genv.cpp

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// $Id: genv.cpp 751 2006-03-31 15:43:49Z alex $
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----------------------------------

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 */
// Envelope shape implementation

/*
$Log: /wxCamelot/Kernel/genv.cpp $
 * 
 * 3     20/07/05 15:39 Luke
 * Intermediate
 * 
 * 2     29/01/97 20:41 Mike
 * New files to hold the envelope class out of moldenv.h / .cpp.
 * 
 * 1     23/01/97 15:56 Mike
 * GEnvelope code taken out of moldenv.cpp

*/

#include "camtypes.h"

#include <math.h>
#include "moldshap.h"
#include "gmould.h"
#include "genv.h"

DECLARE_SOURCE("$Revision: 751 $");

CC_IMPLEMENT_DYNAMIC(GEnvelope, GMould)
CC_IMPLEMENT_DYNAMIC(GEnvelope2x2, GMould)

// Declare smart memory handling in Debug builds
#define new CAM_DEBUG_NEW

//
// GEnvelop.cpp
//

GEnvelope::GEnvelope()
{
    SrcBBox.left   = 0;
    SrcBBox.top    = 3;
    SrcBBox.right  = 3;
    SrcBBox.bottom = 0;

    L0.x = 0 ; L0.y = 0 ;
    L1.x = 0 ; L1.y = 1 ;
    L2.x = 0 ; L2.y = 2 ;
    T0.x = 0 ; T0.y = 3 ;
    T1.x = 1 ; T1.y = 3 ;
    T2.x = 2 ; T2.y = 3 ;
    R0.x = 3 ; R0.y = 3 ;
    R1.x = 3 ; R1.y = 2 ;
    R2.x = 3 ; R2.y = 1 ;
    B0.x = 3 ; B0.y = 0 ;
    B1.x = 2 ; B1.y = 0 ;
    B2.x = 1 ; B2.y = 0 ;

    MinX = 0; MinY = 0;
    MaxX = 3; MaxY = 3;
    Width = 3; Depth = 3;

    ScaleView();
    CalcViewConsts();
}
    

BOOL GEnvelope::Redefine( POINT *P )
{
    L0.x = P[ 0].x ; L0.y = P[ 0].y ;
    L1.x = P[ 1].x ; L1.y = P[ 1].y ;
    L2.x = P[ 2].x ; L2.y = P[ 2].y ;
    T0.x = P[ 3].x ; T0.y = P[ 3].y ;
    T1.x = P[ 4].x ; T1.y = P[ 4].y ;
    T2.x = P[ 5].x ; T2.y = P[ 5].y ;
    R0.x = P[ 6].x ; R0.y = P[ 6].y ;
    R1.x = P[ 7].x ; R1.y = P[ 7].y ;
    R2.x = P[ 8].x ; R2.y = P[ 8].y ;
    B0.x = P[ 9].x ; B0.y = P[ 9].y ;
    B1.x = P[10].x ; B1.y = P[10].y ;
    B2.x = P[11].x ; B2.y = P[11].y ;

    CalcViewBBox();
    if (Width==0 || Depth==0) 
        return FALSE;

    ScaleView();
    CalcViewConsts();

    return TRUE;
}


void GEnvelope::CalcViewBBox()
{
    MinX = MaxX = L0.x ;
    MinY = MaxY = L0.y ;
    MinX=min(MinX, INT32(L1.x)) ; MaxX=max(MaxX, INT32(L1.x)) ; MinY=min(MinY, INT32(L1.y)) ; MaxY=max(MaxY, INT32(L1.y)) ;
    MinX=min(MinX, INT32(L2.x)) ; MaxX=max(MaxX, INT32(L2.x)) ; MinY=min(MinY, INT32(L2.y)) ; MaxY=max(MaxY, INT32(L2.y)) ;
    MinX=min(MinX, INT32(T0.x)) ; MaxX=max(MaxX, INT32(T0.x)) ; MinY=min(MinY, INT32(T0.y)) ; MaxY=max(MaxY, INT32(T0.y)) ;
    MinX=min(MinX, INT32(T1.x)) ; MaxX=max(MaxX, INT32(T1.x)) ; MinY=min(MinY, INT32(T1.y)) ; MaxY=max(MaxY, INT32(T1.y)) ;
    MinX=min(MinX, INT32(T2.x)) ; MaxX=max(MaxX, INT32(T2.x)) ; MinY=min(MinY, INT32(T2.y)) ; MaxY=max(MaxY, INT32(T2.y)) ;
    MinX=min(MinX, INT32(R0.x)) ; MaxX=max(MaxX, INT32(R0.x)) ; MinY=min(MinY, INT32(R0.y)) ; MaxY=max(MaxY, INT32(R0.y)) ;
    MinX=min(MinX, INT32(R1.x)) ; MaxX=max(MaxX, INT32(R1.x)) ; MinY=min(MinY, INT32(R1.y)) ; MaxY=max(MaxY, INT32(R1.y)) ;
    MinX=min(MinX, INT32(R2.x)) ; MaxX=max(MaxX, INT32(R2.x)) ; MinY=min(MinY, INT32(R2.y)) ; MaxY=max(MaxY, INT32(R2.y)) ;
    MinX=min(MinX, INT32(B0.x)) ; MaxX=max(MaxX, INT32(B0.x)) ; MinY=min(MinY, INT32(B0.y)) ; MaxY=max(MaxY, INT32(B0.y)) ;
    MinX=min(MinX, INT32(B1.x)) ; MaxX=max(MaxX, INT32(B1.x)) ; MinY=min(MinY, INT32(B1.y)) ; MaxY=max(MaxY, INT32(B1.y)) ;
    MinX=min(MinX, INT32(B2.x)) ; MaxX=max(MaxX, INT32(B2.x)) ; MinY=min(MinY, INT32(B2.y)) ; MaxY=max(MaxY, INT32(B2.y)) ;
    Width = MaxX-MinX ;
    Depth = MaxY-MinY ;
}


