kicad/polygon/PolyLine.cpp

// PolyLine.cpp ... implementation of CPolyLine class from FreePCB.

//
// implementation for kicad and kbool polygon clipping library
//
#include <math.h>
#include <vector>
#include <algorithm>

#include <fctsys.h>
#include <common.h>     // KiROUND

#include <PolyLine.h>
#include <bezier_curves.h>
#include <polygon_test_point_inside.h>


#define to_int( x ) KiROUND( (x) )

#ifndef MIN
#define MIN( x1, x2 ) ( (x1) > (x2) ? (x2) : (x1) )
#endif
#ifndef MAX
#define MAX( x1, x2 ) ( (x1) > (x2) ? (x1) : (x2) )
#endif

#define pi M_PI

CPolyLine::CPolyLine()
{
    m_hatchStyle = NO_HATCH;
    m_hatchPitch = 0;
    m_Width = 0;
    utility = 0;
    m_Kbool_Poly_Engine = NULL;
}


// destructor, removes display elements
//
CPolyLine::~CPolyLine()
{
    UnHatch();
    if( m_Kbool_Poly_Engine )
        delete m_Kbool_Poly_Engine;
}


/**
 * Function NormalizeWithKbool
 * Use the Kbool Library to clip contours: if outlines are crossing, the self-crossing polygon
 * is converted to non self-crossing polygon by adding extra points at the crossing locations
 * and reordering corners
 * if more than one outside contour are found, extra CPolyLines will be created
 * because copper areas have only one outside contour
 * Therefore, if this results in new CPolyLines, return them as std::vector pa
 * @param aExtraPolyList: pointer on a std::vector<CPolyLine*> to store extra CPolyLines
 * @param bRetainArcs == true, try to retain arcs in polys
 * @return number of external contours, or -1 if error
 */
int CPolyLine::NormalizeWithKbool( std::vector<CPolyLine*> * aExtraPolyList, bool bRetainArcs )
{
    std::vector<CArc>   arc_array;
    std::vector <void*> hole_array; // list of holes
    std::vector<int> *  hole;       // used to store corners for a given hole
    CPolyLine*          polyline;
    int n_ext_cont = 0;             // CPolyLine count

    /* Creates a bool engine from this CPolyLine.
     * Normalized outlines and holes will be in m_Kbool_Poly_Engine
     * If some polygons are self crossing, after running the Kbool Engine, self crossing polygons
     * will be converted in non self crossing polygons by inserting extra points at the crossing locations
     * True holes are combined if possible
     */
    if( bRetainArcs )
        MakeKboolPoly( -1, -1, &arc_array );
    else
        MakeKboolPoly( -1, -1, NULL );

    UnHatch();

    /* now, recreate polys
     * if more than one outside contour are found, extra CPolyLines will be created
     * because copper areas have only one outside contour
     * the first outside contour found is the new "this" outside contour
     * if others outside contours are found we create new CPolyLines
     * Note: if there are holes in polygons, we must store them
     * and when all outside contours are found, search the corresponding outside contour for each hole
     */
    while( m_Kbool_Poly_Engine->StartPolygonGet() )
    {
        // See if the current polygon is flagged as a hole
        if( m_Kbool_Poly_Engine->GetPolygonPointEdgeType() == KB_INSIDE_EDGE )
        {
            hole = new std::vector<int>;
            hole_array.push_back( hole );
            while( m_Kbool_Poly_Engine->PolygonHasMorePoints() )    // store hole
            {
                int x = (int) m_Kbool_Poly_Engine->GetPolygonXPoint();
                int y = (int) m_Kbool_Poly_Engine->GetPolygonYPoint();
                hole->push_back( x );
                hole->push_back( y );
            }

            m_Kbool_Poly_Engine->EndPolygonGet();
        }
        else if( n_ext_cont == 0 )
        {
            // first external contour, replace this poly
            corner.clear();
            side_style.clear();
            bool first = true;
            while( m_Kbool_Poly_Engine->PolygonHasMorePoints() )
            {
                // foreach point in the polygon
                int x = (int) m_Kbool_Poly_Engine->GetPolygonXPoint();
                int y = (int) m_Kbool_Poly_Engine->GetPolygonYPoint();
                if( first )
                {
                    first = false;
                    Start( GetLayer(), x, y, GetHatchStyle() );
                }
                else
                    AppendCorner( x, y );
            }

            m_Kbool_Poly_Engine->EndPolygonGet();
            Close();
            n_ext_cont++;
        }
        else if( aExtraPolyList )                                               // a new outside contour is found: create a new CPolyLine
        {
            polyline = new CPolyLine;                                           // create new poly
            aExtraPolyList->push_back( polyline );                              // put it in array
            bool first = true;
            while( m_Kbool_Poly_Engine->PolygonHasMorePoints() )                // read next external contour
            {
                int x = (int) m_Kbool_Poly_Engine->GetPolygonXPoint();
                int y = (int) m_Kbool_Poly_Engine->GetPolygonYPoint();
                if( first )
                {
                    first = false;
                    polyline->Start( GetLayer(), x, y, GetHatchStyle() );
                }
                else
                    polyline->AppendCorner( x, y );
            }

            m_Kbool_Poly_Engine->EndPolygonGet();
            polyline->Close( STRAIGHT, false );
            n_ext_cont++;
        }
    }

    // now add cutouts to the corresponding CPolyLine(s)
    for( unsigned ii = 0; ii < hole_array.size(); ii++ )
    {
        hole     = (std::vector<int> *)hole_array[ii];
        polyline = NULL;
        if( n_ext_cont == 1 )
        {
            polyline = this;
        }
        else
        {
            // find the polygon that contains this hole
            // testing one corner inside is enought because a hole is entirely inside the polygon
            // so we test only the first corner
            int x = (*hole)[0];
            int y = (*hole)[1];
            if( TestPointInside( x, y ) )
                polyline = this;
            else if( aExtraPolyList )
            {
                for( int ext_ic = 0; ext_ic<n_ext_cont - 1; ext_ic++ )
                {
                    if( (*aExtraPolyList)[ext_ic]->TestPointInside( x, y ) )
                    {
                        polyline = (*aExtraPolyList)[ext_ic];
                        break;
                    }
                }
            }
        }

        if( !polyline )
            wxASSERT( 0 );
        else
        {
            for( unsigned ii = 0; ii< (*hole).size(); ii++ )
            {
                int x = (*hole)[ii]; ii++;
                int y = (*hole)[ii];
                polyline->AppendCorner( x, y, STRAIGHT, false );
            }

            polyline->Close( STRAIGHT, false );
        }
    }

    if( bRetainArcs )
        RestoreArcs( &arc_array, aExtraPolyList );

    delete m_Kbool_Poly_Engine;
    m_Kbool_Poly_Engine = NULL;

