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+//----------------------------------------------------------------------------
+// Anti-Grain Geometry - Version 2.4
+// Copyright (C) 2002-2005 Maxim Shemanarev (http://www.antigrain.com)
+//
+// Permission to copy, use, modify, sell and distribute this software 
+// is granted provided this copyright notice appears in all copies. 
+// This software is provided "as is" without express or implied
+// warranty, and with no claim as to its suitability for any purpose.
+//
+//----------------------------------------------------------------------------
+// Contact: mcseem@antigrain.com
+//          mcseemagg@yahoo.com
+//          http://www.antigrain.com
+//----------------------------------------------------------------------------
+//
+// Perspective 2D transformations
+//
+//----------------------------------------------------------------------------
+#ifndef AGG_TRANS_PERSPECTIVE_INCLUDED
+#define AGG_TRANS_PERSPECTIVE_INCLUDED
+
+#include "agg_trans_affine.h"
+
+namespace agg
+{
+    //=======================================================trans_perspective
+    struct trans_perspective
+    {
+        double sx, shy, w0, shx, sy, w1, tx, ty, w2;
+
+        //------------------------------------------------------- Construction
+        // Identity matrix
+        trans_perspective() : 
+            sx (1), shy(0), w0(0), 
+            shx(0), sy (1), w1(0), 
+            tx (0), ty (0), w2(1) {}
+
+        // Custom matrix
+        trans_perspective(double v0, double v1, double v2, 
+                          double v3, double v4, double v5,
+                          double v6, double v7, double v8) :
+           sx (v0), shy(v1), w0(v2), 
+           shx(v3), sy (v4), w1(v5), 
+           tx (v6), ty (v7), w2(v8) {}
+
+        // Custom matrix from m[9]
+        explicit trans_perspective(const double* m) :
+           sx (m[0]), shy(m[1]), w0(m[2]), 
+           shx(m[3]), sy (m[4]), w1(m[5]), 
+           tx (m[6]), ty (m[7]), w2(m[8]) {}
+
+        // From affine
+        explicit trans_perspective(const trans_affine& a) : 
+           sx (a.sx ), shy(a.shy), w0(0), 
+           shx(a.shx), sy (a.sy ), w1(0), 
+           tx (a.tx ), ty (a.ty ), w2(1) {}
+
+        // Rectangle to quadrilateral
+        trans_perspective(double x1, double y1, double x2, double y2, 
+                          const double* quad);
+
+        // Quadrilateral to rectangle
+        trans_perspective(const double* quad, 
+                          double x1, double y1, double x2, double y2);
+
+        // Arbitrary quadrilateral transformations
+        trans_perspective(const double* src, const double* dst);
+
+        //-------------------------------------- Quadrilateral transformations
+        // The arguments are double[8] that are mapped to quadrilaterals:
+        // x1,y1, x2,y2, x3,y3, x4,y4
+        bool quad_to_quad(const double* qs, const double* qd);
+
+        bool rect_to_quad(double x1, double y1, 
+                          double x2, double y2,
+                          const double* q);
+
+        bool quad_to_rect(const double* q,
+                          double x1, double y1, 
+                          double x2, double y2);
+
+        // Map square (0,0,1,1) to the quadrilateral and vice versa
+        bool square_to_quad(const double* q);
+        bool quad_to_square(const double* q);
+
+
+        //--------------------------------------------------------- Operations
+        // Reset - load an identity matrix
+        const trans_perspective& reset();
+
+        // Invert matrix. Returns false in degenerate case
+        bool invert();
+
+        // Direct transformations operations
+        const trans_perspective& translate(double x, double y);
+        const trans_perspective& rotate(double a);
+        const trans_perspective& scale(double s);
+        const trans_perspective& scale(double x, double y);
+
+        // Multiply the matrix by another one
+        const trans_perspective& multiply(const trans_perspective& m);
+
+        // Multiply "m" by "this" and assign the result to "this"
+        const trans_perspective& premultiply(const trans_perspective& m);
+
+        // Multiply matrix to inverse of another one
+        const trans_perspective& multiply_inv(const trans_perspective& m);
+
+        // Multiply inverse of "m" by "this" and assign the result to "this"
+        const trans_perspective& premultiply_inv(const trans_perspective& m);
+
+        // Multiply the matrix by another one
+        const trans_perspective& multiply(const trans_affine& m);
+
+        // Multiply "m" by "this" and assign the result to "this"
+        const trans_perspective& premultiply(const trans_affine& m);
+
+        // Multiply the matrix by inverse of another one
+        const trans_perspective& multiply_inv(const trans_affine& m);
+
+        // Multiply inverse of "m" by "this" and assign the result to "this"
+        const trans_perspective& premultiply_inv(const trans_affine& m);
+
+        //--------------------------------------------------------- Load/Store
+        void store_to(double* m) const;
+        const trans_perspective& load_from(const double* m);
+
+        //---------------------------------------------------------- Operators
+        // Multiply the matrix by another one
+        const trans_perspective& operator *= (const trans_perspective& m)
+        {
+            return multiply(m);
+        }
+        const trans_perspective& operator *= (const trans_affine& m)
+        {
+            return multiply(m);
+        }
+
+        // Multiply the matrix by inverse of another one
+        const trans_perspective& operator /= (const trans_perspective& m)
+        {
+            return multiply_inv(m);
+        }
+        const trans_perspective& operator /= (const trans_affine& m)
+        {
+            return multiply_inv(m);
+        }
+
+        // Multiply the matrix by another one and return
+        // the result in a separete matrix.