void GEnvelope::CopyShape(POINT* P)
{
    P[ 0].x = L0.x ; P[ 0].y = L0.y ; 
    P[ 1].x = L1.x ; P[ 1].y = L1.y ;
    P[ 2].x = L2.x ; P[ 2].y = L2.y ;
    P[ 3].x = T0.x ; P[ 3].y = T0.y ;
    P[ 4].x = T1.x ; P[ 4].y = T1.y ;
    P[ 5].x = T2.x ; P[ 5].y = T2.y ;
    P[ 6].x = R0.x ; P[ 6].y = R0.y ;
    P[ 7].x = R1.x ; P[ 7].y = R1.y ;
    P[ 8].x = R2.x ; P[ 8].y = R2.y ;
    P[ 9].x = B0.x ; P[ 9].y = B0.y ;
    P[10].x = B1.x ; P[10].y = B1.y ;
    P[11].x = B2.x ; P[11].y = B2.y ;
}
    

void GEnvelope::ScaleView()
{
    VL0.x = (double)(L0.x-MinX)/Width ; VL0.y = (double)(L0.y-MinY)/Depth ;
    VL1.x = (double)(L1.x-MinX)/Width ; VL1.y = (double)(L1.y-MinY)/Depth ;
    VL2.x = (double)(L2.x-MinX)/Width ; VL2.y = (double)(L2.y-MinY)/Depth ;
    VT0.x = (double)(T0.x-MinX)/Width ; VT0.y = (double)(T0.y-MinY)/Depth ;
    VT1.x = (double)(T1.x-MinX)/Width ; VT1.y = (double)(T1.y-MinY)/Depth ;
    VT2.x = (double)(T2.x-MinX)/Width ; VT2.y = (double)(T2.y-MinY)/Depth ;
    VR0.x = (double)(R0.x-MinX)/Width ; VR0.y = (double)(R0.y-MinY)/Depth ;
    VR1.x = (double)(R1.x-MinX)/Width ; VR1.y = (double)(R1.y-MinY)/Depth ;
    VR2.x = (double)(R2.x-MinX)/Width ; VR2.y = (double)(R2.y-MinY)/Depth ;
    VB0.x = (double)(B0.x-MinX)/Width ; VB0.y = (double)(B0.y-MinY)/Depth ;
    VB1.x = (double)(B1.x-MinX)/Width ; VB1.y = (double)(B1.y-MinY)/Depth ;
    VB2.x = (double)(B2.x-MinX)/Width ; VB2.y = (double)(B2.y-MinY)/Depth ;
}

void GEnvelope::CalcViewConsts()
{
    A.x = VL0.x ;
    A.y = VL0.y ;
    B.x = 3*(VB2.x-VL0.x) ;
    B.y = 3*(VB2.y-VL0.y) ;
    C.x = 3*(VL1.x-VL0.x) ;
    C.y = 3*(VL1.y-VL0.y) ;
    D.x = 3*(VT1.x+VR2.x)-2*(VT0.x+VB0.x)-VL0.x-VR0.x-B.x-C.x ;
    D.y = 3*(VT1.y+VR2.y)-2*(VT0.y+VB0.y)-VL0.y-VR0.y-B.y-C.y ;
    E.x = 3*(VL0.x-2*VB2.x+VB1.x) ;
    E.y = 3*(VL0.y-2*VB2.y+VB1.y) ;
    F.x = 3*(VL2.x-2*VL1.x+VL0.x) ;
    F.y = 3*(VL2.y-2*VL1.y+VL0.y) ;
    G.x = 3*(VT2.x-2*VT1.x+VT0.x)-E.x ;
    G.y = 3*(VT2.y-2*VT1.y+VT0.y)-E.y ;
    H.x = 3*(VB0.x-2*VR2.x+VR1.x)-F.x ;
    H.y = 3*(VB0.y-2*VR2.y+VR1.y)-F.y ;
    J.x = VB0.x-3*(VB1.x-VB2.x)-VL0.x ;
    J.y = VB0.y-3*(VB1.y-VB2.y)-VL0.y ;
    K.x = VT0.x-3*(VL2.x-VL1.x)-VL0.x ;
    K.y = VT0.y-3*(VL2.y-VL1.y)-VL0.y ;
    L.x = VR0.x-3*(VT2.x-VT1.x)-VT0.x-J.x ;
    L.y = VR0.y-3*(VT2.y-VT1.y)-VT0.y-J.y ;
    M.x = VR0.x-3*(VR1.x-VR2.x)-VB0.x-K.x ;
    M.y = VR0.y-3*(VR1.y-VR2.y)-VB0.y-K.y ;
}



BOOL GEnvelope::FitPath (
                        CONST POINT* IPoints,
                        CONST BYTE*  ITypes,
                        DWORD ILength,
                        LPPOINT pOPoints,
                        LPBYTE  pOTypes,
                        DWORD pOLength,
                        BOOL Close
                    )
{
    OPoints = pOPoints ;
    OTypes  = pOTypes  ;
    OLength = pOLength ;

    DPOINT     C2, C4 ;
    DPOINT P0, P2, P4, P6, SP ;
    DPOINT T0, T2, T4, T6, ST ;
    ST.x = ST.y = SP.x = SP.y =0;
    while ( ILength )
    {
        switch ( *ITypes & PT_MOVETO )
        {
        case PT_MOVETO :
            --ILength ;
            ScaleSrc ( *IPoints++, P0 ) ; SP.x = P0.x ; SP.y = P0.y ;
            Transform( P0, T0 ) ;         ST.x = T0.x ; ST.y = T0.y ;
            if ( !GenOp( *ITypes++, T0 ) ) return -1 ;
            break ;
        case PT_LINETO :
            --ILength ; ++ITypes ;
            ScaleSrc( *IPoints++, P6 ) ;
            P2.x = (2*P0.x+P6.x)/3 ;
            P2.y = (2*P0.y+P6.y)/3 ;
            P4.x = (P0.x+2*P6.x)/3 ;
            P4.y = (P0.y+2*P6.y)/3 ;
            Transform( P2, T2 ) ;
            Transform( P4, T4 ) ;
            Transform( P6, T6 ) ;
            if ( !GenCurve( P2, P4, P0, P2, P4, P6, T0, T2, T4, T6 ) ) return -1 ;
            P0.x = P6.x ; P0.y = P6.y ;
            T0.x = T6.x ; T0.y = T6.y ;
            break ;
        case PT_BEZIERTO :
            ILength -= 3 ; ITypes += 3 ;
            ScaleSrc( *IPoints++, C2 ) ;
            ScaleSrc( *IPoints++, C4 ) ;
            ScaleSrc( *IPoints++, P6 ) ;
            P2.x = (8*P0.x+12*C2.x+ 6*C4.x+  P6.x)/27 ;
            P2.y = (8*P0.y+12*C2.y+ 6*C4.y+  P6.y)/27 ;
            P4.x = (  P0.x+ 6*C2.x+12*C4.x+8*P6.x)/27 ;
            P4.y = (  P0.y+ 6*C2.y+12*C4.y+8*P6.y)/27 ;
            Transform( P2, T2 ) ;
            Transform( P4, T4 ) ;
            Transform( P6, T6 ) ;
            if ( !GenCurve( C2, C4, P0, P2, P4, P6, T0, T2, T4, T6 ) ) return -1 ;
            P0.x = P6.x ; P0.y = P6.y ;
            T0.x = T6.x ; T0.y = T6.y ;
            break ;
        default :
            return -1 ;
        }