    // free hole list
    for( unsigned ii = 0; ii < hole_array.size(); ii++ )
        delete (std::vector<int> *)hole_array[ii];

    return n_ext_cont;
}


/**
 * Function AddPolygonsToBoolEng
 * Add a CPolyLine to a kbool engine, preparing a boolean op between polygons
 * @param aStart_contour: starting contour number (-1 = all, 0 is the outlines of zone, > 1 = holes in zone
 * @param aEnd_contour: ending contour number (-1 = all after  aStart_contour)
 * @param arc_array: arc converted to poly segments (NULL if not exists)
 * @param aBooleng : pointer on a bool engine (handle a set of polygons)
 * @param aGroup : group to fill (aGroup = GROUP_A or GROUP_B) operations are made between GROUP_A and GROUP_B
 */
int CPolyLine::AddPolygonsToBoolEng( Bool_Engine*        aBooleng,
                                     GroupType           aGroup,
                                     int                 aStart_contour,
                                     int                 aEnd_contour,
                                     std::vector<CArc> * arc_array )
{
    int count = 0;

    if( (aGroup != GROUP_A) && (aGroup != GROUP_B ) )
        return 0; //Error !

    /* Convert the current polyline contour to a kbool polygon: */
    MakeKboolPoly( aStart_contour, aEnd_contour, arc_array );

    /* add the resulting kbool set of polygons to the current kcool engine */
    while( m_Kbool_Poly_Engine->StartPolygonGet() )
    {
        if( aBooleng->StartPolygonAdd( GROUP_A ) )
        {
            while( m_Kbool_Poly_Engine->PolygonHasMorePoints() )
            {
                int x = (int) m_Kbool_Poly_Engine->GetPolygonXPoint();
                int y = (int) m_Kbool_Poly_Engine->GetPolygonYPoint();
                aBooleng->AddPoint( x, y );
                count++;
            }

            aBooleng->EndPolygonAdd();
        }
        m_Kbool_Poly_Engine->EndPolygonGet();
    }

    delete m_Kbool_Poly_Engine;
    m_Kbool_Poly_Engine = NULL;

    return count;
}


/**
 * Function MakeKboolPoly
 * fill a kbool engine with a closed polyline contour
 * approximates arcs with multiple straight-line segments
 * @param aStart_contour: starting contour number (-1 = all, 0 is the outlines of zone, > 1 = holes in zone
 * @param aEnd_contour: ending contour number (-1 = all after  aStart_contour)
 *  combining intersecting contours if possible
 * @param arc_array : return corners computed from arcs approximations in arc_array
 * @param aConvertHoles = mode for holes when a boolean operation is made
 *   true: holes are linked into outer contours by double overlapping segments
 *   false: holes are not linked: in this mode contours are added clockwise
 *          and polygons added counter clockwise are holes (default)
 * @return error: 0 if Ok, 1 if error
 */
int CPolyLine::MakeKboolPoly( int aStart_contour, int aEnd_contour, std::vector<CArc> * arc_array,
                              bool aConvertHoles )
{
    if( m_Kbool_Poly_Engine )
    {
        delete m_Kbool_Poly_Engine;
        m_Kbool_Poly_Engine = NULL;
    }
    if( !GetClosed() && (aStart_contour == (GetNumContours() - 1) || aStart_contour == -1) )
        return 1; // error

    int n_arcs = 0;

    int first_contour = aStart_contour;
    int last_contour  = aEnd_contour;
    if( aStart_contour == -1 )
    {
        first_contour = 0;
        last_contour  = GetNumContours() - 1;
    }
    if( aEnd_contour == -1 )
    {
        last_contour = GetNumContours() - 1;
    }
    if( arc_array )
        arc_array->clear();
    int iarc = 0;
    for( int icont = first_contour; icont<=last_contour; icont++ )
    {
        // Fill a kbool engine for this contour,
        // and combine it with previous contours
        Bool_Engine* booleng = new Bool_Engine();
        ArmBoolEng( booleng, aConvertHoles );

        if( m_Kbool_Poly_Engine )  // a previous contour exists. Put it in new engine
        {
            while( m_Kbool_Poly_Engine->StartPolygonGet() )
            {
                if( booleng->StartPolygonAdd( GROUP_A ) )
                {
                    while( m_Kbool_Poly_Engine->PolygonHasMorePoints() )
                    {
                        int x = (int) m_Kbool_Poly_Engine->GetPolygonXPoint();
                        int y = (int) m_Kbool_Poly_Engine->GetPolygonYPoint();
                        booleng->AddPoint( x, y );
                    }

                    booleng->EndPolygonAdd();
                }
                m_Kbool_Poly_Engine->EndPolygonGet();
            }
        }

        // first, calculate number of vertices in contour
        int n_vertices = 0;
        int ic_st  = GetContourStart( icont );
        int ic_end = GetContourEnd( icont );
        if( !booleng->StartPolygonAdd( GROUP_B ) )
        {
            wxASSERT( 0 );
            return 1;   //error
        }
        for( int ic = ic_st; ic<=ic_end; ic++ )
        {
            int style = side_style[ic];
            if( style == STRAIGHT )
                n_vertices++;
            else
            {
                // style is ARC_CW or ARC_CCW
                int n = CArc::ARC_STEPS;
                n_vertices += n;
                n_arcs++;
            }
        }