+        trans_perspective operator * (const trans_perspective& m) const
+        {
+            return trans_perspective(*this).multiply(m);
+        }
+        trans_perspective operator * (const trans_affine& m) const
+        {
+            return trans_perspective(*this).multiply(m);
+        }
+
+        // Multiply the matrix by inverse of another one 
+        // and return the result in a separete matrix.
+        trans_perspective operator / (const trans_perspective& m) const
+        {
+            return trans_perspective(*this).multiply_inv(m);
+        }
+        trans_perspective operator / (const trans_affine& m) const
+        {
+            return trans_perspective(*this).multiply_inv(m);
+        }
+
+        // Calculate and return the inverse matrix
+        trans_perspective operator ~ () const
+        {
+            trans_perspective ret = *this;
+            ret.invert();
+            return ret;
+        }
+
+        // Equal operator with default epsilon
+        bool operator == (const trans_perspective& m) const
+        {
+            return is_equal(m, affine_epsilon);
+        }
+
+        // Not Equal operator with default epsilon
+        bool operator != (const trans_perspective& m) const
+        {
+            return !is_equal(m, affine_epsilon);
+        }
+
+        //---------------------------------------------------- Transformations
+        // Direct transformation of x and y
+        void transform(double* x, double* y) const;
+
+        // Direct transformation of x and y, affine part only
+        void transform_affine(double* x, double* y) const;
+
+        // Direct transformation of x and y, 2x2 matrix only, no translation
+        void transform_2x2(double* x, double* y) const;
+
+        // Inverse transformation of x and y. It works slow because
+        // it explicitly inverts the matrix on every call. For massive 
+        // operations it's better to invert() the matrix and then use 
+        // direct transformations. 
+        void inverse_transform(double* x, double* y) const;
+
+
+        //---------------------------------------------------------- Auxiliary
+        const trans_perspective& from_affine(const trans_affine& a);
+        double determinant() const;
+        double determinant_reciprocal() const;
+
+        bool is_valid(double epsilon = affine_epsilon) const;
+        bool is_identity(double epsilon = affine_epsilon) const;
+        bool is_equal(const trans_perspective& m, 
+                      double epsilon = affine_epsilon) const;
+
+        // Determine the major affine parameters. Use with caution 
+        // considering possible degenerate cases.
