GeomQueryTool.cpp

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#include "moab/GeomQueryTool.hpp"

#ifdef WIN32               /* windows */
#define _USE_MATH_DEFINES  // For M_PI
#endif
#include <string>
#include <iostream>
#include <fstream>
#include <sstream>
#include <limits>
#include <algorithm>
#include <set>

#include <cctype>
#include <cstring>
#include <cstdlib>
#include <cstdio>

#include "moab/OrientedBoxTreeTool.hpp"

#ifdef __DEBUG
#define MB_GQT_DEBUG
#endif

namespace moab
{

/** \class FindVolume_IntRegCtxt
 *
 *
 *\brief An intersection context used for finding a volume
 *
 * This context is used to find the nearest intersection location
 * and is intended for use with a global surface tree from
 * the GeomTopoTool.
 *
 * The behavior of this context is relatively simple in that it
 * returns only one intersection distance, surface, and facet.
 * Intersections of any orientation are accepted. The positive
 * value of the search window is limited to the current nearest
 * intersection distance.
 *
 */

class FindVolumeIntRegCtxt : public OrientedBoxTreeTool::IntRegCtxt
{

  public:
    // Constructor
    FindVolumeIntRegCtxt()
    {
        // initialize return vectors
        // only one hit is returned in this context
        intersections.push_back( std::numeric_limits< double >::max() );
        sets.push_back( 0 );
        facets.push_back( 0 );
    }

    ErrorCode register_intersection( EntityHandle set,
                                     EntityHandle tri,
                                     double dist,
                                     OrientedBoxTreeTool::IntersectSearchWindow& search_win,
                                     GeomUtil::intersection_type /*it*/ )
    {
        // update dist, set, and triangle hit if
        // we found a new minimum distance
        double abs_dist = fabs( dist );
        if( abs_dist < fabs( intersections[0] ) )
        {
            intersections[0] = dist;
            sets[0]          = set;
            facets[0]        = tri;

            // narrow search window based on the hit distance
            pos               = abs_dist;
            neg               = -abs_dist;
            search_win.first  = &pos;
            search_win.second = &neg;
        }

        return MB_SUCCESS;
    }

    // storage for updated window values during search
    double pos;
    double neg;
};

/** \class GQT_IntRegCtxt
 *
 *\brief An implementation of an Intersection Registration Context for use GQT ray-firing
 *
 * This context uses a variety of tests and conditions to confirm whether or
 * not to accumulate an intersection, to ensure robustness for ray firing.
 *
 * This context only accumulates intersections that are oriented parallel to
 * the 'desiredOrient', if provided, with respect to 'geomVol', using
 * information in the in 'senseTag'.
 *
 * This context only accumulates a single intersection out of a set of
 * multiple intersections that fall in the same 'neighborhood', where a
 * 'neighborhood' is defined as facets that share edges or vertices.
 *
 * This context only accumulates piercing intersections.  This is relevant
 * for intersections that are found to be on an edge or vertex by the
 * Plucker test.  Such intersections are piercing if the ray has the same
 * orientation w.r.t. to all fecets that share that edge or vertex.
 *
 * This context tests intersections against a list of 'prevFacets' to
 * prevent a ray from crossing the same facet more than once.  The user is
 * responsible for ensuring that this list is reset when appropriate.
 *
 * This context accumulates all intersections within 'tol' of the
 * start of the ray and if the number of intersections within the
 * 'tol' of the ray start point is less than 'minTolInt', the next
 * closest intersection. If the desired result is only the closest
 * intersection, 'minTolInt' should be 0.  This function will return all
 * intersections, regardless of distance from the start of the ray, if
 * 'minTolInt' is negative.
 *
 */

class GQT_IntRegCtxt : public OrientedBoxTreeTool::IntRegCtxt
{

  private:
    // Input
    OrientedBoxTreeTool* tool;
    const CartVect ray_origin;
    const CartVect ray_direction;
    const double tol; /* used for box.intersect_ray, radius of
                         neighborhood for adjacent triangles,
                         and old mode of add_intersection */
    const int minTolInt;

    // Optional Input - to screen RTIs by orientation and edge/node intersection
    const EntityHandle* rootSet; /* used for sphere_intersect */
    const EntityHandle* geomVol; /* used for determining surface sense */
    const Tag* senseTag;         /* allows screening by triangle orientation.
                                    both geomVol and senseTag must be used together. */
    const int* desiredOrient;    /* points to desired orientation of ray with
                                    respect to surf normal, if this feature is used.
                                    Must point to -1 (reverse) or 1 (forward).
                                    geomVol and senseTag are needed for this feature */

