static VECTOR2I pushoutForce( const SHAPE_CIRCLE& aA, const SEG& aB, int aClearance )
{
    VECTOR2I f( 0, 0 );

    const VECTOR2I c = aA.GetCenter();
    const VECTOR2I nearest = aB.NearestPoint( c );

    const int r = aA.GetRadius();

    int dist = ( nearest - c ).EuclideanNorm();
    int min_dist = aClearance + r;

    if( dist < min_dist )
    {
        for( int corr = 0; corr < 5; corr++ )
        {
            f = ( aA.GetCenter() - nearest ).Resize( min_dist - dist + corr );

            if( aB.Distance( c + f ) >= min_dist )
                break;
        }
    }

    return f;
}
const SHAPE_LINE_CHAIN PNS_SOLID::Hull( int aClearance, int aWalkaroundThickness ) const
{
    int cl = aClearance + aWalkaroundThickness / 2;

    switch( m_shape->Type() )
    {
    case SH_RECT:
    {
        SHAPE_RECT* rect = static_cast<SHAPE_RECT*>( m_shape );
        return OctagonalHull( rect->GetPosition(), rect->GetSize(), cl + 1, 0.2 * cl );
    }

    case SH_CIRCLE:
    {
        SHAPE_CIRCLE* circle = static_cast<SHAPE_CIRCLE*>( m_shape );
        int r = circle->GetRadius();
        return OctagonalHull( circle->GetCenter() - VECTOR2I( r, r ), VECTOR2I( 2 * r, 2 * r ),
                              cl + 1, 0.52 * ( r + cl ) );
    }

    case SH_SEGMENT:
    {
        SHAPE_SEGMENT* seg = static_cast<SHAPE_SEGMENT*> ( m_shape );
        return SegmentHull( *seg, aClearance, aWalkaroundThickness );
    }

    default:
        break;
    }

    return SHAPE_LINE_CHAIN();
}
static inline bool Collide( const SHAPE_CIRCLE& aA, const SHAPE_CIRCLE& aB, int aClearance,
                            bool aNeedMTV, VECTOR2I& aMTV )
{
    ecoord min_dist = aClearance + aA.GetRadius() + aB.GetRadius();
    ecoord min_dist_sq = min_dist * min_dist;

    const VECTOR2I delta = aB.GetCenter() - aA.GetCenter();

    ecoord dist_sq = delta.SquaredEuclideanNorm();

    if( dist_sq >= min_dist_sq )
        return false;

    if( aNeedMTV )
        aMTV = delta.Resize( min_dist - sqrt( dist_sq ) + 3 );  // fixme: apparent rounding error

    return true;
}
static VECTOR2I pushoutForce( const SHAPE_CIRCLE& aA, const SEG& aB, int aClearance )
{
    VECTOR2I nearest = aB.NearestPoint( aA.GetCenter() );
    VECTOR2I f (0, 0);

    int dist = ( nearest - aA.GetCenter() ).EuclideanNorm();
    int min_dist = aClearance + aA.GetRadius();

    if( dist < min_dist )
        f = ( aA.GetCenter() - nearest ).Resize ( min_dist - dist + 10 );

    return f;
}
static inline bool Collide( const SHAPE_CIRCLE& aA, const SHAPE_SIMPLE& aB, int aClearance,
                            bool aNeedMTV, VECTOR2I& aMTV )
{
    bool found;
    const SHAPE_LINE_CHAIN& lc( aB.Vertices() );

    found = lc.Distance( aA.GetCenter() ) <= aClearance + aA.GetRadius();

    if( !aNeedMTV || !found )
        return found;