        if ( *(ITypes-1) & PT_CLOSEFIGURE ||
                            ( Close && ( ILength==0 || (*ITypes & PT_MOVETO) == PT_MOVETO ) ) )
        {
            P2.x = (2*P0.x+SP.x)/3 ;
            P2.y = (2*P0.y+SP.y)/3 ;
            P4.x = (P0.x+2*SP.x)/3 ;
            P4.y = (P0.y+2*SP.y)/3 ;
            Transform( P2, T2 ) ;
            Transform( P4, T4 ) ;
            if ( !GenCurve( P2, P4, P0, P2, P4, SP, T0, T2, T4, ST ) ) return -1 ;
            *(OTypes-1) |= *(ITypes-1) & PT_CLOSEFIGURE ;
        }
    }

    if ( ILength )
        return -1 ;

    return pOLength-OLength ;
}


void GEnvelope::Transform( DPOINT a, DPOINT& b )
{
    b.x = A.x+a.x*(B.x+a.x*(E.x+a.x*J.x))
             +a.y*(C.x+a.y*(F.x+a.y*K.x)
             +a.x*(D.x+a.x*(G.x+a.x*L.x)
                      +a.y*(H.x+a.y*M.x))) ;
    b.y = A.y+a.x*(B.y+a.x*(E.y+a.x*J.y))
             +a.y*(C.y+a.y*(F.y+a.y*K.y)
             +a.x*(D.y+a.x*(G.y+a.x*L.y)
                      +a.y*(H.y+a.y*M.y))) ;
}




//
//  T0 T1 T2 T3 T4 T5 R0
//  L5       V5       R1
//  L4  (10) V4 (11)  R2
//  L3 H1 H2 MM H4 H5 R3
//  L2  (00) V3 (01)  R4
//  L1       V4       R5
//  L0 B5 B4 B3 B2 B1 B0
//


GEnvelope2x2::GEnvelope2x2()
{
    L0.x = 0 ; L0.y = 0 ;
    L1.x = 0 ; L1.y = 1 ;
    L2.x = 0 ; L2.y = 2 ;
    L3.x = 0 ; L3.y = 3 ;
    L4.x = 0 ; L4.y = 4 ;
    L5.x = 0 ; L5.y = 5 ;

    T0.x = 0 ; T0.y = 6 ;
    T1.x = 1 ; T1.y = 6 ;
    T2.x = 2 ; T2.y = 6 ;
    T3.x = 3 ; T3.y = 6 ;
    T4.x = 4 ; T4.y = 6 ;
    T5.x = 5 ; T5.y = 6 ;

    R0.x = 6 ; R0.y = 6 ;
    R1.x = 6 ; R1.y = 5 ;
    R2.x = 6 ; R2.y = 4 ;
    R3.x = 6 ; R3.y = 3 ;
    R4.x = 6 ; R4.y = 2 ;
    R5.x = 6 ; R5.y = 1 ;

    B0.x = 6 ; B0.y = 0 ;
    B1.x = 5 ; B1.y = 0 ;
    B2.x = 4 ; B2.y = 0 ;
    B3.x = 3 ; B3.y = 0 ;
    B4.x = 2 ; B4.y = 0 ;
    B5.x = 1 ; B5.y = 0 ;

    CalcConsts();
}


BOOL GEnvelope2x2::Redefine( POINT *P )
{
    L0.x = P[ 0].x ; L0.y = P[ 0].y ;
    L1.x = P[ 1].x ; L1.y = P[ 1].y ;
    L2.x = P[ 2].x ; L2.y = P[ 2].y ;
    L3.x = P[ 3].x ; L3.y = P[ 3].y ;
    L4.x = P[ 4].x ; L4.y = P[ 4].y ;
    L5.x = P[ 5].x ; L5.y = P[ 5].y ;
    T0.x = P[ 6].x ; T0.y = P[ 6].y ;
    T1.x = P[ 7].x ; T1.y = P[ 7].y ;
    T2.x = P[ 8].x ; T2.y = P[ 8].y ;
    T3.x = P[ 9].x ; T3.y = P[ 9].y ;
    T4.x = P[10].x ; T4.y = P[10].y ;
    T5.x = P[11].x ; T5.y = P[11].y ;
    R0.x = P[12].x ; R0.y = P[12].y ;
    R1.x = P[13].x ; R1.y = P[13].y ;
    R2.x = P[14].x ; R2.y = P[14].y ;
    R3.x = P[15].x ; R3.y = P[15].y ;
    R4.x = P[16].x ; R4.y = P[16].y ;
    R5.x = P[17].x ; R5.y = P[17].y ;
    B0.x = P[18].x ; B0.y = P[18].y ;
    B1.x = P[19].x ; B1.y = P[19].y ;
    B2.x = P[20].x ; B2.y = P[20].y ;
    B3.x = P[21].x ; B3.y = P[21].y ;
    B4.x = P[22].x ; B4.y = P[22].y ;
    B5.x = P[23].x ; B5.y = P[23].y ;