+        double scale() const;
+        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;
+
+
+
+        //--------------------------------------------------------------------
+        class iterator_x
+        {
+            double den;
+            double den_step;
+            double nom_x;
+            double nom_x_step;
+            double nom_y;
+            double nom_y_step;
+
+        public:
+            double x;
+            double y;
+
+            iterator_x() {}
+            iterator_x(double px, double py, double step, const trans_perspective& m) :
+                den(px * m.w0 + py * m.w1 + m.w2),
+                den_step(m.w0 * step),
+                nom_x(px * m.sx + py * m.shx + m.tx),
+                nom_x_step(step * m.sx),
+                nom_y(px * m.shy + py * m.sy + m.ty),
+                nom_y_step(step * m.shy),
+                x(nom_x / den),
+                y(nom_y / den)
+            {}
+
+            void operator ++ ()
+            {
+                den   += den_step;
+                nom_x += nom_x_step;
+                nom_y += nom_y_step;
+                double d = 1.0 / den;
+                x = nom_x * d;
+                y = nom_y * d;
+            }
+        };
+
+        //--------------------------------------------------------------------
+        iterator_x begin(double x, double y, double step) const
+        {
+            return iterator_x(x, y, step, *this);
+        }
+    };
+
+
+
+
+
+
+
+
+
+   
+
+
+
+
+    //------------------------------------------------------------------------
+    inline bool trans_perspective::square_to_quad(const double* q)
+    {
+        double dx = q[0] - q[2] + q[4] - q[6];
+        double dy = q[1] - q[3] + q[5] - q[7];
+        if(dx == 0.0 && dy == 0.0)
+        {   
+            // Affine case (parallelogram)
+            //---------------
+            sx  = q[2] - q[0];
+            shy = q[3] - q[1];
+            w0  = 0.0;
+            shx = q[4] - q[2];
+            sy  = q[5] - q[3];
+            w1  = 0.0;
+            tx  = q[0];
+            ty  = q[1];
+            w2  = 1.0;
+        }
+        else
+        {
+            double dx1 = q[2] - q[4];
+            double dy1 = q[3] - q[5];
+            double dx2 = q[6] - q[4];
+            double dy2 = q[7] - q[5];
+            double den = dx1 * dy2 - dx2 * dy1;
+            if(den == 0.0)
+            {
+                // Singular case
+                //---------------
+                sx = shy = w0 = shx = sy = w1 = tx = ty = w2 = 0.0;
+                return false;
+            }
+            // General case
+            //---------------
+            double u = (dx * dy2 - dy * dx2) / den;
+            double v = (dy * dx1 - dx * dy1) / den;
+            sx  = q[2] - q[0] + u * q[2];
+            shy = q[3] - q[1] + u * q[3];
+            w0  = u;
+            shx = q[6] - q[0] + v * q[6];
+            sy  = q[7] - q[1] + v * q[7];
+            w1  = v;
+            tx  = q[0];
+            ty  = q[1];
+            w2  = 1.0;
+        }
+        return true;
+    }
+
+    //------------------------------------------------------------------------
+    inline bool trans_perspective::invert()
+    {
+        double d0 = sy  * w2 - w1  * ty;
+        double d1 = w0  * ty - shy * w2;
+        double d2 = shy * w1 - w0  * sy;
+        double d  = sx  * d0 + shx * d1 + tx * d2;
+        if(d == 0.0) 
+        {
+            sx = shy = w0 = shx = sy = w1 = tx = ty = w2 = 0.0;
+            return false;
+        }
+        d = 1.0 / d;
+        trans_perspective a = *this;
+        sx  = d * d0;
+        shy = d * d1;
+        w0  = d * d2;
+        shx = d * (a.w1 *a.tx  - a.shx*a.w2);
+        sy  = d * (a.sx *a.w2  - a.w0 *a.tx);
+        w1  = d * (a.w0 *a.shx - a.sx *a.w1);
+        tx  = d * (a.shx*a.ty  - a.sy *a.tx);
+        ty  = d * (a.shy*a.tx  - a.sx *a.ty);
+        w2  = d * (a.sx *a.sy  - a.shy*a.shx);
+        return true;
+    }
+
+    //------------------------------------------------------------------------
+    inline bool trans_perspective::quad_to_square(const double* q)
+    {
+        if(!square_to_quad(q)) return false;
+        invert();
+        return true;
+    }
+
+    //------------------------------------------------------------------------