        // now enter this contour to booleng
        int ivtx = 0;
        for( int ic = ic_st; ic<=ic_end; ic++ )
        {
            int style = side_style[ic];
            int x1    = corner[ic].x;
            int y1    = corner[ic].y;
            int x2, y2;
            if( ic < ic_end )
            {
                x2 = corner[ic + 1].x;
                y2 = corner[ic + 1].y;
            }
            else
            {
                x2 = corner[ic_st].x;
                y2 = corner[ic_st].y;
            }
            if( style == STRAIGHT )
            {
                booleng->AddPoint( x1, y1 );
                ivtx++;
            }
            else
            {
                // style is arc_cw or arc_ccw
                int    n;                       // number of steps for arcs
                n = CArc::ARC_STEPS;
                double xo, yo, theta1, theta2, a, b;
                a = fabs( (double) (x1 - x2) );
                b = fabs( (double) (y1 - y2) );
                if( style == CPolyLine::ARC_CW )
                {
                    // clockwise arc (ie.quadrant of ellipse)
                    if( x2 > x1 && y2 > y1 )
                    {
                        // first quadrant, draw second quadrant of ellipse
                        xo     = x2;
                        yo     = y1;
                        theta1 = pi;
                        theta2 = pi / 2.0;
                    }
                    else if( x2 < x1 && y2 > y1 )
                    {
                        // second quadrant, draw third quadrant of ellipse
                        xo     = x1;
                        yo     = y2;
                        theta1 = 3.0 * pi / 2.0;
                        theta2 = pi;
                    }
                    else if( x2 < x1 && y2 < y1 )
                    {
                        // third quadrant, draw fourth quadrant of ellipse
                        xo     = x2;
                        yo     = y1;
                        theta1 = 2.0 * pi;
                        theta2 = 3.0 * pi / 2.0;
                    }
                    else
                    {
                        xo     = x1; // fourth quadrant, draw first quadrant of ellipse
                        yo     = y2;
                        theta1 = pi / 2.0;
                        theta2 = 0.0;
                    }
                }
                else
                {
                    // counter-clockwise arc
                    if( x2 > x1 && y2 > y1 )
                    {
                        xo     = x1; // first quadrant, draw fourth quadrant of ellipse
                        yo     = y2;
                        theta1 = 3.0 * pi / 2.0;
                        theta2 = 2.0 * pi;
                    }
                    else if( x2 < x1 && y2 > y1 )
                    {
                        xo     = x2; // second quadrant
                        yo     = y1;
                        theta1 = 0.0;
                        theta2 = pi / 2.0;
                    }
                    else if( x2 < x1 && y2 < y1 )
                    {
                        xo     = x1; // third quadrant
                        yo     = y2;
                        theta1 = pi / 2.0;
                        theta2 = pi;
                    }
                    else
                    {
                        xo     = x2; // fourth quadrant
                        yo     = y1;
                        theta1 = pi;
                        theta2 = 3.0 * pi / 2.0;
                    }
                }

                // now write steps for arc
                if( arc_array )
                {
                    CArc new_arc;
                    new_arc.style   = style;
                    new_arc.n_steps = n;
                    new_arc.xi = x1;
                    new_arc.yi = y1;
                    new_arc.xf = x2;
                    new_arc.yf = y2;
                    arc_array->push_back( new_arc );
                    iarc++;
                }
                for( int is = 0; is<n; is++ )
                {
                    double theta = theta1 + ( (theta2 - theta1) * (double) is ) / n;
                    double x = xo + a* cos( theta );
                    double y = yo + b* sin( theta );
                    if( is == 0 )
                    {
                        x = x1;
                        y = y1;
                    }
                    booleng->AddPoint( x, y );
                    ivtx++;
                }
            }
        }

        if( n_vertices != ivtx )
        {
            wxASSERT( 0 );
        }

        //  close list added to the bool engine
        booleng->EndPolygonAdd();

        /* now combine polygon to the previous polygons.
         * note: the first polygon is the outline contour, and others are holes inside the first polygon
         * The first polygon is ORed with nothing, but is is a trick to sort corners (vertex)
         * clockwise with the kbool engine.
         * Others polygons are substract to the outline and corners will be ordered counter clockwise
         * by the kbool engine
         */
        if( aStart_contour <= 0 && icont != 0 )  // substract hole to outside ( if the outline contour is take in account)
        {
            booleng->Do_Operation( BOOL_A_SUB_B );
        }
        else       // add outside or add holes if we do not use the outline contour
        {
            booleng->Do_Operation( BOOL_OR );
        }

        // now use result as new polygon (delete the old one if exists)
        if( m_Kbool_Poly_Engine )
            delete m_Kbool_Poly_Engine;
        m_Kbool_Poly_Engine = booleng;
    }

    return 0;
}


/**
 * Function ArmBoolEng
 * Initialise parameters used in kbool
 * @param aBooleng = pointer to the Bool_Engine to initialise
 * @param aConvertHoles = mode for holes when a boolean operation is made
 *   true: in resulting polygon, holes are linked into outer contours by double overlapping segments
 *   false: in resulting polygons, holes are not linked: they are separate polygons
 */
void ArmBoolEng( Bool_Engine* aBooleng, bool aConvertHoles )
{
    // set some global vals to arm the boolean engine

    // input points are scaled up with GetDGrid() * GetGrid()

    // DGRID is only meant to make fractional parts of input data which
   /*
      The input data scaled up with DGrid is related to the accuracy the user has in his input data.
      User data with a minimum accuracy of 0.001, means set the DGrid to 1000.
      The input data may contain data with a minimum accuracy much smaller, but by setting the DGrid
      everything smaller than 1/DGrid is rounded.

      DGRID is only meant to make fractional parts of input data which can be
      doubles, part of the integers used in vertexes within the boolean algorithm.
      And therefore DGRID bigger than 1 is not usefull, you would only loose accuracy.
      Within the algorithm all input data is multiplied with DGRID, and the result
      is rounded to an integer.
   */
    double DGRID = 1000.0;     // round coordinate X or Y value in calculations to this (initial value = 1000.0 in kbool example)
                            // kbool uses DGRID to convert float user units to integer
                            // kbool unit = (int)(user unit * DGRID)
                            // Note: in kicad, coordinates are already integer so DGRID could be set to 1
                            // we can choose 1.0,
                            // but choose DGRID = 1000.0 solves some filling problems
//                             (perhaps because this allows a better precision in kbool internal calculations

    double MARGE = 1.0/DGRID;      // snap with in this range points to lines in the intersection routines
                                    // should always be >= 1/DGRID  a  MARGE >= 10/DGRID is ok
                                    // this is also used to remove small segments and to decide when
                                    // two segments are in line. ( initial value = 0.001 )
                                    // For kicad we choose MARGE = 1/DGRID

    double CORRECTIONFACTOR = 0.0;      // correct the polygons by this number: used in BOOL_CORRECTION operation
                                        // this operation shrinks a polygon if CORRECTIONFACTOR < 0
                                        // or stretch it if CORRECTIONFACTOR > 0
                                        // the size change is CORRECTIONFACTOR (holes are correctly handled)
    double CORRECTIONABER   = 1.0;      // the accuracy for the rounded shapes used in correction
    double ROUNDFACTOR  = 1.5;          // when will we round the correction shape to a circle
    double SMOOTHABER   = 10.0;         // accuracy when smoothing a polygon
    double MAXLINEMERGE = 1000.0;       // leave as is, segments of this length in smoothen


