# Program Listing for File BiarcList.cc

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    /*--------------------------------------------------------------------------*\
     |                                                                          |
     |  Copyright (C) 2017                                                      |
     |                                                                          |
     |         , __                 , __                                        |
     |        /|/  \               /|/  \                                       |
     |         | __/ _   ,_         | __/ _   ,_                                |
     |         |   \|/  /  |  |   | |   \|/  /  |  |   |                        |
     |         |(__/|__/   |_/ \_/|/|(__/|__/   |_/ \_/|/                       |
     |                           /|                   /|                        |
     |                           \|                   \|                        |
     |                                                                          |
     |      Enrico Bertolazzi                                                   |
     |      Dipartimento di Ingegneria Industriale                              |
     |      Universita` degli Studi di Trento                                   |
     |      email: enrico.bertolazzi@unitn.it                                   |
     |                                                                          |
    \*--------------------------------------------------------------------------*/

    #include "Clothoids.hh"

    #include <cfloat>
    #include <limits>

    #ifdef __GNUC__
    #pragma GCC diagnostic push
    #pragma GCC diagnostic ignored "-Wsign-conversion"
    #endif
    #ifdef __clang__
    #pragma clang diagnostic push
    #pragma clang diagnostic ignored "-Wsign-conversion"
    #endif

    namespace G2lib {

      using std::numeric_limits;
      using std::lower_bound;
      using std::vector;
      using std::swap;
      using std::abs;

      /*\
       |   ____ _       _   _           _     _ _     _     _
       |  / ___| | ___ | |_| |__   ___ (_) __| | |   (_)___| |_
       | | |   | |/ _ \| __| '_ \ / _ \| |/ _` | |   | / __| __|
       | | |___| | (_) | |_| | | | (_) | | (_| | |___| \__ \ |_
       |  \____|_|\___/ \__|_| |_|\___/|_|\__,_|_____|_|___/\__|
       |
      \*/

      BiarcList::BiarcList( LineSegment const & LS )
      : BaseCurve(G2LIB_BIARC_LIST)
      , m_aabb_done(false)
      {
        this->resetLastInterval();
        this->init();
        this->push_back( LS );
      }

      BiarcList::BiarcList( CircleArc const & C )
      : BaseCurve(G2LIB_BIARC_LIST)
      , m_aabb_done(false)
      {
        this->resetLastInterval();
        this->init();
        this->push_back( C );
      }

      BiarcList::BiarcList( Biarc const & C )
      : BaseCurve(G2LIB_BIARC_LIST)
      , m_aabb_done(false)
      {
        this->resetLastInterval();
        this->init();
        this->push_back( C );
      }

      BiarcList::BiarcList( PolyLine const & pl )
      : BaseCurve(G2LIB_BIARC_LIST)
      , m_aabb_done(false)
      {
        this->resetLastInterval();
        this->init();
        this->push_back( pl );
      }

      BiarcList::BiarcList( BaseCurve const & C )
      : BaseCurve(G2LIB_BIARC_LIST)
      , m_aabb_done(false)
      {
        this->resetLastInterval();
        this->init();
        switch ( C.type() ) {
        case G2LIB_LINE:
          push_back( *static_cast<LineSegment const *>(&C) );
          break;
        case G2LIB_CIRCLE:
          push_back( *static_cast<CircleArc const *>(&C) );
          break;
        case G2LIB_BIARC:
          push_back( *static_cast<Biarc const *>(&C) );
          break;
        case G2LIB_BIARC_LIST:
          copy( *static_cast<BiarcList const *>(&C) );
          break;
        case G2LIB_POLYLINE:
          push_back( *static_cast<PolyLine const *>(&C) );
          break;
        case G2LIB_CLOTHOID:
        case G2LIB_CLOTHOID_LIST:
          UTILS_ERROR(
            "BiarcList constructor cannot convert from: {}\n",
            CurveType_name[C.type()]
          );
        }
      }

      // - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

      void
      BiarcList::init() {
        m_s0.clear();
        m_biarcList.clear();
        this->resetLastInterval();
        m_aabb_done = false;
      }

      // - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

      void
      BiarcList::copy( BiarcList const & L ) {
        this->init();
        m_biarcList.reserve(L.m_biarcList.size());
        std::copy( L.m_biarcList.begin(),
                   L.m_biarcList.end(),
                   back_inserter(m_biarcList) );
        m_s0.reserve(L.m_s0.size());
        std::copy( L.m_s0.begin(), L.m_s0.end(), back_inserter(m_s0) );
      }

      // - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

      int_type
      BiarcList::findAtS( real_type & s ) const {
        bool ok;
        int_type & lastInterval = *m_lastInterval.search( std::this_thread::get_id(), ok );
        Utils::searchInterval<int_type,real_type>(
          static_cast<int_type>(m_s0.size()),
          &m_s0.front(), s, lastInterval, false, true
        );
        return lastInterval;
      }

      // - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

      void
      BiarcList::reserve( int_type n ) {
        m_s0.reserve(size_t(n+1));
        m_biarcList.reserve(size_t(n));
      }

      // - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

      void
      BiarcList::push_back( LineSegment const & LS ) {
        if ( m_biarcList.empty() ) {
          m_s0.push_back(0);
          m_s0.push_back(LS.length());
        } else {
          m_s0.push_back(m_s0.back()+LS.length());
        }
        m_biarcList.push_back(Biarc(LS));
      }

      // - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

      void
      BiarcList::push_back( CircleArc const & C ) {
        if ( m_biarcList.empty() ) {
          m_s0.push_back(0);
          m_s0.push_back(C.length());
        } else {
          m_s0.push_back(m_s0.back()+C.length());
        }
        m_biarcList.push_back(Biarc(C));
      }

      // - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

      void
      BiarcList::push_back( Biarc const & c ) {
        if ( m_biarcList.empty() ) {
          m_s0.push_back(0);
          m_s0.push_back(c.length());
        } else {
          m_s0.push_back(m_s0.back()+c.length());
        }
        m_biarcList.push_back(c);
      }

      // - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

      void
      BiarcList::push_back( PolyLine const & c ) {
        m_s0.reserve( m_s0.size() + c.m_polylineList.size() + 1 );
        m_biarcList.reserve( m_biarcList.size() + c.m_polylineList.size() );

        if ( m_s0.empty() ) m_s0.push_back(0);

        vector<LineSegment>::const_iterator ip = c.m_polylineList.begin();
        for (; ip != c.m_polylineList.end(); ++ip ) {
          m_s0.push_back(m_s0.back()+ip->length());
          m_biarcList.push_back(Biarc(*ip));
        }
      }

      // - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

      void
      BiarcList::push_back_G1(
        real_type x1,
        real_type y1,
        real_type theta1
      ) {
        UTILS_ASSERT0(
          !m_biarcList.empty(),
          "BiarcList::push_back_G1(...) empty list!\n"
        );
        Biarc c;
        real_type x0     = m_biarcList.back().xEnd();
        real_type y0     = m_biarcList.back().yEnd();
        real_type theta0 = m_biarcList.back().thetaEnd();
        c.build( x0, y0, theta0, x1, y1, theta1 );
        push_back( c );
      }

      // - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

      void
      BiarcList::push_back_G1(
        real_type x0,
        real_type y0,
        real_type theta0,
        real_type x1,
        real_type y1,
        real_type theta1
      ) {
        Biarc c;
        c.build( x0, y0, theta0, x1, y1, theta1 );
        push_back( c );
      }

      // - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

      bool
      BiarcList::build_G1(
        int_type          n,
        real_type const * x,
        real_type const * y,
        real_type const * theta
      ) {
        UTILS_ASSERT0(
          n > 1,
          "BiarcList::build_G1, at least 2 points are necessary\n"
        );
        init();
        reserve( n-1 );
        Biarc c;
        for ( int_type k = 1; k < n; ++k ) {
          c.build( x[k-1], y[k-1], theta[k-1], x[k], y[k], theta[k] );
          this->push_back(c);
        }
        return true;
      }

      // - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

      bool
      BiarcList::build_G1(
        int_type          n,
        real_type const * x,
        real_type const * y
      ) {
        size_t nn = size_t(n);
        Utils::Malloc<real_type> mem( "BiarcList::build_G1" );
        mem.allocate( 5 * nn );
        real_type * theta     = mem( nn );
        real_type * theta_min = mem( nn );
        real_type * theta_max = mem( nn );
        real_type * omega     = mem( nn );
        real_type * len       = mem( nn );
        G2lib::xy_to_guess_angle(
          n, x, y, theta, theta_min, theta_max, omega, len
        );
        return this->build_G1( n, x, y, theta );
      }

      // - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

      Biarc const &
      BiarcList::get( int_type idx ) const {
        UTILS_ASSERT(
          !m_biarcList.empty(),
          "BiarcList::get( {} ) empty list\n", idx
        );
        UTILS_ASSERT(
          idx >= 0 && idx < int_type(m_biarcList.size()),
          "BiarcList::get( {} ) bad index, must be in [0,{}]\n",
          idx, m_biarcList.size()-1
        );
        return m_biarcList[idx];
      }

      // - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

      Biarc const &
      BiarcList::getAtS( real_type s ) const
      { return this->get(findAtS(s)); }

      /*\
       |   _                  _   _
       |  | | ___ _ __   __ _| |_| |__
       |  | |/ _ \ '_ \ / _` | __| '_ \
       |  | |  __/ | | | (_| | |_| | | |
       |  |_|\___|_| |_|\__, |\__|_| |_|
       |                |___/
      \*/

      real_type
      BiarcList::length() const {
        return m_s0.back() - m_s0.front();
      }

      real_type
      BiarcList::length_ISO( real_type offs ) const {
        real_type L = 0;
        vector<Biarc>::const_iterator is = m_biarcList.begin();
        for (; is != m_biarcList.end(); ++is ) L += is->length_ISO( offs );
        return L;
      }

      real_type
      BiarcList::segment_length( int_type nseg ) const {
        Biarc const & c = this->get( nseg );
        return c.length();
      }

      real_type
      BiarcList::segment_length_ISO( int_type nseg, real_type offs ) const {
        Biarc const & c = this->get( nseg );
        return c.length_ISO( offs );
      }

