shy * sa;
        double t2 = shx * ca - sy * sa;
        double t4 = tx  * ca - ty * sa;
        shy = sx  * sa + shy * ca;
        sy  = shx * sa + sy * ca; 
        ty  = tx  * sa + ty * ca;
        sx  = t0;
        shx = t2;
        tx  = t4;
        return *this;
    }

    //------------------------------------------------------------------------
    inline const trans_affine& trans_affine::scale(double x, double y) 
    {
        double mm0 = x; // Possible hint for the optimizer
        double mm3 = y; 
        sx  *= mm0;
        shx *= mm0;
        tx  *= mm0;
        shy *= mm3;
        sy  *= mm3;
        ty  *= mm3;
        return *this;
    }

    //------------------------------------------------------------------------
    inline const trans_affine& trans_affine::scale(double s) 
    {
        double m = s; // Possible hint for the optimizer
        sx  *= m;
        shx *= m;
        tx  *= m;
        shy *= m;
        sy  *= m;
        ty  *= m;
        return *this;
    }

    //------------------------------------------------------------------------
    inline const trans_affine& trans_affine::premultiply(const trans_affine& m)
    {
        trans_affine t = m;
        return *this = t.multiply(*this);
    }

    //------------------------------------------------------------------------
    inline const trans_affine& trans_affine::multiply_inv(const trans_affine& m)
    {
        trans_affine t = m;
        t.invert();
        return multiply(t);
    }

    //------------------------------------------------------------------------
    inline const trans_affine& trans_affine::premultiply_inv(const trans_affine& m)
    {
        trans_affine t = m;
        t.invert();
        return *this = t.multiply(*this);
    }

    //------------------------------------------------------------------------
    inline void trans_affine::scaling_abs(double* x, double* y) const
    {
        // Used to calculate scaling coefficients in image resampling. 
        // When there is considerable shear this method gives us much
        // better estimation than just sx, sy.
        *x = sqrt(sx  * sx  + shx * shx);
        *y = sqrt(shy * shy + sy  * sy);
    }

    //====================================================trans_affine_rotation
    // Rotation matrix. sin() and cos() are calculated twice for the same angle.
    // There's no harm because the performance of sin()/cos() is very good on all
    // modern processors. Besides, this operation is not going to be invoked too 
    // often.
    class trans_affine_rotation : public trans_affine
    {
    public:
        trans_affine_rotation(double a) : 
          trans_affine(cos(a), sin(a), -sin(a), cos(a), 0.0, 0.0)
        {}
    };

    //====================================================trans_affine_scaling
    // Scaling matrix. x, y - scale coefficients by X and Y respectively
    class trans_affine_scaling : public trans_affine
    {
    public:
        trans_affine_scaling(double x, double y) : 
          trans_affine(x, 0.0, 0.0, y, 0.0, 0.0)
        {}

        trans_affine_scaling(double s) : 
          trans_affine(s, 0.0, 0.0, s, 0.0, 0.0)
        {}
    };

    //================================================trans_affine_translation
    // Translation matrix
    class trans_affine_translation : public trans_affine
    {
    public:
        trans_affine_translation(double x, double y) : 
          trans_affine(1.0, 0.0, 0.0, 1.0, x, y)
        {}
    };

    //====================================================trans_affine_skewing
    // Sckewing (shear) matrix
    class trans_affine_skewing : public trans_affine
    {
    public:
        trans_affine_skewing(double x, double y) : 
          trans_affine(1.0, tan(y), tan(x), 1.0, 0.0, 0.0)
        {}
    };


    //===============================================trans_affine_line_segment
    // Rotate, Scale and Translate, associating 0...dist with line segment 
    // x1,y1,x2,y2
    class trans_affine_line_segment : public trans_affine
    {
    public:
        trans_affine_line_segment(double x1, double y1, double x2, double y2, 
                                  double dist)
        {
            double dx = x2 - x1;
            double dy = y2 - y1;
            if(dist > 0.0)
            {
                multiply(trans_affine_scaling(sqrt(dx * dx + dy * dy) / dist));
            }
            multiply(trans_affine_rotation(atan2(dy, dx)));
            multiply(trans_affine_translation(x1, y1));
        }
    };


    //============================================trans_affine_reflection_unit
    // Reflection matrix. Reflect coordinates across the line through 
    // the origin containing the unit vector (ux, uy).
    // Contributed by John Horigan
    class trans_affine_reflection_unit : public trans_affine
    {
    public:
        trans_affine_reflection_unit(double ux, double uy) :
          trans_affine(2.0 * ux * ux - 1.0, 
                       2.0 * ux * uy, 
                       2.0 * ux * uy, 
                       2.0 * uy * uy - 1.0, 
                       0.0, 0.0)
        {}
    };


    //=================================================trans_affine_reflection
    // Reflection matrix. Reflect coordinates across the line through 
    // the origin at the angle a or containing the non-unit vector (x, y).
    // Contributed by John Horigan
    class trans_affine_reflection : public trans_affine_reflection_unit
    {
    public:
        trans_affine_reflection(double a) :
          trans_affine_reflection_unit(cos(a), sin(a))
        {}


        trans_affine_reflection(double x, double y) :
          trans_affine_reflection_unit(x / sqrt(x * x + y * y), y / sqrt(x * x + y * y))
        {}
    };

}


#endif