+    inline bool trans_perspective::quad_to_quad(const double* qs, 
+                                                const double* qd)
+    {
+        trans_perspective p;
+        if(!  quad_to_square(qs)) return false;
+        if(!p.square_to_quad(qd)) return false;
+        multiply(p);
+        return true;
+    }
+
+    //------------------------------------------------------------------------
+    inline bool trans_perspective::rect_to_quad(double x1, double y1, 
+                                                double x2, double y2,
+                                                const double* q)
+    {
+        double r[8];
+        r[0] = r[6] = x1;
+        r[2] = r[4] = x2;
+        r[1] = r[3] = y1;
+        r[5] = r[7] = y2;
+        return quad_to_quad(r, q);
+    }
+
+    //------------------------------------------------------------------------
+    inline bool trans_perspective::quad_to_rect(const double* q,
+                                                double x1, double y1, 
+                                                double x2, double y2)
+    {
+        double r[8];
+        r[0] = r[6] = x1;
+        r[2] = r[4] = x2;
+        r[1] = r[3] = y1;
+        r[5] = r[7] = y2;
+        return quad_to_quad(q, r);
+    }
+
+    //------------------------------------------------------------------------
+    inline trans_perspective::trans_perspective(double x1, double y1, 
+                                                double x2, double y2, 
+                                                const double* quad)
+    {
+        rect_to_quad(x1, y1, x2, y2, quad);
+    }
+
+    //------------------------------------------------------------------------
+    inline trans_perspective::trans_perspective(const double* quad, 
+                                                double x1, double y1, 
+                                                double x2, double y2)
+    {
+        quad_to_rect(quad, x1, y1, x2, y2);
+    }
+
+    //------------------------------------------------------------------------
+    inline trans_perspective::trans_perspective(const double* src, 
+                                                const double* dst) 
+    {
+        quad_to_quad(src, dst);
+    }
+
+    //------------------------------------------------------------------------
+    inline const trans_perspective& trans_perspective::reset()
+    {
+        sx  = 1; shy = 0; w0 = 0; 
+        shx = 0; sy  = 1; w1 = 0;
+        tx  = 0; ty  = 0; w2 = 1;
+        return *this;
+    }
+
+    //------------------------------------------------------------------------
+    inline const trans_perspective& 
+    trans_perspective::multiply(const trans_perspective& a)
+    {
+        trans_perspective b = *this;
+        sx  = a.sx *b.sx  + a.shx*b.shy + a.tx*b.w0;
+        shx = a.sx *b.shx + a.shx*b.sy  + a.tx*b.w1;
+        tx  = a.sx *b.tx  + a.shx*b.ty  + a.tx*b.w2;
+        shy = a.shy*b.sx  + a.sy *b.shy + a.ty*b.w0;
+        sy  = a.shy*b.shx + a.sy *b.sy  + a.ty*b.w1;
+        ty  = a.shy*b.tx  + a.sy *b.ty  + a.ty*b.w2;
+        w0  = a.w0 *b.sx  + a.w1 *b.shy + a.w2*b.w0;
+        w1  = a.w0 *b.shx + a.w1 *b.sy  + a.w2*b.w1;
+        w2  = a.w0 *b.tx  + a.w1 *b.ty  + a.w2*b.w2;
+        return *this;
+    }
+
+    //------------------------------------------------------------------------
+    inline const trans_perspective& 
+    trans_perspective::multiply(const trans_affine& a)
+    {
+        trans_perspective b = *this;
+        sx  = a.sx *b.sx  + a.shx*b.shy + a.tx*b.w0;
+        shx = a.sx *b.shx + a.shx*b.sy  + a.tx*b.w1;
+        tx  = a.sx *b.tx  + a.shx*b.ty  + a.tx*b.w2;
+        shy = a.shy*b.sx  + a.sy *b.shy + a.ty*b.w0;
+        sy  = a.shy*b.shx + a.sy *b.sy  + a.ty*b.w1;
+        ty  = a.shy*b.tx  + a.sy *b.ty  + a.ty*b.w2;
+        return *this;
+    }
+
+    //------------------------------------------------------------------------
+    inline const trans_perspective& 
+    trans_perspective::premultiply(const trans_perspective& b)
+    {
+        trans_perspective a = *this;
+        sx  = a.sx *b.sx  + a.shx*b.shy + a.tx*b.w0;
+        shx = a.sx *b.shx + a.shx*b.sy  + a.tx*b.w1;
+        tx  = a.sx *b.tx  + a.shx*b.ty  + a.tx*b.w2;
+        shy = a.shy*b.sx  + a.sy *b.shy + a.ty*b.w0;