    return CalcConsts();
}


BOOL GEnvelope2x2::CalcConsts()
{
    MM.x = (-  B0.x +  2*B3.x -   L0.x +  2*L3.x -   R0.x +  2*R3.x -   T0.x +  2*T3.x)/ 4 ;
    MM.y = (-  B0.y +  2*B3.y -   L0.y +  2*L3.y -   R0.y +  2*R3.y -   T0.y +  2*T3.y)/ 4 ;
    H1.x = (-  B0.x +  6*B5.x - 5*L0.x + 10*L3.x -   R0.x +  2*R3.x - 5*T0.x +  6*T1.x)/12 ;
    H1.y = (-  B0.y +  6*B5.y - 5*L0.y + 10*L3.y -   R0.y +  2*R3.y - 5*T0.y +  6*T1.y)/12 ;
    H2.x = (-  B0.x +  3*B4.x - 2*L0.x +  4*L3.x -   R0.x +  2*R3.x - 2*T0.x +  3*T2.x)/ 6 ;
    H2.y = (-  B0.y +  3*B4.y - 2*L0.y +  4*L3.y -   R0.y +  2*R3.y - 2*T0.y +  3*T2.y)/ 6 ;
    H4.x = (-2*B0.x +  3*B2.x -   L0.x +  2*L3.x - 2*R0.x +  4*R3.x -   T0.x +  3*T4.x)/ 6 ;
    H4.y = (-2*B0.y +  3*B2.y -   L0.y +  2*L3.y - 2*R0.y +  4*R3.y -   T0.y +  3*T4.y)/ 6 ;
    H5.x = (-5*B0.x +  6*B1.x -   L0.x +  2*L3.x - 5*R0.x + 10*R3.x -   T0.x +  6*T5.x)/12 ;
    H5.y = (-5*B0.y +  6*B1.y -   L0.y +  2*L3.y - 5*R0.y + 10*R3.y -   T0.y +  6*T5.y)/12 ;
    V1.x = (-5*B0.x + 10*B3.x - 5*L0.x +  6*L1.x -   R0.x +  6*R5.x -   T0.x +  2*T3.x)/12 ;
    V1.y = (-5*B0.y + 10*B3.y - 5*L0.y +  6*L1.y -   R0.y +  6*R5.y -   T0.y +  2*T3.y)/12 ;
    V2.x = (-2*B0.x +  4*B3.x - 2*L0.x +  3*L2.x -   R0.x +  3*R4.x -   T0.x +  2*T3.x)/ 6 ;
    V2.y = (-2*B0.y +  4*B3.y - 2*L0.y +  3*L2.y -   R0.y +  3*R4.y -   T0.y +  2*T3.y)/ 6 ;
    V4.x = (-  B0.x +  2*B3.x -   L0.x +  3*L4.x - 2*R0.x +  3*R2.x - 2*T0.x +  4*T3.x)/ 6 ;
    V4.y = (-  B0.y +  2*B3.y -   L0.y +  3*L4.y - 2*R0.y +  3*R2.y - 2*T0.y +  4*T3.y)/ 6 ;
    V5.x = (-  B0.x +  2*B3.x -   L0.x +  6*L5.x - 5*R0.x +  6*R1.x - 5*T0.x + 10*T3.x)/12 ;
    V5.y = (-  B0.y +  2*B3.y -   L0.y +  6*L5.y - 5*R0.y +  6*R1.y - 5*T0.y + 10*T3.y)/12 ;
    SmoothX = T4.x-T3.x == T3.x-T2.x && T4.y-T3.y == T3.y-T2.y &&
              B4.x-B3.x == B3.x-B2.x && B4.y-B3.y == B3.y-B2.y ;
    SmoothY = L4.x-L3.x == L3.x-L2.x && L4.y-L3.y == L3.y-L2.y &&
              R4.x-R3.x == R3.x-R2.x && R4.y-R3.y == R3.y-R2.y ;

    CalcViewBBox() ;
    if (Width==0 || Depth==0)
        return FALSE;
    
    ScaleView() ;
    CalcViewConsts() ;

    return TRUE;
}



void GEnvelope2x2::CopyShape(POINT* P)
{
    P[ 0].x = L0.x ; P[ 0].y = L0.y ; 
    P[ 1].x = L1.x ; P[ 1].y = L1.y ;
    P[ 2].x = L2.x ; P[ 2].y = L2.y ;
    P[ 3].x = L3.x ; P[ 3].y = L3.y ; 
    P[ 4].x = L4.x ; P[ 4].y = L4.y ;
    P[ 5].x = L5.x ; P[ 5].y = L5.y ;
    P[ 6].x = T0.x ; P[ 6].y = T0.y ; 
    P[ 7].x = T1.x ; P[ 7].y = T1.y ;
    P[ 8].x = T2.x ; P[ 8].y = T2.y ;
    P[ 9].x = T3.x ; P[ 9].y = T3.y ; 
    P[10].x = T4.x ; P[10].y = T4.y ;
    P[11].x = T5.x ; P[11].y = T5.y ;
    P[12].x = R0.x ; P[12].y = R0.y ; 
    P[13].x = R1.x ; P[13].y = R1.y ;
    P[14].x = R2.x ; P[14].y = R2.y ;
    P[15].x = R3.x ; P[15].y = R3.y ; 
    P[16].x = R4.x ; P[16].y = R4.y ;
    P[17].x = R5.x ; P[17].y = R5.y ;
    P[18].x = B0.x ; P[18].y = B0.y ; 
    P[19].x = B1.x ; P[19].y = B1.y ;
    P[20].x = B2.x ; P[20].y = B2.y ;
    P[21].x = B3.x ; P[21].y = B3.y ; 
    P[22].x = B4.x ; P[22].y = B4.y ;
    P[23].x = B5.x ; P[23].y = B5.y ;
}