   /*
        Grid makes sure that the integer data used within the algorithm has room for extra intersections
        smaller than the smallest number within the input data.
        The input data scaled up with DGrid is related to the accuracy the user has in his input data.
        Another scaling with Grid is applied on top of it to create space in the integer number for
        even smaller numbers.
   */
    int GRID = (int) ( 10000.0 / DGRID );  // initial value = 10000 in kbool example but we use
                                           // 10000/DGRID because the scaling is made by DGRID
                                           // on integer pcbnew units and the global scaling
                                           // ( GRID*DGRID) must be < 30000 to avoid overflow
                                           // in calculations (made in long long in kbool)
    if ( GRID <= 1 )    // Cannot be null!
        GRID = 1;

    aBooleng->SetMarge( MARGE );
    aBooleng->SetGrid( GRID );
    aBooleng->SetDGrid( DGRID );
    aBooleng->SetCorrectionFactor( CORRECTIONFACTOR );
    aBooleng->SetCorrectionAber( CORRECTIONABER );
    aBooleng->SetSmoothAber( SMOOTHABER );
    aBooleng->SetMaxlinemerge( MAXLINEMERGE );
    aBooleng->SetRoundfactor( ROUNDFACTOR );
    aBooleng->SetWindingRule( true );           // This is the default kbool value

    if( aConvertHoles )
    {
#if 1   // Can be set to 1 for kbool version >= 2.1, must be set to 0 for previous versions
        // SetAllowNonTopHoleLinking() exists only in kbool >= 2.1
        aBooleng->SetAllowNonTopHoleLinking( false );    // Default = true, but i have problems (filling errors) when true
#endif
        aBooleng->SetLinkHoles( true );                 // holes will be connected by double overlapping segments
        aBooleng->SetOrientationEntryMode( false );     // all polygons are contours, not holes
    }
    else
    {
        aBooleng->SetLinkHoles( false );                // holes will not be connected by double overlapping segments
        aBooleng->SetOrientationEntryMode( true );      // holes are entered counter clockwise
    }
}


int CPolyLine::NormalizeAreaOutlines( std::vector<CPolyLine*> * pa, bool bRetainArcs )
{
    return NormalizeWithKbool( pa, bRetainArcs );
}


// Restore arcs to a polygon where they were replaced with steps
// If pa != NULL, also use polygons in pa array
//
int CPolyLine::RestoreArcs( std::vector<CArc> * arc_array, std::vector<CPolyLine*> * pa )
{
    // get poly info
    int n_polys = 1;

    if( pa )
        n_polys += pa->size();
    CPolyLine* poly;

    // undraw polys and clear utility flag for all corners
    for( int ip = 0; ip<n_polys; ip++ )
    {
        if( ip == 0 )
            poly = this;
        else
            poly = (*pa)[ip - 1];
        poly->UnHatch();
        for( int ic = 0; ic<poly->GetNumCorners(); ic++ )
            poly->SetUtility( ic, 0 );

        // clear utility flag
    }

    // find arcs and replace them
    bool bFound;
    int  arc_start = 0;
    int  arc_end   = 0;
    for( unsigned iarc = 0; iarc<arc_array->size(); iarc++ )
    {
        int arc_xi  = (*arc_array)[iarc].xi;
        int arc_yi  = (*arc_array)[iarc].yi;
        int arc_xf  = (*arc_array)[iarc].xf;
        int arc_yf  = (*arc_array)[iarc].yf;
        int n_steps = (*arc_array)[iarc].n_steps;
        int style   = (*arc_array)[iarc].style;
        bFound = false;

        // loop through polys
        for( int ip = 0; ip<n_polys; ip++ )
        {
            if( ip == 0 )
                poly = this;
            else
                poly = (*pa)[ip - 1];
            for( int icont = 0; icont<poly->GetNumContours(); icont++ )
            {
                int ic_start = poly->GetContourStart( icont );
                int ic_end   = poly->GetContourEnd( icont );
                if( (ic_end - ic_start) > n_steps )
                {
                    for( int ic = ic_start; ic<=ic_end; ic++ )
                    {
                        int ic_next = ic + 1;
                        if( ic_next > ic_end )
                            ic_next = ic_start;
                        int xi = poly->GetX( ic );
                        int yi = poly->GetY( ic );
                        if( xi == arc_xi && yi == arc_yi )
                        {
                            // test for forward arc
                            int ic2 = ic + n_steps;
                            if( ic2 > ic_end )
                                ic2 = ic2 - ic_end + ic_start - 1;
                            int xf = poly->GetX( ic2 );
                            int yf = poly->GetY( ic2 );
                            if( xf == arc_xf && yf == arc_yf )
                            {
                                // arc from ic to ic2
                                bFound    = true;
                                arc_start = ic;
                                arc_end   = ic2;
                            }
                            else
                            {
                                // try reverse arc
                                ic2 = ic - n_steps;
                                if( ic2 < ic_start )
                                    ic2 = ic2 - ic_start + ic_end + 1;
                                xf = poly->GetX( ic2 );
                                yf = poly->GetY( ic2 );
                                if( xf == arc_xf && yf == arc_yf )
                                {
                                    // arc from ic2 to ic
                                    bFound    = true;
                                    arc_start = ic2;
                                    arc_end   = ic;
                                    style = 3 - style;
                                }
                            }
                            if( bFound )
                            {
                                poly->side_style[arc_start] = style;

                                // mark corners for deletion from arc_start+1 to arc_end-1
                                for( int i = arc_start + 1; i!=arc_end; )
                                {
                                    if( i > ic_end )
                                        i = ic_start;
                                    poly->SetUtility( i, 1 );
                                    if( i == ic_end )
                                        i = ic_start;
                                    else
                                        i++;
                                }