    // Optional Input - to avoid returning these as RTIs
    const std::vector< EntityHandle >* prevFacets; /* intersections on these triangles
                                                      will not be returned */

    // Other Variables
    std::vector< std::vector< EntityHandle > > neighborhoods;
    std::vector< EntityHandle > neighborhood;

    void add_intersection( EntityHandle set,
                           EntityHandle tri,
                           double dist,
                           OrientedBoxTreeTool::IntersectSearchWindow& search_win );
    void append_intersection( EntityHandle set, EntityHandle facet, double dist );
    void set_intersection( int len_idx, EntityHandle set, EntityHandle facet, double dist );
    void add_mode1_intersection( EntityHandle set,
                                 EntityHandle facet,
                                 double dist,
                                 OrientedBoxTreeTool::IntersectSearchWindow& search_win );
    bool edge_node_piercing_intersect( const EntityHandle tri,
                                       const CartVect& ray_direction,
                                       const GeomUtil::intersection_type int_type,
                                       const std::vector< EntityHandle >& close_tris,
                                       const std::vector< int >& close_senses,
                                       const Interface* MBI,
                                       std::vector< EntityHandle >* neighborhood_tris = 0 );

    bool in_prevFacets( const EntityHandle tri );
    bool in_neighborhoods( const EntityHandle tri );

  public:
    GQT_IntRegCtxt( OrientedBoxTreeTool* obbtool,
                    const double ray_point[3],
                    const double ray_dir[3],
                    double tolerance,
                    int min_tolerance_intersections,
                    const EntityHandle* root_set,
                    const EntityHandle* geom_volume,
                    const Tag* sense_tag,
                    const int* desired_orient,
                    const std::vector< EntityHandle >* prev_facets )
        : tool( obbtool ), ray_origin( ray_point ), ray_direction( ray_dir ), tol( tolerance ),
          minTolInt( min_tolerance_intersections ), rootSet( root_set ), geomVol( geom_volume ), senseTag( sense_tag ),
          desiredOrient( desired_orient ), prevFacets( prev_facets ){

                                           };

    virtual ErrorCode register_intersection( EntityHandle set,
                                             EntityHandle triangle,
                                             double distance,
                                             OrientedBoxTreeTool::IntersectSearchWindow&,
                                             GeomUtil::intersection_type int_type );

    virtual ErrorCode update_orient( EntityHandle set, int* surfTriOrient );
    virtual const int* getDesiredOrient()
    {
        return desiredOrient;
    };
};

ErrorCode GQT_IntRegCtxt::update_orient( EntityHandle set, int* surfTriOrient )
{

    ErrorCode rval;

    // Get desired orientation of surface wrt volume. Use this to return only
    // exit or entrance intersections.
    if( geomVol && senseTag && desiredOrient && surfTriOrient )
    {
        if( 1 != *desiredOrient && -1 != *desiredOrient )
        {
            std::cerr << "error: desired orientation must be 1 (forward) or -1 (reverse)" << std::endl;
        }
        EntityHandle vols[2];
        rval = tool->get_moab_instance()->tag_get_data( *senseTag, &set, 1, vols );
        assert( MB_SUCCESS == rval );
        if( MB_SUCCESS != rval ) return rval;
        if( vols[0] == vols[1] )
        {
            std::cerr << "error: surface has positive and negative sense wrt same volume" << std::endl;
            return MB_FAILURE;
        }
        // surfTriOrient will be used by plucker_ray_tri_intersect to avoid
        // intersections with wrong orientation.
        if( *geomVol == vols[0] )
        {
            *surfTriOrient = *desiredOrient * 1;
        }
        else if( *geomVol == vols[1] )
        {
            *surfTriOrient = *desiredOrient * ( -1 );
        }
        else
        {
            assert( false );
            return MB_FAILURE;
        }
    }

    return MB_SUCCESS;
}

bool GQT_IntRegCtxt::in_prevFacets( const EntityHandle tri )
{
    return ( prevFacets && ( ( *prevFacets ).end() != find( ( *prevFacets ).begin(), ( *prevFacets ).end(), tri ) ) );
}

bool GQT_IntRegCtxt::in_neighborhoods( const EntityHandle tri )
{
    bool same_neighborhood = false;
    for( unsigned i = 0; i < neighborhoods.size(); ++i )
    {
        if( neighborhoods[i].end() != find( neighborhoods[i].begin(), neighborhoods[i].end(), tri ) )
        {
            same_neighborhood = true;
            continue;
        }
    }
    return same_neighborhood;
}