+        sy  = a.shy*b.shx + a.sy *b.sy  + a.ty*b.w1;
+        ty  = a.shy*b.tx  + a.sy *b.ty  + a.ty*b.w2;
+        w0  = a.w0 *b.sx  + a.w1 *b.shy + a.w2*b.w0;
+        w1  = a.w0 *b.shx + a.w1 *b.sy  + a.w2*b.w1;
+        w2  = a.w0 *b.tx  + a.w1 *b.ty  + a.w2*b.w2;
+        return *this;
+    }
+
+    //------------------------------------------------------------------------
+    inline const trans_perspective& 
+    trans_perspective::premultiply(const trans_affine& b)
+    {
+        trans_perspective a = *this;
+        sx  = a.sx *b.sx  + a.shx*b.shy;
+        shx = a.sx *b.shx + a.shx*b.sy;
+        tx  = a.sx *b.tx  + a.shx*b.ty  + a.tx;
+        shy = a.shy*b.sx  + a.sy *b.shy;
+        sy  = a.shy*b.shx + a.sy *b.sy;
+        ty  = a.shy*b.tx  + a.sy *b.ty  + a.ty;
+        w0  = a.w0 *b.sx  + a.w1 *b.shy;
+        w1  = a.w0 *b.shx + a.w1 *b.sy;
+        w2  = a.w0 *b.tx  + a.w1 *b.ty  + a.w2;
+        return *this;
+    }
+
+    //------------------------------------------------------------------------
+    const trans_perspective& 
+    trans_perspective::multiply_inv(const trans_perspective& m)
+    {
+        trans_perspective t = m;
+        t.invert();
+        return multiply(t);
+    }
+
+    //------------------------------------------------------------------------
+    const trans_perspective&
+    trans_perspective::multiply_inv(const trans_affine& m)
+    {
+        trans_affine t = m;
+        t.invert();
+        return multiply(t);
+    }
+
+    //------------------------------------------------------------------------
+    const trans_perspective&
+    trans_perspective::premultiply_inv(const trans_perspective& m)
+    {
+        trans_perspective t = m;
+        t.invert();
+        return *this = t.multiply(*this);
+    }
+
+    //------------------------------------------------------------------------
+    const trans_perspective&
+    trans_perspective::premultiply_inv(const trans_affine& m)
+    {
+        trans_perspective t(m);
+        t.invert();
+        return *this = t.multiply(*this);
+    }
+
+    //------------------------------------------------------------------------
+    inline const trans_perspective& 
+    trans_perspective::translate(double x, double y)
+    {
+        tx += x;
+        ty += y;
+        return *this;
+    }
+
+    //------------------------------------------------------------------------
+    inline const trans_perspective& trans_perspective::rotate(double a)
+    {
+        multiply(trans_affine_rotation(a));
+        return *this;
+    }
+
+    //------------------------------------------------------------------------
+    inline const trans_perspective& trans_perspective::scale(double s)
+    {
+        multiply(trans_affine_scaling(s));
+        return *this;
+    }
+
+    //------------------------------------------------------------------------
+    inline const trans_perspective& trans_perspective::scale(double x, double y)
+    {
+        multiply(trans_affine_scaling(x, y));
+        return *this;
+    }
+
+    //------------------------------------------------------------------------
+    inline void trans_perspective::transform(double* px, double* py) const
+    {
+        double x = *px;
+        double y = *py;
+        double m = 1.0 / (x*w0 + y*w1 + w2);
+        *px = m * (x*sx  + y*shx + tx);
+        *py = m * (x*shy + y*sy  + ty);
+    }
+
+    //------------------------------------------------------------------------
+    inline void trans_perspective::transform_affine(double* x, double* y) const
+    {
+        double tmp = *x;
+        *x = tmp * sx  + *y * shx + tx;
+        *y = tmp * shy + *y * sy  + ty;
+    }
+
+    //------------------------------------------------------------------------
+    inline void trans_perspective::transform_2x2(double* x, double* y) const
+    {
+        double tmp = *x;
+        *x = tmp * sx  + *y * shx;
+        *y = tmp * shy + *y * sy;
+    }
+
+    //------------------------------------------------------------------------
+    inline void trans_perspective::inverse_transform(double* x, double* y) const
+    {
+        trans_perspective t(*this);
+        if(t.invert()) t.transform(x, y);
+    }
+
+    //------------------------------------------------------------------------