                                break;
                            }
                        }
                        if( bFound )
                            break;
                    }
                }
                if( bFound )
                    break;
            }
        }

        if( bFound )
            (*arc_array)[iarc].bFound = true;
    }

    // now delete all marked corners
    for( int ip = 0; ip<n_polys; ip++ )
    {
        if( ip == 0 )
            poly = this;
        else
            poly = (*pa)[ip - 1];
        for( int ic = poly->GetNumCorners() - 1; ic>=0; ic-- )
        {
            if( poly->GetUtility( ic ) )
                poly->DeleteCorner( ic, false );
        }
    }

    return 0;
}


// initialize new polyline
// set layer, width, selection box size, starting point, id and pointer
//
// if sel_box = 0, don't create selection elements at all
//
// if polyline is board outline, enter with:
//	id.type = ID_BOARD
//	id.st = ID_BOARD_OUTLINE
//	id.i = 0
//	ptr = NULL
//
// if polyline is copper area, enter with:
//	id.type = ID_NET;
//	id.st = ID_AREA
//	id.i = index to area
//	ptr = pointer to net
//
void CPolyLine::Start( int layer, int x, int y, int hatch )
{
    m_layer      = layer;
    SetHatchStyle( (enum hatch_style) hatch );
    CPolyPt poly_pt( x, y );
    poly_pt.end_contour = false;

    corner.push_back( poly_pt );
    side_style.push_back( 0 );
}


// add a corner to unclosed polyline
//
void CPolyLine::AppendCorner( int x, int y, int style, bool bDraw )
{
    UnHatch();
    CPolyPt poly_pt( x, y );
    poly_pt.end_contour = false;

    // add entries for new corner and side
    corner.push_back( poly_pt );
    side_style.push_back( style );
    if( corner.size() > 0 && !corner[corner.size() - 1].end_contour )
        side_style[corner.size() - 1] = style;
    if( bDraw )
        Hatch();
}


// close last polyline contour
//
void CPolyLine::Close( int style, bool bDraw )
{
    if( GetClosed() )
    {
        wxASSERT( 0 );
    }
    UnHatch();
    side_style[corner.size() - 1] = style;
    corner[corner.size() - 1].end_contour = true;
    if( bDraw )
        Hatch();
}


// move corner of polyline
//
void CPolyLine::MoveCorner( int ic, int x, int y )
{
    UnHatch();
    corner[ic].x = x;
    corner[ic].y = y;
    Hatch();
}


// delete corner and adjust arrays
//
void CPolyLine::DeleteCorner( int ic, bool bDraw )
{
    UnHatch();
    int  icont   = GetContour( ic );
    int  istart  = GetContourStart( icont );
    int  iend    = GetContourEnd( icont );
    bool bClosed = icont < GetNumContours() - 1 || GetClosed();

    if( !bClosed )
    {
        // open contour, must be last contour
        corner.erase( corner.begin() + ic );

        if( ic != istart )
            side_style.erase( side_style.begin() + ic - 1 );
    }
    else
    {
        // closed contour
        corner.erase( corner.begin() + ic );
        side_style.erase( side_style.begin() + ic );
        if( ic == iend )
            corner[ic - 1].end_contour = true;
    }
    if( bClosed && GetContourSize( icont ) < 3 )
    {
        // delete the entire contour
        RemoveContour( icont );
    }
    if( bDraw )
        Hatch();
}


/******************************************/
void CPolyLine::RemoveContour( int icont )
/******************************************/

/**
 * Function RemoveContour
 * @param icont = contour number to remove
 * remove a contour only if there is more than 1 contour
 */
{
    UnHatch();
    int istart = GetContourStart( icont );
    int iend   = GetContourEnd( icont );

    if( icont == 0 && GetNumContours() == 1 )
    {
        // remove the only contour
        wxASSERT( 0 );
    }
    else if( icont == GetNumContours() - 1 )
    {
        // remove last contour
        corner.erase( corner.begin() + istart, corner.end() );
        side_style.erase( side_style.begin() + istart, side_style.end() );
    }
    else
    {
        // remove closed contour
        for( int ic = iend; ic>=istart; ic-- )
        {
            corner.erase( corner.begin() + ic );
            side_style.erase( side_style.begin() + ic );
        }
    }
    Hatch();
}


CPolyLine* CPolyLine::Chamfer( unsigned int aDistance )
{
    CPolyLine* newPoly = new CPolyLine;

    if( !aDistance )
    {
        newPoly->Copy( this );
        return newPoly;
    }

    for( int contour = 0; contour < GetNumContours(); contour++ )
    {
        unsigned int startIndex = GetContourStart( contour );
        unsigned int endIndex = GetContourEnd( contour );

        for( unsigned int index = startIndex; index <= endIndex; index++ )
        {
            int x1, y1, nx, ny;
            long long xa, ya, xb, yb;

            x1 = corner[index].x;
            y1 = corner[index].y;

            if( index == startIndex )
            {
                xa = corner[endIndex].x - x1;
                ya = corner[endIndex].y - y1;
            }
            else
            {
                xa = corner[index-1].x - x1;
                ya = corner[index-1].y - y1;
            }

            if( index == endIndex )
            {
                xb = corner[startIndex].x - x1;
                yb = corner[startIndex].y - y1;
            }
            else
            {
                xb = corner[index+1].x - x1;
                yb = corner[index+1].y - y1;
            }

            unsigned int lena = (unsigned int)sqrt( (double)(xa*xa + ya*ya) );
            unsigned int lenb = (unsigned int)sqrt( (double)(xb*xb + yb*yb) );
            unsigned int distance = aDistance;

            // Chamfer one half of an edge at most
            if( 0.5*lena < distance )
                distance = (unsigned int)(0.5*(double)lena);

            if( 0.5*lenb < distance )
                distance = (unsigned int)(0.5*(double)lenb);

            nx = (int) ( (double) (distance*xa)/sqrt( (double) (xa*xa + ya*ya) ) );
            ny = (int) ( (double) (distance*ya)/sqrt( (double) (xa*xa + ya*ya) ) );

            if( index == startIndex )
                newPoly->Start( GetLayer(), x1 + nx, y1 + ny, GetHatchStyle() );
            else
                newPoly->AppendCorner( x1 + nx, y1 + ny );

            nx = (int) ( (double) (distance*xb)/sqrt( (double) (xb*xb + yb*yb) ) );
            ny = (int) ( (double) (distance*yb)/sqrt( (double) (xb*xb + yb*yb) ) );
            newPoly->AppendCorner( x1 + nx, y1 + ny );
        }
        newPoly->Close();
    }

    return newPoly;
}


CPolyLine* CPolyLine::Fillet( unsigned int aRadius, unsigned int aSegments )
{
    CPolyLine* newPoly = new CPolyLine;

