agg_trans_bilinear.h

//----------------------------------------------------------------------------
// 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
//----------------------------------------------------------------------------
//
// Bilinear 2D transformations
//
//----------------------------------------------------------------------------
#ifndef AGG_TRANS_BILINEAR_INCLUDED
#define AGG_TRANS_BILINEAR_INCLUDED

#include "agg_basics.h"
#include "agg_simul_eq.h"

namespace agg
{

    //==========================================================trans_bilinear
    class trans_bilinear
    {
    public:
        //--------------------------------------------------------------------
        trans_bilinear() : m_valid(false) {}

        //--------------------------------------------------------------------
        // Arbitrary quadrangle transformations
        trans_bilinear(const double* src, const double* dst) 
        {
            quad_to_quad(src, dst);
        }


        //--------------------------------------------------------------------
        // Direct transformations 
        trans_bilinear(double x1, double y1, double x2, double y2, 
                       const double* quad)
        {
            rect_to_quad(x1, y1, x2, y2, quad);
        }


        //--------------------------------------------------------------------
        // Reverse transformations 
        trans_bilinear(const double* quad, 
                       double x1, double y1, double x2, double y2)
        {
            quad_to_rect(quad, x1, y1, x2, y2);
        }


        //--------------------------------------------------------------------
        // Set the transformations using two arbitrary quadrangles.
        void quad_to_quad(const double* src, const double* dst)
        {
            double left[4][4];
            double right[4][2];

            unsigned i;
            for(i = 0; i < 4; i++)
            {
                unsigned ix = i * 2;
                unsigned iy = ix + 1;
                left[i][0] = 1.0;
                left[i][1] = src[ix] * src[iy];
                left[i][2] = src[ix];
                left[i][3] = src[iy];

                right[i][0] = dst[ix];
                right[i][1] = dst[iy];
            }
            m_valid = simul_eq<4, 2>::solve(left, right, m_mtx);
        }


        //--------------------------------------------------------------------
        // Set the direct transformations, i.e., rectangle -> quadrangle
        void rect_to_quad(double x1, double y1, double x2, double y2, 
                          const double* quad)
        {
            double src[8];
            src[0] = src[6] = x1;
            src[2] = src[4] = x2;
            src[1] = src[3] = y1;
            src[5] = src[7] = y2;
            quad_to_quad(src, quad);
        }


        //--------------------------------------------------------------------
        // Set the reverse transformations, i.e., quadrangle -> rectangle
        void quad_to_rect(const double* quad, 
                          double x1, double y1, double x2, double y2)
        {
            double dst[8];
            dst[0] = dst[6] = x1;
            dst[2] = dst[4] = x2;
            dst[1] = dst[3] = y1;
            dst[5] = dst[7] = y2;
            quad_to_quad(quad, dst);
        }

        //--------------------------------------------------------------------
        // Check if the equations were solved successfully
        bool is_valid() const { return m_valid; }

        //--------------------------------------------------------------------
        // Transform a point (x, y)
        void transform(double* x, double* y) const
        {
            double tx = *x;
            double ty = *y;
            double xy = tx * ty;
            *x = m_mtx[0][0] + m_mtx[1][0] * xy + m_mtx[2][0] * tx + m_mtx[3][0] * ty;
            *y = m_mtx[0][1] + m_mtx[1][1] * xy + m_mtx[2][1] * tx + m_mtx[3][1] * ty;
        }


        //--------------------------------------------------------------------
        class iterator_x
        {
            double inc_x;
            double inc_y;

        public:
            double x;
            double y;

            iterator_x() {}
            iterator_x(double tx, double ty, double step, const double m[4][2]) :
                inc_x(m[1][0] * step * ty + m[2][0] * step),
                inc_y(m[1][1] * step * ty + m[2][1] * step),
                x(m[0][0] + m[1][0] * tx * ty + m[2][0] * tx + m[3][0] * ty),
                y(m[0][1] + m[1][1] * tx * ty + m[2][1] * tx + m[3][1] * ty)
            {
            }

            void operator ++ ()
            {
                x += inc_x;
                y += inc_y;
            }
        };

        iterator_x begin(double x, double y, double step) const
        {
            return iterator_x(x, y, step, m_mtx);
        }

    private:
        double m_mtx[4][2];
        bool   m_valid;
    };

}

#endif