      /*\
       |   _    _   _____    _                _
       |  | |__| |_|_   _| _(_)__ _ _ _  __ _| |___
       |  | '_ \ '_ \| || '_| / _` | ' \/ _` | / -_)
       |  |_.__/_.__/|_||_| |_\__,_|_||_\__, |_\___|
       |                                |___/
      \*/

      void
      BiarcList::bbTriangles(
        vector<Triangle2D> & tvec,
        real_type            max_angle,
        real_type            max_size,
        int_type             icurve
      ) const {
        vector<Biarc>::const_iterator ic = m_biarcList.begin();
        for ( int_type ipos = icurve; ic != m_biarcList.end(); ++ic, ++ipos )
          ic->bbTriangles( tvec, max_angle, max_size, ipos );
      }

      void
      BiarcList::bbTriangles_ISO(
        real_type            offs,
        vector<Triangle2D> & tvec,
        real_type            max_angle,
        real_type            max_size,
        int_type             icurve
      ) const {
        vector<Biarc>::const_iterator ic = m_biarcList.begin();
        for ( int_type ipos = icurve; ic != m_biarcList.end(); ++ic, ++ipos )
          ic->bbTriangles_ISO( offs, tvec, max_angle, max_size, ipos );
      }

      void
      BiarcList::bbTriangles_SAE(
        real_type            offs,
        vector<Triangle2D> & tvec,
        real_type            max_angle,
        real_type            max_size,
        int_type             icurve
      ) const {
        vector<Biarc>::const_iterator ic = m_biarcList.begin();
        for ( int_type ipos = icurve; ic != m_biarcList.end(); ++ic, ++ipos )
          ic->bbTriangles_SAE( offs, tvec, max_angle, max_size, ipos );
      }

      /*\
       |   _     _
       |  | |__ | |__   _____  __
       |  | '_ \| '_ \ / _ \ \/ /
       |  | |_) | |_) | (_) >  <
       |  |_.__/|_.__/ \___/_/\_\
      \*/

      void
      BiarcList::bbox_ISO(
        real_type   offs,
        real_type & xmin,
        real_type & ymin,
        real_type & xmax,
        real_type & ymax
      ) const {
        vector<Triangle2D> tvec;
        bbTriangles_ISO( offs, tvec, Utils::m_pi/18, 1e100 );
        xmin = ymin = numeric_limits<real_type>::infinity();
        xmax = ymax = -xmin;
        vector<Triangle2D>::const_iterator it;
        for ( it = tvec.begin(); it != tvec.end(); ++it ) {
          // - - - - - - - - - - - - - - - - - - - -
          if      ( it->x1() < xmin ) xmin = it->x1();
          else if ( it->x1() > xmax ) xmax = it->x1();
          if      ( it->x2() < xmin ) xmin = it->x2();
          else if ( it->x2() > xmax ) xmax = it->x2();
          if      ( it->x3() < xmin ) xmin = it->x3();
          else if ( it->x3() > xmax ) xmax = it->x3();
          // - - - - - - - - - - - - - - - - - - - -
          if      ( it->y1() < ymin ) ymin = it->y1();
          else if ( it->y1() > ymax ) ymax = it->y1();
          if      ( it->y2() < ymin ) ymin = it->y2();
          else if ( it->y2() > ymax ) ymax = it->y2();
          if      ( it->y3() < ymin ) ymin = it->y3();
          else if ( it->y3() > ymax ) ymax = it->y3();
        }
      }

      /*\
       |  _   _          _
       | | |_| |__   ___| |_ __ _
       | | __| '_ \ / _ \ __/ _` |
       | | |_| | | |  __/ || (_| |
       |  \__|_| |_|\___|\__\__,_|
      \*/

      real_type
      BiarcList::theta( real_type s ) const {
        int_type idx = this->findAtS( s );
        Biarc const & c = this->get( idx );
        return c.theta( s - m_s0[idx] );
      }

      // - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

      real_type
      BiarcList::theta_D( real_type s ) const {
        int_type idx = this->findAtS( s );
        Biarc const & c = this->get( idx );
        return c.theta_D( s - m_s0[idx] );
      }

      // - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

      real_type
      BiarcList::theta_DD( real_type s ) const  {
        int_type idx = this->findAtS( s );
        Biarc const & c = this->get( idx );
        return c.theta_DD( s - m_s0[idx] );
      }

      // - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

      real_type
      BiarcList::theta_DDD( real_type s ) const {
        int_type idx = this->findAtS( s );
        Biarc const & c = this->get( idx );
        return c.theta_DDD( s - m_s0[idx] );
      }

      /*\
       |  _____                   _   _   _
       | |_   _|   __ _ _ __   __| | | \ | |
       |   | |    / _` | '_ \ / _` | |  \| |
       |   | |   | (_| | | | | (_| | | |\  |
       |   |_|    \__,_|_| |_|\__,_| |_| \_|
      \*/

      real_type
      BiarcList::tx( real_type s ) const {
        int_type idx = this->findAtS( s );
        Biarc const & c = this->get( idx );
        return c.tx( s - m_s0[idx] );
      }

      // - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

      real_type
      BiarcList::ty( real_type s ) const {
        int_type idx = this->findAtS( s );
        Biarc const & c = this->get( idx );
        return c.ty( s - m_s0[idx] );
      }

      // - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

      real_type
      BiarcList::tx_D( real_type s ) const {
        int_type idx = this->findAtS( s );
        Biarc const & c = this->get( idx );
        return c.tx_D( s - m_s0[idx] );
      }

      // - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

      real_type
      BiarcList::ty_D( real_type s ) const {
        int_type idx = this->findAtS( s );
        Biarc const & c = this->get( idx );
        return c.ty_D( s - m_s0[idx] );
      }

      // - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

      real_type
      BiarcList::tx_DD( real_type s ) const {
        int_type idx = this->findAtS( s );
        Biarc const & c = this->get( idx );
        return c.tx_DD( s - m_s0[idx] );
      }

      // - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

      real_type
      BiarcList::ty_DD( real_type s ) const {
        int_type idx = this->findAtS( s );
        Biarc const & c = this->get( idx );
        return c.ty_DD( s - m_s0[idx] );
      }

      // - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

      real_type
      BiarcList::tx_DDD( real_type s ) const {
        int_type idx = this->findAtS( s );
        Biarc const & c = this->get( idx );
        return c.tx_DDD( s - m_s0[idx] );
      }

      // - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

      real_type
      BiarcList::ty_DDD( real_type s ) const {
        int_type idx = this->findAtS( s );
        Biarc const & c = this->get( idx );
        return c.ty_DDD( s - m_s0[idx] );
      }

      // - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

      void
      BiarcList::tg(
        real_type   s,
        real_type & tg_x,
        real_type & tg_y
      ) const {
        int_type idx = this->findAtS( s );
        Biarc const & c = this->get( idx );
        return c.tg( s - m_s0[idx], tg_x, tg_y );
      }

      // - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

      void
      BiarcList::tg_D(
        real_type   s,
        real_type & tg_x_D,
        real_type & tg_y_D
      ) const {
        int_type idx = this->findAtS( s );
        Biarc const & c = this->get( idx );
        return c.tg_D( s - m_s0[idx], tg_x_D, tg_y_D );
      }

      // - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

      void
      BiarcList::tg_DD(
        real_type   s,
        real_type & tg_x_DD,
        real_type & tg_y_DD
      ) const {
        int_type idx = this->findAtS( s );
        Biarc const & c = this->get( idx );
        return c.tg_DD( s - m_s0[idx], tg_x_DD, tg_y_DD );
      }

      // - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

      void
      BiarcList::tg_DDD(
        real_type   s,
        real_type & tg_x_DDD,
        real_type & tg_y_DDD
      ) const {
        int_type idx = this->findAtS( s );
        Biarc const & c = this->get( idx );
        return c.tg_DDD( s - m_s0[idx], tg_x_DDD, tg_y_DDD );
      }

      // - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

      void
      BiarcList::evaluate(
        real_type   s,
        real_type & th,
        real_type & k,
        real_type & x,
        real_type & y
      ) const {
        int_type idx = this->findAtS( s );
        Biarc const & c = this->get( idx );
        c.evaluate( s - m_s0[idx], th, k, x, y );
      }

      // - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

      void
      BiarcList::evaluate_ISO(
        real_type   s,
        real_type   offs,
        real_type & th,
        real_type & k,
        real_type & x,
        real_type & y
      ) const {
        int_type idx = this->findAtS( s );
        Biarc const & c = this->get( idx );
        c.evaluate_ISO( s - m_s0[idx], offs, th, k, x, y );
      }

      // - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

      real_type
      BiarcList::X( real_type s ) const {
        int_type idx = this->findAtS( s );
        Biarc const & c = this->get( idx );
        return c.X( s - m_s0[idx] );
      }

      // - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

      real_type
      BiarcList::Y( real_type s ) const  {
        int_type idx = this->findAtS( s );
        Biarc const & c = this->get( idx );
        return c.Y( s - m_s0[idx] );
      }

      // - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

      real_type
      BiarcList::X_D( real_type s ) const {
        int_type idx = this->findAtS( s );
        Biarc const & c = this->get( idx );
        return c.X_D( s - m_s0[idx] );
      }

      // - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

      real_type
      BiarcList::Y_D( real_type s ) const {
        int_type idx = this->findAtS( s );
        Biarc const & c = this->get( idx );
        return c.Y_D( s - m_s0[idx] );
      }

      // - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

      real_type
      BiarcList::X_DD( real_type s ) const {
        int_type idx = this->findAtS( s );
        Biarc const & c = this->get( idx );
        return c.X_DD( s - m_s0[idx] );
      }

      // - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

      real_type
      BiarcList::Y_DD( real_type s ) const {
        int_type idx = this->findAtS( s );
        Biarc const & c = this->get( idx );
        return c.Y_DD( s - m_s0[idx] );
      }

      // - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

      real_type
      BiarcList::X_DDD( real_type s ) const {
        int_type idx = this->findAtS( s );
        Biarc const & c = this->get( idx );
        return c.X_DDD( s - m_s0[idx] );
      }

      // - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

      real_type
      BiarcList::Y_DDD( real_type s ) const {
        int_type idx = this->findAtS( s );
        Biarc const & c = this->get( idx );
        return c.Y_DDD( s - m_s0[idx] );
      }

      // - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

      void
      BiarcList::eval(
        real_type   s,
        real_type & x,
        real_type & y
      ) const {
        int_type idx = this->findAtS( s );
        Biarc const & c = this->get( idx );
        return c.eval( s - m_s0[idx], x, y );
      }

      // - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

      void
      BiarcList::eval_D(
        real_type   s,
        real_type & x_D,
        real_type & y_D
      ) const {
        int_type idx = this->findAtS( s );
        Biarc const & c = this->get( idx );
        return c.eval_D( s - m_s0[idx], x_D, y_D );
      }

      // - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

      void
      BiarcList::eval_DD(
        real_type   s,
        real_type & x_DD,
        real_type & y_DD
      ) const {
        int_type idx = this->findAtS( s );
        Biarc const & c = this->get( idx );
        return c.eval_DD( s - m_s0[idx], x_DD, y_DD );
      }

      // - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

      void
      BiarcList::eval_DDD(
        real_type   s,
        real_type & x_DDD,
        real_type & y_DDD
      ) const {
        int_type idx = this->findAtS( s );
        Biarc const & c = this->get( idx );
        return c.eval_DDD( s - m_s0[idx], x_DDD, y_DDD );
      }

      /*\
       |         __  __          _
       |   ___  / _|/ _|___  ___| |_
       |  / _ \| |_| |_/ __|/ _ \ __|
       | | (_) |  _|  _\__ \  __/ |_
       |  \___/|_| |_| |___/\___|\__|
      \*/

      real_type
      BiarcList::X_ISO( real_type s, real_type offs ) const {
        int_type idx = this->findAtS( s );
        Biarc const & c = this->get( idx );
        return c.X_ISO( s - m_s0[idx], offs );
      }

      // - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

      real_type
      BiarcList::Y_ISO( real_type s, real_type offs ) const {
        int_type idx = this->findAtS( s );
        Biarc const & c = this->get( idx );
        return c.Y_ISO( s - m_s0[idx], offs );
      }

      // - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

      real_type
      BiarcList::X_ISO_D( real_type s, real_type offs ) const {
        int_type idx = this->findAtS( s );
        Biarc const & c = this->get( idx );
        return c.X_ISO_D( s - m_s0[idx], offs );
      }

      // - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

      real_type
      BiarcList::Y_ISO_D( real_type s, real_type offs ) const {
        int_type idx = this->findAtS( s );
        Biarc const & c = this->get( idx );
        return c.Y_ISO_D( s - m_s0[idx], offs );
      }

      // - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

      real_type
      BiarcList::X_ISO_DD( real_type s, real_type offs ) const {
        int_type idx = this->findAtS( s );
        Biarc const & c = this->get( idx );
        return c.X_ISO_DD( s - m_s0[idx], offs );
      }

      // - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

      real_type
      BiarcList::Y_ISO_DD( real_type s, real_type offs ) const {
        int_type idx = this->findAtS( s );
        Biarc const & c = this->get( idx );
        return c.Y_ISO_DD( s - m_s0[idx], offs );
      }

      // - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

      real_type
      BiarcList::X_ISO_DDD( real_type s, real_type offs ) const {
        int_type idx = this->findAtS( s );
        Biarc const & c = this->get( idx );
        return c.X_ISO_DDD( s - m_s0[idx], offs );
      }

      // - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

      real_type
      BiarcList::Y_ISO_DDD( real_type s, real_type offs ) const {
        int_type idx = this->findAtS( s );
        Biarc const & c = this->get( idx );
        return c.Y_ISO_DDD( s - m_s0[idx], offs );
      }

      // - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

      void
      BiarcList::eval_ISO(
        real_type   s,
        real_type   offs,
        real_type & x,
        real_type & y
      ) const {
        int_type idx = this->findAtS( s );
        Biarc const & c = this->get( idx );
        return c.eval_ISO( s - m_s0[idx], offs, x, y );
      }

      // - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

      void
      BiarcList::eval_ISO_D(
        real_type   s,
        real_type   offs,
        real_type & x_D,
        real_type & y_D
      ) const {
        int_type idx = this->findAtS( s );
        Biarc const & c = this->get( idx );
        return c.eval_ISO_D( s - m_s0[idx], offs, x_D, y_D );
      }

      // - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

      void
      BiarcList::eval_ISO_DD(
        real_type   s,
        real_type   offs,
        real_type & x_DD,
        real_type & y_DD
      ) const {
        int_type idx = this->findAtS( s );
        Biarc const & c = this->get( idx );
        return c.eval_ISO_DD( s - m_s0[idx], offs, x_DD, y_DD );
      }

      // - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

      void
      BiarcList::eval_ISO_DDD(
        real_type   s,
        real_type   offs,
        real_type & x_DDD,
        real_type & y_DDD
      ) const {
        int_type idx = this->findAtS( s );
        Biarc const & c = this->get( idx );
        return c.eval_ISO_DDD( s - m_s0[idx], offs, x_DDD, y_DDD );
      }

      /*\
       |  _                        __
       | | |_ _ __ __ _ _ __  ___ / _| ___  _ __ _ __ ___
       | | __| '__/ _` | '_ \/ __| |_ / _ \| '__| '_ ` _ \
       | | |_| | | (_| | | | \__ \  _| (_) | |  | | | | | |
       |  \__|_|  \__,_|_| |_|___/_|  \___/|_|  |_| |_| |_|
      \*/

      void
      BiarcList::translate( real_type tx, real_type ty ) {
        vector<Biarc>::iterator ic = m_biarcList.begin();
        for (; ic != m_biarcList.end(); ++ic ) ic->translate( tx, ty );
      }

      // - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

      void
      BiarcList::rotate( real_type angle, real_type cx, real_type cy ) {
        vector<Biarc>::iterator ic = m_biarcList.begin();
        for (; ic != m_biarcList.end(); ++ic ) ic->rotate( angle, cx, cy );
      }

      // - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

      void
      BiarcList::scale( real_type sfactor ) {
        vector<Biarc>::iterator ic = m_biarcList.begin();
        real_type newx0 = ic->xBegin();
        real_type newy0 = ic->yBegin();
        m_s0[0] = 0;
        for ( size_t k=0; ic != m_biarcList.end(); ++ic, ++k ) {
          ic->scale( sfactor );
          ic->changeOrigin( newx0, newy0 );
          newx0     = ic->xEnd();
          newy0     = ic->yEnd();
          m_s0[k+1] = m_s0[k] + ic->length();
        }
      }

      // - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

      void
      BiarcList::reverse() {
        std::reverse( m_biarcList.begin(), m_biarcList.end() );
        vector<Biarc>::iterator ic = m_biarcList.begin();
        ic->reverse();
        real_type newx0 = ic->xEnd();
        real_type newy0 = ic->yEnd();
        m_s0[0] = 0;
        m_s0[1] = ic->length();
        size_t k = 1;
        for ( ++ic; ic != m_biarcList.end(); ++ic, ++k ) {
          ic->reverse();
          ic->changeOrigin( newx0, newy0 );
          newx0     = ic->xEnd();
          newy0     = ic->yEnd();
          m_s0[k+1] = m_s0[k] + ic->length();
        }
      }

      // - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

      void
      BiarcList::changeOrigin( real_type newx0, real_type newy0 ) {
        vector<Biarc>::iterator ic = m_biarcList.begin();
        for (; ic != m_biarcList.end(); ++ic ) {
          ic->changeOrigin( newx0, newy0 );
          newx0 = ic->xEnd();
          newy0 = ic->yEnd();
        }
      }

      // - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

      void
      BiarcList::trim( real_type s_begin, real_type s_end ) {
        UTILS_ASSERT(
          s_begin >= m_s0.front() && s_end <= m_s0.back() && s_end > s_begin,
          "BiarcList::trim( s_begin={}, s_end={} ) bad range, must be in [ {}, {} ]\n",
          s_begin, s_end, m_s0.front(), m_s0.back()
        );

        size_t i_begin = size_t( findAtS( s_begin ) );
        size_t i_end   = size_t( findAtS( s_end ) );
        if ( i_begin == i_end ) {
          m_biarcList[i_begin].trim( s_begin-m_s0[i_begin], s_end-m_s0[i_begin] );
        } else {
          m_biarcList[i_begin].trim( s_begin-m_s0[i_begin], m_s0[i_begin+1]-m_s0[i_begin] );
          m_biarcList[i_end].trim( 0, s_end-m_s0[i_end] );
        }
        m_biarcList.erase( m_biarcList.begin()+i_end+1, m_biarcList.end() );
        m_biarcList.erase( m_biarcList.begin(), m_biarcList.begin()+i_begin );
        if ( m_biarcList.back().length() <= machepsi100 ) m_biarcList.pop_back();
        vector<Biarc>::iterator ic = m_biarcList.begin();
        m_s0.resize( m_biarcList.size() + 1 );
        m_s0[0] = 0;
        size_t k = 0;
        for ( ++ic; ic != m_biarcList.end(); ++ic, ++k )
          m_s0[k+1] = m_s0[k] + ic->length();
        this->resetLastInterval();
      }

      /*\
       |     _        _    ____  ____  _
       |    / \      / \  | __ )| __ )| |_ _ __ ___  ___
       |   / _ \    / _ \ |  _ \|  _ \| __| '__/ _ \/ _ \
       |  / ___ \  / ___ \| |_) | |_) | |_| | |  __/  __/
       | /_/   \_\/_/   \_\____/|____/ \__|_|  \___|\___|
      \*/

      #ifndef DOXYGEN_SHOULD_SKIP_THIS
      void
      BiarcList::build_AABBtree_ISO(
        real_type offs,
        real_type max_angle,
        real_type max_size
      ) const {

        if ( m_aabb_done &&
             Utils::isZero( offs-m_aabb_offs ) &&
             Utils::isZero( max_angle-m_aabb_max_angle ) &&
             Utils::isZero( max_size-m_aabb_max_size ) ) return;

        #ifdef G2LIB_USE_CXX11
        vector<shared_ptr<BBox const> > bboxes;
        #else
        vector<BBox const *> bboxes;
        #endif

        bbTriangles_ISO( offs, m_aabb_tri, max_angle, max_size );
        bboxes.reserve(m_aabb_tri.size());
        vector<Triangle2D>::const_iterator it;
        int_type ipos = 0;
        for ( it = m_aabb_tri.begin(); it != m_aabb_tri.end(); ++it, ++ipos ) {
          real_type xmin, ymin, xmax, ymax;
          it->bbox( xmin, ymin, xmax, ymax );
          #ifdef G2LIB_USE_CXX11
          bboxes.push_back( make_shared<BBox const>(
            xmin, ymin, xmax, ymax, G2LIB_CLOTHOID, ipos
          ) );
          #else
          bboxes.push_back(
            new BBox( xmin, ymin, xmax, ymax, G2LIB_CLOTHOID, ipos )
          );
          #endif
        }
        m_aabb_tree.build(bboxes);
        m_aabb_done      = true;
        m_aabb_offs      = offs;
        m_aabb_max_angle = max_angle;
        m_aabb_max_size  = max_size;
      }
      #endif

      /*\
       |   _       _                          _
       |  (_)_ __ | |_ ___ _ __ ___  ___  ___| |_
       |  | | '_ \| __/ _ \ '__/ __|/ _ \/ __| __|
       |  | | | | | ||  __/ |  \__ \  __/ (__| |_
       |  |_|_| |_|\__\___|_|  |___/\___|\___|\__|
      \*/

      // - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

      bool
      BiarcList::collision( BiarcList const & C ) const {
        this->build_AABBtree_ISO( 0 );
        C.build_AABBtree_ISO( 0 );
        T2D_collision_list_ISO fun( this, 0, &C, 0 );
        return m_aabb_tree.collision( C.m_aabb_tree, fun, false );
      }

      // - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

      bool
      BiarcList::collision_ISO(
        real_type            offs,
        BiarcList const & C,
        real_type            offs_C
      ) const {
        this->build_AABBtree_ISO( offs );
        C.build_AABBtree_ISO( offs_C );
        T2D_collision_list_ISO fun( this, offs, &C, offs_C );
        return m_aabb_tree.collision( C.m_aabb_tree, fun, false );
      }

      /*\
       |   _       _                          _
       |  (_)_ __ | |_ ___ _ __ ___  ___  ___| |_
       |  | | '_ \| __/ _ \ '__/ __|/ _ \/ __| __|
       |  | | | | | ||  __/ |  \__ \  __/ (__| |_
       |  |_|_| |_|\__\___|_|  |___/\___|\___|\__|
       |
      \*/

      void
      BiarcList::intersect_ISO(
        real_type         offs,
        BiarcList const & CL,
        real_type         offs_CL,
        IntersectList   & ilist,
        bool              swap_s_vals
      ) const {
        if ( intersect_with_AABBtree ) {
          this->build_AABBtree_ISO( offs );
          CL.build_AABBtree_ISO( offs_CL );
          AABBtree::VecPairPtrBBox iList;
          m_aabb_tree.intersect( CL.m_aabb_tree, iList );

          AABBtree::VecPairPtrBBox::const_iterator ip;
          for ( ip = iList.begin(); ip != iList.end(); ++ip ) {
            size_t ipos1 = size_t(ip->first->Ipos());
            size_t ipos2 = size_t(ip->second->Ipos());

            Triangle2D const & T1 = m_aabb_tri[ipos1];
            Triangle2D const & T2 = CL.m_aabb_tri[ipos2];

            Biarc const & C1 = m_biarcList[T1.Icurve()];
            Biarc const & C2 = CL.m_biarcList[T2.Icurve()];

            IntersectList ilist1;
            C1.intersect_ISO( offs, C2, offs_CL, ilist1, false );

            for ( IntersectList::const_iterator it = ilist1.begin();
                  it != ilist1.end(); ++it ) {
              real_type ss1 = it->first  + m_s0[T1.Icurve()];
              real_type ss2 = it->second + CL.m_s0[T2.Icurve()];
              if ( swap_s_vals ) swap( ss1, ss2 );
              ilist.push_back( Ipair( ss1, ss2 ) );
            }
          }
        } else {
          bbTriangles_ISO( offs, m_aabb_tri, Utils::m_pi/18, 1e100 );
          CL.bbTriangles_ISO( offs_CL, CL.m_aabb_tri, Utils::m_pi/18, 1e100 );
          vector<Triangle2D>::const_iterator i1, i2;
          for ( i1 = m_aabb_tri.begin(); i1 != m_aabb_tri.end(); ++i1 ) {
            for ( i2 = CL.m_aabb_tri.begin(); i2 != CL.m_aabb_tri.end(); ++i2 ) {
              Triangle2D const & T1 = *i1;
              Triangle2D const & T2 = *i2;

              Biarc const & C1 = m_biarcList[T1.Icurve()];
              Biarc const & C2 = CL.m_biarcList[T2.Icurve()];

              IntersectList ilist1;
              C1.intersect_ISO( offs, C2, offs_CL, ilist1, false );

              for ( IntersectList::const_iterator it = ilist1.begin();
                    it != ilist1.end(); ++it ) {
                real_type ss1 = it->first  + m_s0[T1.Icurve()];
                real_type ss2 = it->second + CL.m_s0[T2.Icurve()];
                if ( swap_s_vals ) swap( ss1, ss2 );
                ilist.push_back( Ipair( ss1, ss2 ) );
              }
            }
          }

        }
      }

      /*\
       |      _ _     _
       |   __| (_)___| |_ __ _ _ __   ___ ___
       |  / _` | / __| __/ _` | '_ \ / __/ _ \
       | | (_| | \__ \ || (_| | | | | (_|  __/
       |  \__,_|_|___/\__\__,_|_| |_|\___\___|
      \*/

      int_type
      BiarcList::closestPoint_internal(
        real_type   qx,
        real_type   qy,
        real_type   offs,
        real_type & x,
        real_type & y,
        real_type & s,
        real_type & DST
      ) const {

        this->build_AABBtree_ISO( offs );

        AABBtree::VecPtrBBox candidateList;
        m_aabb_tree.min_distance( qx, qy, candidateList );
        AABBtree::VecPtrBBox::const_iterator ic;
        UTILS_ASSERT0(
          candidateList.size() > 0,
          "BiarcList::closestPoint no candidate\n"
        );
        int_type icurve = 0;
        DST = numeric_limits<real_type>::infinity();
        for ( ic = candidateList.begin(); ic != candidateList.end(); ++ic ) {
          size_t ipos = size_t((*ic)->Ipos());
          Triangle2D const & T = m_aabb_tri[ipos];
          real_type dst = T.distMin( qx, qy );
          if ( dst < DST ) {
            // refine distance
            real_type xx, yy, ss, tt;
            m_biarcList[T.Icurve()].closestPoint_ISO( qx, qy, offs, xx, yy, ss, tt, dst );
            if ( dst < DST ) {
              DST    = dst;
              s      = ss + m_s0[T.Icurve()];
              x      = xx;
              y      = yy;
              icurve = T.Icurve();
            }
          }
        }
        return icurve;
      }

      int_type
      BiarcList::closestPoint_ISO(
        real_type   qx,
        real_type   qy,
        real_type   offs,
        real_type & x,
        real_type & y,
        real_type & s,
        real_type & t,
        real_type & DST
      ) const {

        int_type icurve = this->closestPoint_internal( qx, qy, offs, x, y, s, DST );