    if( !aRadius )
    {
        newPoly->Copy( this );
        return newPoly;
    }

    for( int contour = 0; contour < GetNumContours(); contour++ )
    {
        unsigned int startIndex = GetContourStart( contour );
        unsigned int endIndex = GetContourEnd( contour );

        for( unsigned int index = startIndex; index <= endIndex; index++ )
        {

            int x1, y1; // Current vertex
            long long xa, ya; // Previous vertex
            long long xb, yb; // Next vertex
            double nx, ny;

            x1 = corner[index].x;
            y1 = corner[index].y;

            if( index == startIndex )
            {
                xa = corner[endIndex].x - x1;
                ya = corner[endIndex].y - y1;
            }
            else
            {
                xa = corner[index-1].x - x1;
                ya = corner[index-1].y - y1;
            }

            if( index == endIndex )
            {
                xb = corner[startIndex].x - x1;
                yb = corner[startIndex].y - y1;
            }
            else
            {
                xb = corner[index+1].x - x1;
                yb = corner[index+1].y - y1;
            }

            double lena = sqrt( (double) (xa*xa + ya*ya) );
            double lenb = sqrt( (double) (xb*xb + yb*yb) );
            double cosine = ( xa*xb + ya*yb )/( lena*lenb );

            unsigned int radius = aRadius;
            double denom = sqrt( 2.0/( 1+cosine )-1 );

            // Limit rounding distance to one half of an edge
            if( 0.5*lena*denom < radius )
                radius = (unsigned int)(0.5*lena*denom);

            if( 0.5*lenb*denom < radius )
                radius = (unsigned int)(0.5*lenb*denom);

            // Calculate fillet arc absolute center point (xc, yx)
            double k = radius / sqrt( .5*( 1-cosine ) );
            double lenab = sqrt( ( xa/lena + xb/lenb )*( xa/lena + xb/lenb ) +
                                 ( ya/lena + yb/lenb )*( ya/lena + yb/lenb ) );
            double xc = x1 + k*( xa/lena + xb/lenb )/lenab;
            double yc = y1 + k*( ya/lena + yb/lenb )/lenab;

            // Calculate arc start and end vectors
            k = radius / sqrt( 2/( 1+cosine )-1 );
            double xs = x1 + k*xa/lena - xc;
            double ys = y1 + k*ya/lena - yc;
            double xe = x1 + k*xb/lenb - xc;
            double ye = y1 + k*yb/lenb - yc;

            // Cosine of arc angle
            double argument = ( xs*xe + ys*ye ) / ( radius*radius );

            if( argument < -1 ) // Just in case...
                argument = -1;
            else if( argument > 1 )
                argument = 1;

            double arcAngle = acos( argument );

            // Calculate the number of segments
            double tempSegments = (double)aSegments * ( arcAngle / ( 2*M_PI ) );

            if( tempSegments - (int)tempSegments > 0 )
                tempSegments++;
            unsigned int segments = (unsigned int) tempSegments;

            double deltaAngle = arcAngle / segments;
            double startAngle = atan2( -ys, xs );

            // Flip arc for inner corners
            if( xa*yb - ya*xb <= 0 )
                deltaAngle *= -1;

            nx = xc + xs + 0.5;
            ny = yc + ys + 0.5;
            if( index == startIndex )
                newPoly->Start( GetLayer(), (int)nx, (int)ny, GetHatchStyle() );
            else
                newPoly->AppendCorner( (int)nx, (int)ny );

            unsigned int nVertices = 0;
            for( unsigned int j = 0; j < segments; j++ )
            {
                nx = xc + cos( startAngle + (j+1)*deltaAngle )*radius + 0.5;
                ny = yc - sin( startAngle + (j+1)*deltaAngle )*radius + 0.5;
                newPoly->AppendCorner( (int)nx, (int)ny );
                nVertices++;
            }
        }
        newPoly->Close();
    }
    return newPoly;
}


/******************************************/
void CPolyLine::RemoveAllContours( void )
/******************************************/

/**
 * function RemoveAllContours
 * removes all corners from the lists.
 * Others params are not chnaged
 */
{
    corner.clear();
    side_style.clear();
}


/**
 * Function InsertCorner
 * insert a new corner between two existing corners
 * @param ic = index for the insertion point: the corner is inserted AFTER ic
 * @param x, y = coordinates corner to insert
 */
void CPolyLine::InsertCorner( int ic, int x, int y )
{
    UnHatch();
    if( (unsigned) (ic) >= corner.size() )
    {
        corner.push_back( CPolyPt( x, y ) );
        side_style.push_back( STRAIGHT );
    }
    else
    {
        corner.insert( corner.begin() + ic + 1, CPolyPt( x, y ) );
        side_style.insert( side_style.begin() + ic + 1, STRAIGHT );
    }

    if( (unsigned) (ic + 1) < corner.size() )
    {
        if( corner[ic].end_contour )
        {
            corner[ic + 1].end_contour = true;
            corner[ic].end_contour = false;
        }
    }
    Hatch();
}


// undraw polyline by removing all graphic elements from display list
//
void CPolyLine::UnHatch()
{
    m_HatchLines.clear();
}


int CPolyLine::GetEndContour( int ic )
{
    return corner[ic].end_contour;
}


CRect CPolyLine::GetBounds()
{
    CRect r = GetCornerBounds();

    r.left   -= m_Width / 2;
    r.right  += m_Width / 2;
    r.bottom -= m_Width / 2;
    r.top += m_Width / 2;
    return r;
}