+    inline void trans_perspective::store_to(double* m) const
+    {
+        *m++ = sx;  *m++ = shy; *m++ = w0; 
+        *m++ = shx; *m++ = sy;  *m++ = w1;
+        *m++ = tx;  *m++ = ty;  *m++ = w2;
+    }
+
+    //------------------------------------------------------------------------
+    inline const trans_perspective& trans_perspective::load_from(const double* m)
+    {
+        sx  = *m++; shy = *m++; w0 = *m++; 
+        shx = *m++; sy  = *m++; w1 = *m++;
+        tx  = *m++; ty  = *m++; w2 = *m++;
+        return *this;
+    }
+
+    //------------------------------------------------------------------------
+    inline const trans_perspective& 
+    trans_perspective::from_affine(const trans_affine& a)
+    {
+        sx  = a.sx;  shy = a.shy; w0 = 0; 
+        shx = a.shx; sy  = a.sy;  w1 = 0;
+        tx  = a.tx;  ty  = a.ty;  w2 = 1;
+        return *this;
+    }
+
+    //------------------------------------------------------------------------
+    inline double trans_perspective::determinant() const
+    {
+        return sx  * (sy  * w2 - ty  * w1) +
+               shx * (ty  * w0 - shy * w2) +
+               tx  * (shy * w1 - sy  * w0);
+    }
+  
+    //------------------------------------------------------------------------
+    inline double trans_perspective::determinant_reciprocal() const
+    {
+        return 1.0 / determinant();
+    }
+
+    //------------------------------------------------------------------------
+    inline bool trans_perspective::is_valid(double epsilon) const
+    {
+        return fabs(sx) > epsilon && fabs(sy) > epsilon && fabs(w2) > epsilon;
+    }
+
+    //------------------------------------------------------------------------
+    inline bool trans_perspective::is_identity(double epsilon) const
+    {
+        return is_equal_eps(sx,  1.0, epsilon) &&
+               is_equal_eps(shy, 0.0, epsilon) &&
+               is_equal_eps(w0,  0.0, epsilon) &&
+               is_equal_eps(shx, 0.0, epsilon) && 
+               is_equal_eps(sy,  1.0, epsilon) &&
+               is_equal_eps(w1,  0.0, epsilon) &&
+               is_equal_eps(tx,  0.0, epsilon) &&
+               is_equal_eps(ty,  0.0, epsilon) &&
+               is_equal_eps(w2,  1.0, epsilon);
+    }
+
+    //------------------------------------------------------------------------
+    inline bool trans_perspective::is_equal(const trans_perspective& m, 
+                                            double epsilon) const
+    {
+        return is_equal_eps(sx,  m.sx,  epsilon) &&
+               is_equal_eps(shy, m.shy, epsilon) &&
+               is_equal_eps(w0,  m.w0,  epsilon) &&
+               is_equal_eps(shx, m.shx, epsilon) && 
+               is_equal_eps(sy,  m.sy,  epsilon) &&
+               is_equal_eps(w1,  m.w1,  epsilon) &&
+               is_equal_eps(tx,  m.tx,  epsilon) &&
+               is_equal_eps(ty,  m.ty,  epsilon) &&
+               is_equal_eps(w2,  m.w2,  epsilon);
+    }
+
+    //------------------------------------------------------------------------
+    inline double trans_perspective::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 double trans_perspective::rotation() const
+    {
+        double x1 = 0.0;
+        double y1 = 0.0;
+        double x2 = 1.0;
+        double y2 = 0.0;
+        transform(&x1, &y1);
+        transform(&x2, &y2);
+        return atan2(y2-y1, x2-x1);
+    }
+
+    //------------------------------------------------------------------------
+    void trans_perspective::translation(double* dx, double* dy) const
+    {
+        *dx = tx;
+        *dy = ty;
+    }
+
+    //------------------------------------------------------------------------
+    void trans_perspective::scaling(double* x, double* y) const
+    {
+        double x1 = 0.0;
+        double y1 = 0.0;
+        double x2 = 1.0;
+        double y2 = 1.0;
+        trans_perspective t(*this);
+        t *= trans_affine_rotation(-rotation());
+        t.transform(&x1, &y1);
+        t.transform(&x2, &y2);
+        *x = x2 - x1;
+        *y = y2 - y1;
+    }
+
+    //------------------------------------------------------------------------
+    void trans_perspective::scaling_abs(double* x, double* y) const
+    {
+        *x = sqrt(sx  * sx  + shx * shx);
+        *y = sqrt(shy * shy + sy  * sy);
+    }
+
+
+}
+
+#endif
+