void GEnvelope2x2::CalcViewBBox()
{
    MinX = MaxX = L0.x ;
    MinY = MaxY = L0.y ;
    MinX=min(MinX, INT32(L1.x)) ; MaxX=max(MaxX, INT32(L1.x)) ; MinY=min(MinY, INT32(L1.y)) ; MaxY=max(MaxY, INT32(L1.y)) ;
    MinX=min(MinX, INT32(L2.x)) ; MaxX=max(MaxX, INT32(L2.x)) ; MinY=min(MinY, INT32(L2.y)) ; MaxY=max(MaxY, INT32(L2.y)) ;
    MinX=min(MinX, INT32(L3.x)) ; MaxX=max(MaxX, INT32(L3.x)) ; MinY=min(MinY, INT32(L3.y)) ; MaxY=max(MaxY, INT32(L3.y)) ;
    MinX=min(MinX, INT32(L4.x)) ; MaxX=max(MaxX, INT32(L4.x)) ; MinY=min(MinY, INT32(L4.y)) ; MaxY=max(MaxY, INT32(L4.y)) ;
    MinX=min(MinX, INT32(L5.x)) ; MaxX=max(MaxX, INT32(L5.x)) ; MinY=min(MinY, INT32(L5.y)) ; MaxY=max(MaxY, INT32(L5.y)) ;
    MinX=min(MinX, INT32(T0.x)) ; MaxX=max(MaxX, INT32(T0.x)) ; MinY=min(MinY, INT32(T0.y)) ; MaxY=max(MaxY, INT32(T0.y)) ;
    MinX=min(MinX, INT32(T1.x)) ; MaxX=max(MaxX, INT32(T1.x)) ; MinY=min(MinY, INT32(T1.y)) ; MaxY=max(MaxY, INT32(T1.y)) ;
    MinX=min(MinX, INT32(T2.x)) ; MaxX=max(MaxX, INT32(T2.x)) ; MinY=min(MinY, INT32(T2.y)) ; MaxY=max(MaxY, INT32(T2.y)) ;
    MinX=min(MinX, INT32(T3.x)) ; MaxX=max(MaxX, INT32(T3.x)) ; MinY=min(MinY, INT32(T3.y)) ; MaxY=max(MaxY, INT32(T3.y)) ;
    MinX=min(MinX, INT32(T4.x)) ; MaxX=max(MaxX, INT32(T4.x)) ; MinY=min(MinY, INT32(T4.y)) ; MaxY=max(MaxY, INT32(T4.y)) ;
    MinX=min(MinX, INT32(T5.x)) ; MaxX=max(MaxX, INT32(T5.x)) ; MinY=min(MinY, INT32(T5.y)) ; MaxY=max(MaxY, INT32(T5.y)) ;
    MinX=min(MinX, INT32(R0.x)) ; MaxX=max(MaxX, INT32(R0.x)) ; MinY=min(MinY, INT32(R0.y)) ; MaxY=max(MaxY, INT32(R0.y)) ;
    MinX=min(MinX, INT32(R1.x)) ; MaxX=max(MaxX, INT32(R1.x)) ; MinY=min(MinY, INT32(R1.y)) ; MaxY=max(MaxY, INT32(R1.y)) ;
    MinX=min(MinX, INT32(R2.x)) ; MaxX=max(MaxX, INT32(R2.x)) ; MinY=min(MinY, INT32(R2.y)) ; MaxY=max(MaxY, INT32(R2.y)) ;
    MinX=min(MinX, INT32(R3.x)) ; MaxX=max(MaxX, INT32(R3.x)) ; MinY=min(MinY, INT32(R3.y)) ; MaxY=max(MaxY, INT32(R3.y)) ;
    MinX=min(MinX, INT32(R4.x)) ; MaxX=max(MaxX, INT32(R4.x)) ; MinY=min(MinY, INT32(R4.y)) ; MaxY=max(MaxY, INT32(R4.y)) ;
    MinX=min(MinX, INT32(R5.x)) ; MaxX=max(MaxX, INT32(R5.x)) ; MinY=min(MinY, INT32(R5.y)) ; MaxY=max(MaxY, INT32(R5.y)) ;
    MinX=min(MinX, INT32(B0.x)) ; MaxX=max(MaxX, INT32(B0.x)) ; MinY=min(MinY, INT32(B0.y)) ; MaxY=max(MaxY, INT32(B0.y)) ;
    MinX=min(MinX, INT32(B1.x)) ; MaxX=max(MaxX, INT32(B1.x)) ; MinY=min(MinY, INT32(B1.y)) ; MaxY=max(MaxY, INT32(B1.y)) ;
    MinX=min(MinX, INT32(B2.x)) ; MaxX=max(MaxX, INT32(B2.x)) ; MinY=min(MinY, INT32(B2.y)) ; MaxY=max(MaxY, INT32(B2.y)) ;
    MinX=min(MinX, INT32(B3.x)) ; MaxX=max(MaxX, INT32(B3.x)) ; MinY=min(MinY, INT32(B3.y)) ; MaxY=max(MaxY, INT32(B3.y)) ;
    MinX=min(MinX, INT32(B4.x)) ; MaxX=max(MaxX, INT32(B4.x)) ; MinY=min(MinY, INT32(B4.y)) ; MaxY=max(MaxY, INT32(B4.y)) ;
    MinX=min(MinX, INT32(B5.x)) ; MaxX=max(MaxX, INT32(B5.x)) ; MinY=min(MinY, INT32(B5.y)) ; MaxY=max(MaxY, INT32(B5.y)) ;
    Width = MaxX-MinX ;
    Depth = MaxY-MinY ;
}



void GEnvelope2x2::ScaleView()
{
    VL0.x = (double)(L0.x-MinX)/Width ; VL0.y = (double)(L0.y-MinY)/Depth ;
    VL1.x = (double)(L1.x-MinX)/Width ; VL1.y = (double)(L1.y-MinY)/Depth ;
    VL2.x = (double)(L2.x-MinX)/Width ; VL2.y = (double)(L2.y-MinY)/Depth ;
    VL3.x = (double)(L3.x-MinX)/Width ; VL3.y = (double)(L3.y-MinY)/Depth ;
    VL4.x = (double)(L4.x-MinX)/Width ; VL4.y = (double)(L4.y-MinY)/Depth ;
    VL5.x = (double)(L5.x-MinX)/Width ; VL5.y = (double)(L5.y-MinY)/Depth ;
    VT0.x = (double)(T0.x-MinX)/Width ; VT0.y = (double)(T0.y-MinY)/Depth ;
    VT1.x = (double)(T1.x-MinX)/Width ; VT1.y = (double)(T1.y-MinY)/Depth ;
    VT2.x = (double)(T2.x-MinX)/Width ; VT2.y = (double)(T2.y-MinY)/Depth ;
    VT3.x = (double)(T3.x-MinX)/Width ; VT3.y = (double)(T3.y-MinY)/Depth ;
    VT4.x = (double)(T4.x-MinX)/Width ; VT4.y = (double)(T4.y-MinY)/Depth ;
    VT5.x = (double)(T5.x-MinX)/Width ; VT5.y = (double)(T5.y-MinY)/Depth ;
    VR0.x = (double)(R0.x-MinX)/Width ; VR0.y = (double)(R0.y-MinY)/Depth ;
    VR1.x = (double)(R1.x-MinX)/Width ; VR1.y = (double)(R1.y-MinY)/Depth ;
    VR2.x = (double)(R2.x-MinX)/Width ; VR2.y = (double)(R2.y-MinY)/Depth ;
    VR3.x = (double)(R3.x-MinX)/Width ; VR3.y = (double)(R3.y-MinY)/Depth ;
    VR4.x = (double)(R4.x-MinX)/Width ; VR4.y = (double)(R4.y-MinY)/Depth ;
    VR5.x = (double)(R5.x-MinX)/Width ; VR5.y = (double)(R5.y-MinY)/Depth ;
    VB0.x = (double)(B0.x-MinX)/Width ; VB0.y = (double)(B0.y-MinY)/Depth ;
    VB1.x = (double)(B1.x-MinX)/Width ; VB1.y = (double)(B1.y-MinY)/Depth ;
    VB2.x = (double)(B2.x-MinX)/Width ; VB2.y = (double)(B2.y-MinY)/Depth ;
    VB3.x = (double)(B3.x-MinX)/Width ; VB3.y = (double)(B3.y-MinY)/Depth ;
    VB4.x = (double)(B4.x-MinX)/Width ; VB4.y = (double)(B4.y-MinY)/Depth ;
    VB5.x = (double)(B5.x-MinX)/Width ; VB5.y = (double)(B5.y-MinY)/Depth ;
    VMM.x = (double)(MM.x-MinX)/Width ; VMM.y = (double)(MM.y-MinY)/Depth ;
    VH1.x = (double)(H1.x-MinX)/Width ; VH1.y = (double)(H1.y-MinY)/Depth ;
    VH2.x = (double)(H2.x-MinX)/Width ; VH2.y = (double)(H2.y-MinY)/Depth ;
    VH4.x = (double)(H4.x-MinX)/Width ; VH4.y = (double)(H4.y-MinY)/Depth ;
    VH5.x = (double)(H5.x-MinX)/Width ; VH5.y = (double)(H5.y-MinY)/Depth ;
    VV1.x = (double)(V1.x-MinX)/Width ; VV1.y = (double)(V1.y-MinY)/Depth ;
    VV2.x = (double)(V2.x-MinX)/Width ; VV2.y = (double)(V2.y-MinY)/Depth ;
    VV4.x = (double)(V4.x-MinX)/Width ; VV4.y = (double)(V4.y-MinY)/Depth ;
    VV5.x = (double)(V5.x-MinX)/Width ; VV5.y = (double)(V5.y-MinY)/Depth ;
}