CRect CPolyLine::GetCornerBounds()
{
    CRect r;

    r.left  = r.bottom = INT_MAX;
    r.right = r.top = INT_MIN;
    for( unsigned i = 0; i<corner.size(); i++ )
    {
        r.left   = min( r.left, corner[i].x );
        r.right  = max( r.right, corner[i].x );
        r.bottom = min( r.bottom, corner[i].y );
        r.top    = max( r.top, corner[i].y );
    }

    return r;
}


CRect CPolyLine::GetCornerBounds( int icont )
{
    CRect r;

    r.left  = r.bottom = INT_MAX;
    r.right = r.top = INT_MIN;
    int istart = GetContourStart( icont );
    int iend   = GetContourEnd( icont );
    for( int i = istart; i<=iend; i++ )
    {
        r.left   = MIN( r.left, corner[i].x );
        r.right  = MAX( r.right, corner[i].x );
        r.bottom = MIN( r.bottom, corner[i].y );
        r.top    = MAX( r.top, corner[i].y );
    }

    return r;
}


int CPolyLine::GetNumCorners()
{
    return corner.size();
}


int CPolyLine::GetNumSides()
{
    if( GetClosed() )
        return corner.size();
    else
        return corner.size() - 1;
}


int CPolyLine::GetNumContours()
{
    int ncont = 0;

    if( !corner.size() )
        return 0;

    for( unsigned ic = 0; ic<corner.size(); ic++ )
        if( corner[ic].end_contour )
            ncont++;

    if( !corner[corner.size() - 1].end_contour )
        ncont++;
    return ncont;
}


int CPolyLine::GetContour( int ic )
{
    int ncont = 0;

    for( int i = 0; i<ic; i++ )
    {
        if( corner[i].end_contour )
            ncont++;
    }

    return ncont;
}


int CPolyLine::GetContourStart( int icont )
{
    if( icont == 0 )
        return 0;

    int ncont = 0;
    for( unsigned i = 0; i<corner.size(); i++ )
    {
        if( corner[i].end_contour )
        {
            ncont++;
            if( ncont == icont )
                return i + 1;
        }
    }

    wxASSERT( 0 );
    return 0;
}


int CPolyLine::GetContourEnd( int icont )
{
    if( icont < 0 )
        return 0;

    if( icont == GetNumContours() - 1 )
        return corner.size() - 1;

    int ncont = 0;
    for( unsigned i = 0; i<corner.size(); i++ )
    {
        if( corner[i].end_contour )
        {
            if( ncont == icont )
                return i;
            ncont++;
        }
    }

    wxASSERT( 0 );
    return 0;
}


int CPolyLine::GetContourSize( int icont )
{
    return GetContourEnd( icont ) - GetContourStart( icont ) + 1;
}


void CPolyLine::SetSideStyle( int is, int style )
{
    UnHatch();
    CPoint p1, p2;
    if( is == (int) (corner.size() - 1) )
    {
        p1.x = corner[corner.size() - 1].x;
        p1.y = corner[corner.size() - 1].y;
        p2.x = corner[0].x;
        p2.y = corner[0].y;
    }
    else
    {
        p1.x = corner[is].x;
        p1.y = corner[is].y;
        p2.x = corner[is + 1].x;
        p2.y = corner[is + 1].y;
    }
    if( p1.x == p2.x || p1.y == p2.y )
        side_style[is] = STRAIGHT;
    else
        side_style[is] = style;
    Hatch();
}


int CPolyLine::GetSideStyle( int is )
{
    return side_style[is];
}


int CPolyLine::GetClosed()
{
    if( corner.size() == 0 )
        return 0;
    else
        return corner[corner.size() - 1].end_contour;
}


// Creates hatch lines inside the outline of the complex polygon
//
// sort function used in ::Hatch to sort points by descending CPoint.x values
bool sort_ends_by_descending_X( const CPoint& ref,  const CPoint& tst )
{
    return tst.x < ref.x;
}
void CPolyLine::Hatch()
{
    m_HatchLines.clear();

    if( m_hatchStyle == NO_HATCH || m_hatchPitch == 0 )
        return;

    if( !GetClosed() )   // If not closed, the poly is beeing created and not finalised. Not not hatch
        return;

    // define range for hatch lines
    int    min_x = corner[0].x;
    int    max_x = corner[0].x;
    int    min_y = corner[0].y;
    int    max_y = corner[0].y;
    for( unsigned ic = 1; ic < corner.size(); ic++ )
    {
        if( corner[ic].x < min_x )
            min_x = corner[ic].x;
        if( corner[ic].x > max_x )
            max_x = corner[ic].x;
        if( corner[ic].y < min_y )
            min_y = corner[ic].y;
        if( corner[ic].y > max_y )
            max_y = corner[ic].y;
    }

    // Calculate spacing betwwen 2 hatch lines
    int    spacing;
    if( m_hatchStyle == DIAGONAL_EDGE )
        spacing = m_hatchPitch;
    else
        spacing = m_hatchPitch * 2;

    // set the "lenght" of hatch lines (the lenght on horizontal axis)
    double hatch_line_len = m_hatchPitch;

    // To have a better look, give a slope depending on the layer
    int layer = GetLayer();
    int slope_flag = (layer & 1) ? 1 : -1; // 1 or -1
    double slope = 0.707106 * slope_flag;   // 45 degrees slope
    int max_a, min_a;
    if( slope_flag == 1 )
    {
        max_a = (int) (max_y - slope * min_x);
        min_a = (int) (min_y - slope * max_x);
    }
    else
    {
        max_a = (int) (max_y - slope * max_x);
        min_a = (int) (min_y - slope * min_x);
    }
    min_a = (min_a / spacing) * spacing;

    // calculate an offset depending on layer number,
    // for a better look of hatches on a multilayer board
    int offset = (layer * 7) / 8;
    min_a += offset;

    // now calculate and draw hatch lines
    int nc = corner.size();

    // loop through hatch lines
    #define MAXPTS 200      // Usually we store only few values per one hatch line
                            // depending on the compexity of the zone outline

    static std::vector <CPoint> pointbuffer;
    pointbuffer.clear();
    pointbuffer.reserve(MAXPTS+2);

    for( int a = min_a; a < max_a; a += spacing )
    {
        // get intersection points for this hatch line

        // Note: because we should have an even number of intersections with the
        // current hatch line and the zone outline (a closed polygon,
        // or a set of closed polygons), if an odd count is found
        // we skip this line (should not occur)
        pointbuffer.clear();
        int i_start_contour = 0;
        for( int ic = 0; ic<nc; ic++ )
        {
            double x, y, x2, y2;
            int    ok;
            if( corner[ic].end_contour || ( ic == (int) (corner.size() - 1) ) )
            {
                ok = FindLineSegmentIntersection( a, slope,
                    corner[ic].x, corner[ic].y,
                    corner[i_start_contour].x,
                    corner[i_start_contour].y,
                    side_style[ic],
                    &x, &y, &x2, &y2 );
                i_start_contour = ic + 1;
            }
            else
            {
                ok = FindLineSegmentIntersection( a, slope,
                    corner[ic].x, corner[ic].y,
                    corner[ic + 1].x, corner[ic + 1].y,
                    side_style[ic],
                    &x, &y, &x2, &y2 );
            }
            if( ok )
            {
                CPoint point( (int) x, (int) y);
                pointbuffer.push_back( point );
            }
            if( ok == 2 )
            {
                CPoint point( (int) x2, (int) y2);
                pointbuffer.push_back( point );
            }
            if( pointbuffer.size() >= MAXPTS )    // overflow
            {
                wxASSERT( 0 );
                break;
            }
        }