        // check if projection is orthogonal
        real_type nx, ny;
        m_biarcList[icurve].nor_ISO( s - m_s0[icurve], nx, ny );
        real_type qxx = qx - x;
        real_type qyy = qy - y;
        t = qxx * nx + qyy * ny - offs; // signed distance
        real_type pt = abs(qxx * ny - qyy * nx);
        G2LIB_DEBUG_MESSAGE(
          "BiarcList::closestPoint_ISO\n"
          "||P-P0|| = {} and {}, |(P-P0).T| = {}\n",
          DST, hypot(qxx,qyy), pt
        );
        return pt > GLIB2_TOL_ANGLE*hypot(qxx,qyy) ? -(icurve+1) : icurve;
      }

      // - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

      int_type
      BiarcList::closestPoint_ISO(
        real_type   qx,
        real_type   qy,
        real_type & x,
        real_type & y,
        real_type & s,
        real_type & t,
        real_type & dst
      ) const {
        return closestPoint_ISO( qx, qy, 0, x, y, s, t, dst );
      }

      // - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      // - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      // - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      // - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

      void
      BiarcList::getSTK(
        real_type * s,
        real_type * theta,
        real_type * kappa
      ) const {
        vector<Biarc>::const_iterator ic = m_biarcList.begin();
        int_type  k  = 0;
        real_type ss = 0;
        while ( ic != m_biarcList.end() ) {
          s[k]     = ss;
          theta[k] = ic->thetaBegin();
          kappa[k] = ic->kappaBegin();
          ss      += ic->length();
          ++k;
          ++ic;
        }
        --ic;
        s[k]     = ss;
        theta[k] = ic->thetaEnd();
        kappa[k] = ic->kappaEnd();
      }

      // - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

      void
      BiarcList::getXY( real_type * x, real_type * y ) const {
        vector<Biarc>::const_iterator ic = m_biarcList.begin();
        int_type k  = 0;
        while ( ic != m_biarcList.end() ) {
          x[k] = ic->xBegin();
          y[k] = ic->yBegin();
          ++k; ++ic;
        }
        --ic;
        x[k] = ic->xEnd();
        y[k] = ic->yEnd();
      }

      // - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

      int_type
      BiarcList::findST1(
        real_type   x,
        real_type   y,
        real_type & s,
        real_type & t
      ) const {

        UTILS_ASSERT0( !m_biarcList.empty(), "BiarcList::findST, empty list\n" );
        vector<Biarc>::const_iterator     ic = m_biarcList.begin();
        vector<real_type>::const_iterator is = m_s0.begin();

        s = t = 0;
        int_type  ipos = 0;
        int_type  iseg = 0;
        real_type S, T;
        bool ok = ic->findST_ISO( x, y, S, T );
        if ( ok ) {
          s    = *is + S;
          t    = T;
          iseg = 0;
        }

        for ( ++ic, ++is, ++ipos;
              ic != m_biarcList.end();
              ++ic, ++is, ++ipos ) {
          bool ok1 = ic->findST_ISO( x, y, S, T );
          if ( ok && ok1 ) ok1 = abs(T) < abs(t);
          if ( ok1 ) {
            ok   = true;
            s    = *is + S;
            t    = T;
            iseg = ipos;
          }
        }

        return ok ? iseg : -(1+iseg);
      }

      // - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

      int_type
      BiarcList::findST1(
        int_type    ibegin,
        int_type    iend,
        real_type   x,
        real_type   y,
        real_type & s,
        real_type & t
      ) const {

        UTILS_ASSERT0(
          !m_biarcList.empty(), "BiarcList::findST, empty list\n"
        );
        UTILS_ASSERT(
          ibegin >= 0 && ibegin <= iend &&
          iend < int_type(m_biarcList.size()),
          "BiarcList::findST( ibegin={}, iend={}, x, y, s, t )\n"
          "bad range not in [0,{}]\n",
          ibegin, iend, m_biarcList.size()-1
        );
        s = t = 0;
        int_type iseg = 0;
        bool ok = false;
        for ( int_type k = ibegin; k <= iend; ++k ) {
          Biarc const & ck = m_biarcList[k];
          real_type S, T;
          bool ok1 = ck.findST_ISO( x, y, S, T );
          if ( ok && ok1 ) ok1 = abs(T) < abs(t);
          if ( ok1 ) {
            ok   = true;
            s    = m_s0[k] + S;
            t    = T;
            iseg = k;
          }
        }
        return ok ? iseg : -(1+iseg);
      }

      // - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

      ostream_type &
      operator << ( ostream_type & stream, BiarcList const & CL ) {
        vector<Biarc>::const_iterator ic = CL.m_biarcList.begin();
        for (; ic != CL.m_biarcList.end(); ++ic )
          stream << *ic << '\n';
        return stream;
      }

      // - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    }

    // EOF: BiarcList.cc