void GEnvelope2x2::CalcViewConsts()
{
    A00.x = VL0.x ;
    A00.y = VL0.y ;
    B00.x = 3*(VB5.x-VL0.x) ;
    B00.y = 3*(VB5.y-VL0.y) ;
    C00.x = 3*(VL1.x-VL0.x) ;
    C00.y = 3*(VL1.y-VL0.y) ;
    D00.x = 3*(VH1.x+VV1.x)-2*(VL3.x+VB3.x)-VL0.x-VMM.x-B00.x-C00.x ;
    D00.y = 3*(VH1.y+VV1.y)-2*(VL3.y+VB3.y)-VL0.y-VMM.y-B00.y-C00.y ;
    E00.x = 3*(VL0.x-2*VB5.x+VB4.x) ;
    E00.y = 3*(VL0.y-2*VB5.y+VB4.y) ;
    F00.x = 3*(VL2.x-2*VL1.x+VL0.x) ;
    F00.y = 3*(VL2.y-2*VL1.y+VL0.y) ;
    G00.x = 3*(VH2.x-2*VH1.x+VL3.x)-E00.x ;
    G00.y = 3*(VH2.y-2*VH1.y+VL3.y)-E00.y ;
    H00.x = 3*(VB3.x-2*VV1.x+VV2.x)-F00.x ;
    H00.y = 3*(VB3.y-2*VV1.y+VV2.y)-F00.y ;
    J00.x = VB3.x-3*(VB4.x-VB5.x)-VL0.x ;
    J00.y = VB3.y-3*(VB4.y-VB5.y)-VL0.y ;
    K00.x = VL3.x-3*(VL2.x-VL1.x)-VL0.x ;
    K00.y = VL3.y-3*(VL2.y-VL1.y)-VL0.y ;
    L00.x = VMM.x-3*(VH2.x-VH1.x)-VL3.x-J00.x ;
    L00.y = VMM.y-3*(VH2.y-VH1.y)-VL3.y-J00.y ;
    M00.x = VMM.x-3*(VV2.x-VV1.x)-VB3.x-K00.x ;
    M00.y = VMM.y-3*(VV2.y-VV1.y)-VB3.y-K00.y ;

    A01.x = VB3.x ;
    A01.y = VB3.y ;
    B01.x = 3*(VB2.x-VB3.x) ;
    B01.y = 3*(VB2.y-VB3.y) ;
    C01.x = 3*(VV1.x-VB3.x) ;
    C01.y = 3*(VV1.y-VB3.y) ;
    D01.x = 3*(VH4.x+VR5.x)-2*(VMM.x+VB0.x)-VB3.x-VR3.x-B01.x-C01.x ;
    D01.y = 3*(VH4.y+VR5.y)-2*(VMM.y+VB0.y)-VB3.y-VR3.y-B01.y-C01.y ;
    E01.x = 3*(VB3.x-2*VB2.x+VB1.x) ;
    E01.y = 3*(VB3.y-2*VB2.y+VB1.y) ;
    F01.x = 3*(VV2.x-2*VV1.x+VB3.x) ;
    F01.y = 3*(VV2.y-2*VV1.y+VB3.y) ;
    G01.x = 3*(VH5.x-2*VH4.x+VMM.x)-E01.x ;
    G01.y = 3*(VH5.y-2*VH4.y+VMM.y)-E01.y ;
    H01.x = 3*(VB0.x-2*VR5.x+VR4.x)-F01.x ;
    H01.y = 3*(VB0.y-2*VR5.y+VR4.y)-F01.y ;
    J01.x = VB0.x-3*(VB1.x-VB2.x)-VB3.x ;
    J01.y = VB0.y-3*(VB1.y-VB2.y)-VB3.y ;
    K01.x = VMM.x-3*(VV2.x-VV1.x)-VB3.x ;
    K01.y = VMM.y-3*(VV2.y-VV1.y)-VB3.y ;
    L01.x = VR3.x-3*(VH5.x-VH4.x)-VMM.x-J01.x ;
    L01.y = VR3.y-3*(VH5.y-VH4.y)-VMM.y-J01.y ;
    M01.x = VR3.x-3*(VR4.x-VR5.x)-VB0.x-K01.x ;
    M01.y = VR3.y-3*(VR4.y-VR5.y)-VB0.y-K01.y ;