        // ensure we have found an even intersection points count
        // because intersections are the ends of segments
        // inside the polygon(s) and a segment has 2 ends.
        // if not, this is a strange case (a bug ?) so skip this hatch
        if( pointbuffer.size() % 2 != 0 )
            continue;

        // sort points in order of descending x (if more than 2) to
        // ensure the starting point and the ending point of the same segment
        // are stored one just after the other.
        if( pointbuffer.size() > 2 )
            sort( pointbuffer.begin(), pointbuffer.end(), sort_ends_by_descending_X );

        // creates lines or short segments inside the complex polygon
        for( unsigned ip = 0; ip < pointbuffer.size(); ip += 2 )
        {
            double dx = pointbuffer[ip + 1].x - pointbuffer[ip].x;
            // Push only one line for diagonal hatch,
            // or for small lines < twice the line len
            // else push 2 small lines
            if( m_hatchStyle == DIAGONAL_FULL || fabs( dx ) < 2 * hatch_line_len )
            {
                m_HatchLines.push_back( CSegment( pointbuffer[ip].x,
                                                  pointbuffer[ip].y,
                                                  pointbuffer[ip + 1].x,
                                                  pointbuffer[ip + 1].y ) );
            }
            else
            {
                double dy    = pointbuffer[ip + 1].y - pointbuffer[ip].y;
                double slope = dy / dx;

                if( dx > 0 )
                    dx = hatch_line_len;
                else
                    dx = -hatch_line_len;

                double x1 = pointbuffer[ip].x + dx;
                double x2 = pointbuffer[ip + 1].x - dx;
                double y1 = pointbuffer[ip].y + dx * slope;
                double y2 = pointbuffer[ip + 1].y - dx * slope;

                m_HatchLines.push_back( CSegment( pointbuffer[ip].x,
                                                  pointbuffer[ip].y,
                                                  to_int( x1 ), to_int( y1 ) ) );

                m_HatchLines.push_back( CSegment( pointbuffer[ip + 1].x,
                                                  pointbuffer[ip + 1].y,
                                                  to_int( x2 ), to_int( y2 ) ) );
            }
        }
    }
}


// test to see if a point is inside polyline
//
bool CPolyLine::TestPointInside( int px, int py )
{
    if( !GetClosed() )
    {
        wxASSERT( 0 );
    }

    // Test all polygons.
    // Since the first is the main outline, and other are hole,
    // if the tested point is inside only one contour, it is inside the whole polygon
    // (in fact inside the main outline, and outside all holes).
    // if inside 2 contours (the main outline + an hole), it is outside the poly.
    int polycount = GetNumContours();
    bool inside = false;
    for( int icont = 0; icont < polycount; icont++ )
    {
        int istart = GetContourStart( icont );
        int iend   = GetContourEnd( icont );

        // Test this polygon:
        if( TestPointInsidePolygon( corner, istart, iend, px, py) )   // test point inside the current polygon
            inside = not inside;
    }

    return inside;
}

// copy data from another poly, but don't draw it
//
void CPolyLine::Copy( CPolyLine* src )
{
    UnHatch();
    m_hatchStyle = src->m_hatchStyle;
    m_hatchPitch = src->m_hatchPitch;
    // copy corners, using vector copy
    corner = src->corner;
    // copy side styles, using vector copy
    side_style = src->side_style;
}


/*******************************************/
bool CPolyLine::IsCutoutContour( int icont )
/*******************************************/

/*
 * return true if the corner icont is inside the outline (i.e it is a hole)
 */
{
    int ncont = GetContour( icont );

    if( ncont == 0 )  // the first contour is the main outline, not an hole
        return false;
    return true;
}


void CPolyLine::MoveOrigin( int x_off, int y_off )
{
    UnHatch();
    for( int ic = 0; ic < GetNumCorners(); ic++ )
    {
        SetX( ic, GetX( ic ) + x_off );
        SetY( ic, GetY( ic ) + y_off );
    }

    Hatch();
}


// Set various parameters:
//   the calling function should UnHatch() before calling them,
//   and Draw() after
//
void CPolyLine::SetX( int ic, int x )
{
    corner[ic].x = x;
}


void CPolyLine::SetY( int ic, int y )
{
    corner[ic].y = y;
}


void CPolyLine::SetEndContour( int ic, bool end_contour )
{
    corner[ic].end_contour = end_contour;
}


void CPolyLine::AppendArc( int xi, int yi, int xf, int yf, int xc, int yc, int num )
{
    // get radius
    double r = sqrt( (double) (xi - xc) * (xi - xc) + (double) (yi - yc) * (yi - yc) );

    // get angles of start and finish
    double th_i  = atan2( (double) (yi - yc), (double) (xi - xc) );
    double th_f  = atan2( (double) (yf - yc), (double) (xf - xc) );
    double th_d  = (th_f - th_i) / (num - 1);
    double theta = th_i;

    // generate arc
    for( int ic = 0; ic<num; ic++ )
    {
        int x = to_int( xc + r * cos( theta ) );
        int y = to_int( yc + r * sin( theta ) );
        AppendCorner( x, y, STRAIGHT, 0 );
        theta += th_d;
    }

    Close( STRAIGHT );
}

// Bezier Support
void CPolyLine::AppendBezier(int x1, int y1, int x2, int y2, int x3, int y3) {
    std::vector<wxPoint> bezier_points;

    bezier_points = Bezier2Poly(x1,y1,x2,y2,x3,y3);
    for( unsigned int i = 0; i < bezier_points.size() ; i++)
        AppendCorner( bezier_points[i].x, bezier_points[i].y);
}

void CPolyLine::AppendBezier(int x1, int y1, int x2, int y2, int x3, int y3, int x4, int y4){
    std::vector<wxPoint> bezier_points;

    bezier_points = Bezier2Poly(x1,y1,x2,y2,x3,y3,x4,y4);
    for( unsigned int i = 0; i < bezier_points.size() ; i++)
        AppendCorner( bezier_points[i].x, bezier_points[i].y);
}