    SHAPE_CIRCLE cmoved( aA );
    VECTOR2I f_total( 0, 0 );

    for( int s = 0; s < lc.SegmentCount(); s++ )
    {
        VECTOR2I f = pushoutForce( cmoved, lc.CSegment( s ), aClearance );
        cmoved.SetCenter( cmoved.GetCenter() + f );
        f_total += f;
    }

    aMTV = f_total;
    return found;
}
static inline bool Collide( const SHAPE_RECT& aA, const SHAPE_CIRCLE& aB, int aClearance,
                            bool aNeedMTV, VECTOR2I& aMTV )
{
    const VECTOR2I c = aB.GetCenter();
    const VECTOR2I p0 = aA.GetPosition();
    const VECTOR2I size = aA.GetSize();
    const int r = aB.GetRadius();
    const int min_dist = aClearance + r;

    const VECTOR2I vts[] =
    {
        VECTOR2I( p0.x,          p0.y ),
        VECTOR2I( p0.x,          p0.y + size.y ),
        VECTOR2I( p0.x + size.x, p0.y + size.y ),
        VECTOR2I( p0.x + size.x, p0.y ),
        VECTOR2I( p0.x,          p0.y )
    };

    int nearest_seg_dist = INT_MAX;
    VECTOR2I nearest;

    bool inside = c.x >= p0.x && c.x <= ( p0.x + size.x )
                  && c.y >= p0.y && c.y <= ( p0.y + size.y );


    if( !aNeedMTV && inside )
        return true;

    for( int i = 0; i < 4; i++ )
    {
        const SEG seg( vts[i], vts[i + 1] );

        VECTOR2I pn = seg.NearestPoint( c );

        int d = ( pn - c ).EuclideanNorm();

        if( ( d < min_dist ) && !aNeedMTV )
            return true;

        if( d < nearest_seg_dist )
        {
            nearest = pn;
            nearest_seg_dist = d;
        }
    }

    if( nearest_seg_dist >= min_dist && !inside )
        return false;

    VECTOR2I delta = c - nearest;

    if( !aNeedMTV )
        return true;


    if( inside )
        aMTV = -delta.Resize( abs( min_dist + 1 + nearest_seg_dist ) + 1 );
    else
        aMTV = delta.Resize( abs( min_dist + 1 - nearest_seg_dist ) + 1 );


    return true;
}
static inline  bool Collide( const SHAPE_RECT& aA, const SHAPE_CIRCLE& aB, int aClearance,
                             bool aNeedMTV, VECTOR2I& aMTV )
{
    const VECTOR2I c = aB.GetCenter();
    const VECTOR2I p0 = aA.GetPosition();
    const VECTOR2I size = aA.GetSize();
    const ecoord r = aB.GetRadius();
    const ecoord min_dist = aClearance + r;
    const ecoord min_dist_sq = min_dist * min_dist;

    if( aA.BBox( 0 ).Contains( c ) )
        return true;

    const VECTOR2I vts[] =
    {
        VECTOR2I( p0.x,          p0.y ),
        VECTOR2I( p0.x,          p0.y + size.y ),
        VECTOR2I( p0.x + size.x, p0.y + size.y ),
        VECTOR2I( p0.x + size.x, p0.y ),
        VECTOR2I( p0.x,          p0.y )
    };

    ecoord nearest_seg_dist_sq = VECTOR2I::ECOORD_MAX;
    VECTOR2I nearest;

    bool inside = c.x >= p0.x && c.x <= ( p0.x + size.x )
                  && c.y >= p0.y && c.y <= ( p0.y + size.y );

    if( !inside )
    {
        for( int i = 0; i < 4; i++ )
        {
            const SEG seg( vts[i], vts[i + 1] );
            ecoord dist_sq = seg.SquaredDistance( c );

            if( dist_sq < min_dist_sq )
            {
                if( !aNeedMTV )
                    return true;
                else
                {
                    nearest = seg.NearestPoint( c );
                    nearest_seg_dist_sq = dist_sq;
                }
            }
        }
    }

    if( nearest_seg_dist_sq >= min_dist_sq && !inside )
        return false;

    VECTOR2I delta = c - nearest;

    if( !aNeedMTV )
        return true;

    if( inside )
        aMTV = -delta.Resize( sqrt( abs( r * r + nearest_seg_dist_sq ) + 1 ) );
    else
        aMTV = delta.Resize( sqrt( abs( r * r - nearest_seg_dist_sq ) + 1 ) );

    return true;
}