    A10.x = VL3.x ;
    A10.y = VL3.y ;
    B10.x = 3*(VH1.x-VL3.x) ;
    B10.y = 3*(VH1.y-VL3.y) ;
    C10.x = 3*(VL4.x-VL3.x) ;
    C10.y = 3*(VL4.y-VL3.y) ;
    D10.x = 3*(VT1.x+VV4.x)-2*(VT0.x+VMM.x)-VL3.x-VT3.x-B10.x-C10.x ;
    D10.y = 3*(VT1.y+VV4.y)-2*(VT0.y+VMM.y)-VL3.y-VT3.y-B10.y-C10.y ;
    E10.x = 3*(VL3.x-2*VH1.x+VH2.x) ;
    E10.y = 3*(VL3.y-2*VH1.y+VH2.y) ;
    F10.x = 3*(VL5.x-2*VL4.x+VL3.x) ;
    F10.y = 3*(VL5.y-2*VL4.y+VL3.y) ;
    G10.x = 3*(VT2.x-2*VT1.x+VT0.x)-E10.x ;
    G10.y = 3*(VT2.y-2*VT1.y+VT0.y)-E10.y ;
    H10.x = 3*(VMM.x-2*VV4.x+VV5.x)-F10.x ;
    H10.y = 3*(VMM.y-2*VV4.y+VV5.y)-F10.y ;
    J10.x = VMM.x-3*(VH2.x-VH1.x)-VL3.x ;
    J10.y = VMM.y-3*(VH2.y-VH1.y)-VL3.y ;
    K10.x = VT0.x-3*(VL5.x-VL4.x)-VL3.x ;
    K10.y = VT0.y-3*(VL5.y-VL4.y)-VL3.y ;
    L10.x = VT3.x-3*(VT2.x-VT1.x)-VT0.x-J10.x ;
    L10.y = VT3.y-3*(VT2.y-VT1.y)-VT0.y-J10.y ;
    M10.x = VT3.x-3*(VV5.x-VV4.x)-VMM.x-K10.x ;
    M10.y = VT3.y-3*(VV5.y-VV4.y)-VMM.y-K10.y ;

    A11.x = VMM.x ;
    A11.y = VMM.y ;
    B11.x = 3*(VH4.x-VMM.x) ;
    B11.y = 3*(VH4.y-VMM.y) ;
    C11.x = 3*(VV4.x-VMM.x) ;
    C11.y = 3*(VV4.y-VMM.y) ;
    D11.x = 3*(VT4.x+VR2.x)-2*(VT3.x+VR3.x)-VMM.x-VR0.x-B11.x-C11.x ;
    D11.y = 3*(VT4.y+VR2.y)-2*(VT3.y+VR3.y)-VMM.y-VR0.y-B11.y-C11.y ;
    E11.x = 3*(VMM.x-2*VH4.x+VH5.x) ;
    E11.y = 3*(VMM.y-2*VH4.y+VH5.y) ;
    F11.x = 3*(VV5.x-2*VV4.x+VMM.x) ;
    F11.y = 3*(VV5.y-2*VV4.y+VMM.y) ;
    G11.x = 3*(VT5.x-2*VT4.x+VT3.x)-E11.x ;
    G11.y = 3*(VT5.y-2*VT4.y+VT3.y)-E11.y ;
    H11.x = 3*(VR3.x-2*VR2.x+VR1.x)-F11.x ;
    H11.y = 3*(VR3.y-2*VR2.y+VR1.y)-F11.y ;
    J11.x = VR3.x-3*(VH5.x-VH4.x)-VMM.x ;
    J11.y = VR3.y-3*(VH5.y-VH4.y)-VMM.y ;
    K11.x = VT3.x-3*(VV5.x-VV4.x)-VMM.x ;
    K11.y = VT3.y-3*(VV5.y-VV4.y)-VMM.y ;
    L11.x = VR0.x-3*(VT5.x-VT4.x)-VT3.x-J11.x ;
    L11.y = VR0.y-3*(VT5.y-VT4.y)-VT3.y-J11.y ;
    M11.x = VR0.x-3*(VR1.x-VR2.x)-VR3.x-K11.x ;
    M11.y = VR0.y-3*(VR1.y-VR2.y)-VR3.y-K11.y ;
}


BOOL GEnvelope2x2::FitPath (
                        CONST POINT* IPoints, 
                        CONST BYTE* ITypes, 
                        DWORD ILength,
                        LPPOINT pOPoints, 
                        LPBYTE pOTypes, 
                        DWORD pOLength,
                        BOOL Close
                    )
{
    OPoints = pOPoints ;
    OTypes  = pOTypes  ;
    OLength = pOLength ;

    DPOINT     C2, C4 ;
    DPOINT P0, P2, P4, P6, SP;
    DPOINT T0, T2, T4, T6, ST;
    SP.x=SP.y=ST.x=ST.y=0; // silence compiler whinging
    while ( ILength )
    {
        switch ( *ITypes & PT_MOVETO )
        {
        case PT_MOVETO :
            --ILength ; ++ITypes ;
            ScaleSrc ( *IPoints++, P0 ) ; SP.x = P0.x ; SP.y = P0.y ;
            Transform( P0, T0 ) ;         ST.x = T0.x ; ST.y = T0.y ;
            if ( !GenMove( T0 ) ) return -1 ;
            break ;
        case PT_LINETO :
            --ILength ; ++ITypes ;
            ScaleSrc( *IPoints++, P6 ) ;
            Transform( P6, T6 ) ;
            if ( !GenLine( P0,P6,T0,T6 ) ) return -1 ;
            P0.x = P6.x ; P0.y = P6.y ;
            T0.x = T6.x ; T0.y = T6.y ;
            break ;
        case PT_BEZIERTO :
            ILength -= 3 ; ITypes += 3 ;
            ScaleSrc( *IPoints++, C2 ) ;
            ScaleSrc( *IPoints++, C4 ) ;
            ScaleSrc( *IPoints++, P6 ) ;
            P2.x = (8*P0.x+12*C2.x+ 6*C4.x+  P6.x)/27 ;
            P2.y = (8*P0.y+12*C2.y+ 6*C4.y+  P6.y)/27 ;
            P4.x = (  P0.x+ 6*C2.x+12*C4.x+8*P6.x)/27 ;
            P4.y = (  P0.y+ 6*C2.y+12*C4.y+8*P6.y)/27 ;
            Transform( P2, T2 ) ;
            Transform( P4, T4 ) ;
            Transform( P6, T6 ) ;
            if ( !GenCurve( C2, C4, P0, P2, P4, P6, T0, T2, T4, T6 ) ) return -1 ;
            P0.x = P6.x ; P0.y = P6.y ;
            T0.x = T6.x ; T0.y = T6.y ;
            break ;
        default :
            return -1 ;
        }
        if ( *(ITypes-1) & PT_CLOSEFIGURE ||
                            ( Close && ( ILength==0 || (*ITypes & PT_MOVETO) == PT_MOVETO ) ) )
        {
            if ( !GenLine( P0,SP,T0,ST ) ) return -1 ;
            *(OTypes-1) |= *(ITypes-1) & PT_CLOSEFIGURE ;
        }
    }
    if ( ILength )
        return -1 ;
    return pOLength-OLength ;
}


BOOL GEnvelope2x2::GenLine( DPOINT P0, DPOINT P6, DPOINT T0, DPOINT T6 )
{
    BOOL F0 = !SmoothX && ((P0.x<0.5 && P6.x>0.5) || (P0.x>0.5 && P6.x<0.5)) ;
    BOOL F1 = !SmoothY && ((P0.y<0.5 && P6.y>0.5) || (P0.y>0.5 && P6.y<0.5)) ;
    if ( F0 || F1 )
    {
        DPOINT P1,P2,P3,P4,P5 ;
        DPOINT T1,T2,T3,T4,T5 ;
        P3.x=P3.y=0;
        if ( F0 )
        {
            P3.x = 0.5 ;
            P3.y = P0.y+(0.5-P0.x)*(P6.y-P0.y)/(P6.x-P0.x) ;
        }
        else if ( F1 )
        {
            P3.x = P0.x+(0.5-P0.y)*(P6.x-P0.x)/(P6.y-P0.y) ;
            P3.y = 0.5 ;
        }
        P1.x = (2*P0.x+P3.x)/3 ;
        P1.y = (2*P0.y+P3.y)/3 ;
        P2.x = (P0.x+2*P3.x)/3 ;
        P2.y = (P0.y+2*P3.y)/3 ;
        P4.x = (2*P3.x+P6.x)/3 ;
        P4.y = (2*P3.y+P6.y)/3 ;
        P5.x = (P3.x+2*P6.x)/3 ;
        P5.y = (P3.y+2*P6.y)/3 ;
        Transform( P1, T1 ) ;
        Transform( P2, T2 ) ;
        Transform( P3, T3 ) ;
        Transform( P4, T4 ) ;
        Transform( P5, T5 ) ;
        return GenCurve( P1, P2, P0, P1, P2, P3, T0, T1, T2, T3 ) &&
               GenCurve( P4, P5, P3, P4, P5, P6, T3, T4, T5, T6 ) ;
    }
    else
    {
        DPOINT P2,P4 ;
        DPOINT T2,T4 ;
        P2.x = (2*P0.x+P6.x)/3 ;
        P2.y = (2*P0.y+P6.y)/3 ;
        P4.x = (P0.x+2*P6.x)/3 ;
        P4.y = (P0.y+2*P6.y)/3 ;
        Transform( P2, T2 ) ;
        Transform( P4, T4 ) ;
        return GenCurve( P2, P4, P0, P2, P4, P6, T0, T2, T4, T6 ) ;
    }
}


void GEnvelope2x2::Transform( DPOINT a, DPOINT& b )
{
    a.x *= 2.0 ;
    a.y *= 2.0 ;
    if ( a.y<1.0 )
        if ( a.x<1.0 )
        {
            b.x = A00.x+a.x*(B00.x+a.x*(E00.x+a.x*J00.x))
                       +a.y*(C00.x+a.y*(F00.x+a.y*K00.x)
                       +a.x*(D00.x+a.x*(G00.x+a.x*L00.x)
                                  +a.y*(H00.x+a.y*M00.x))) ;
            b.y = A00.y+a.x*(B00.y+a.x*(E00.y+a.x*J00.y))
                       +a.y*(C00.y+a.y*(F00.y+a.y*K00.y)
                       +a.x*(D00.y+a.x*(G00.y+a.x*L00.y)
                                  +a.y*(H00.y+a.y*M00.y))) ;
        }
        else
        {
            a.x-- ;
            b.x = A01.x+a.x*(B01.x+a.x*(E01.x+a.x*J01.x))
                       +a.y*(C01.x+a.y*(F01.x+a.y*K01.x)
                       +a.x*(D01.x+a.x*(G01.x+a.x*L01.x)
                                  +a.y*(H01.x+a.y*M01.x))) ;
            b.y = A01.y+a.x*(B01.y+a.x*(E01.y+a.x*J01.y))
                       +a.y*(C01.y+a.y*(F01.y+a.y*K01.y)
                       +a.x*(D01.y+a.x*(G01.y+a.x*L01.y)
                                  +a.y*(H01.y+a.y*M01.y))) ;
        }
    else
    {
        a.y-- ;
        if ( a.x<1.0 )
        {
            b.x = A10.x+a.x*(B10.x+a.x*(E10.x+a.x*J10.x))
                       +a.y*(C10.x+a.y*(F10.x+a.y*K10.x)
                       +a.x*(D10.x+a.x*(G10.x+a.x*L10.x)
                                  +a.y*(H10.x+a.y*M10.x))) ;
            b.y = A10.y+a.x*(B10.y+a.x*(E10.y+a.x*J10.y))
                       +a.y*(C10.y+a.y*(F10.y+a.y*K10.y)
                       +a.x*(D10.y+a.x*(G10.y+a.x*L10.y)
                                  +a.y*(H10.y+a.y*M10.y))) ;
        }
        else
        {
            a.x-- ;
            b.x = A11.x+a.x*(B11.x+a.x*(E11.x+a.x*J11.x))
                       +a.y*(C11.x+a.y*(F11.x+a.y*K11.x)
                       +a.x*(D11.x+a.x*(G11.x+a.x*L11.x)
                                  +a.y*(H11.x+a.y*M11.x))) ;
            b.y = A11.y+a.x*(B11.y+a.x*(E11.y+a.x*J11.y))
                       +a.y*(C11.y+a.y*(F11.y+a.y*K11.y)
                       +a.x*(D11.y+a.x*(G11.y+a.x*L11.y)
                                  +a.y*(H11.y+a.y*M11.y))) ;
        }
    }
}

---