/**\brief Determine if a ray-edge/node intersection is glancing or piercing.
 *        This function avoids asking for upward adjacencies to prevent their
 *        creation.
 *\param tri           The intersected triangle
 *\param ray_dir       The direction of the ray
 *\param int_type      The type of intersection (EDGE0, EDGE1, NODE2, ...)
 *\param close_tris    Vector of triangles in the proximity of the intersection
 *\param close_senses  Vector of surface senses for tris in the proximity of
 *                     the intersection
 *\param neighborhood  Vector of triangles in the topological neighborhood of the intersection
 *\return              True if piercing, false otherwise.
 */
bool GQT_IntRegCtxt::edge_node_piercing_intersect( const EntityHandle tri,
                                                   const CartVect& ray_dir,
                                                   const GeomUtil::intersection_type int_type,
                                                   const std::vector< EntityHandle >& close_tris,
                                                   const std::vector< int >& close_senses,
                                                   const Interface* MBI,
                                                   std::vector< EntityHandle >* neighborhood_tris )
{

    // get the node of the triangle
    const EntityHandle* conn = NULL;
    int len                  = 0;
    ErrorCode rval           = MBI->get_connectivity( tri, conn, len );MB_CHK_ERR_RET_VAL( rval, false );
    // NOTE: original code is next line, but return type was wrong; returning true to get same net effect
    if( 3 != len ) return false;

    // get adjacent tris (and keep their corresponding senses)
    std::vector< EntityHandle > adj_tris;
    std::vector< int > adj_senses;

    // node intersection
    if( GeomUtil::NODE0 == int_type || GeomUtil::NODE1 == int_type || GeomUtil::NODE2 == int_type )
    {

        // get the intersected node
        EntityHandle node;
        if( GeomUtil::NODE0 == int_type )
            node = conn[0];
        else if( GeomUtil::NODE1 == int_type )
            node = conn[1];
        else
            node = conn[2];

        // get tris adjacent to node
        for( unsigned i = 0; i < close_tris.size(); ++i )
        {
            const EntityHandle* con = NULL;
            rval                    = MBI->get_connectivity( close_tris[i], con, len );MB_CHK_ERR_RET_VAL( rval, false );
            if( 3 != len ) return false;

            if( node == con[0] || node == con[1] || node == con[2] )
            {
                adj_tris.push_back( close_tris[i] );
                adj_senses.push_back( close_senses[i] );
            }
        }
        if( adj_tris.empty() )
        {
            std::cerr << "error: no tris are adjacent to the node" << std::endl;
            return false;
        }
        // edge intersection
    }
    else if( GeomUtil::EDGE0 == int_type || GeomUtil::EDGE1 == int_type || GeomUtil::EDGE2 == int_type )
    {

        // get the endpoints of the edge
        EntityHandle endpts[2];
        if( GeomUtil::EDGE0 == int_type )
        {
            endpts[0] = conn[0];
            endpts[1] = conn[1];
        }
        else if( GeomUtil::EDGE1 == int_type )
        {
            endpts[0] = conn[1];
            endpts[1] = conn[2];
        }
        else
        {
            endpts[0] = conn[2];
            endpts[1] = conn[0];
        }

        // get tris adjacent to edge
        for( unsigned i = 0; i < close_tris.size(); ++i )
        {
            const EntityHandle* con = NULL;
            rval                    = MBI->get_connectivity( close_tris[i], con, len );MB_CHK_ERR_RET_VAL( rval, false );
            if( 3 != len ) return false;

            // check both orientations in case close_tris are not on the same surface
            if( ( endpts[0] == con[0] && endpts[1] == con[1] ) || ( endpts[0] == con[1] && endpts[1] == con[0] ) ||
                ( endpts[0] == con[1] && endpts[1] == con[2] ) || ( endpts[0] == con[2] && endpts[1] == con[1] ) ||
                ( endpts[0] == con[2] && endpts[1] == con[0] ) || ( endpts[0] == con[0] && endpts[1] == con[2] ) )
            {
                adj_tris.push_back( close_tris[i] );
                adj_senses.push_back( close_senses[i] );
            }
        }
        // In a 2-manifold each edge is adjacent to exactly 2 tris
        if( 2 != adj_tris.size() )
        {
            std::cerr << "error: edge of a manifold must be topologically adjacent to exactly 2 tris" << std::endl;
            MBI->list_entities( endpts, 2 );
            return true;
        }
    }
    else
    {
        std::cerr << "error: special case not an node/edge intersection" << std::endl;
        return false;
    }

    // The close tris were in proximity to the intersection. The adj_tris are
    // topologically adjacent to the intersection (the neighborhood).
    if( neighborhood_tris ) ( *neighborhood_tris ).assign( adj_tris.begin(), adj_tris.end() );

    // determine glancing/piercing
    // If a desired_orientation was used in this call to ray_intersect_sets,
    // the plucker_ray_tri_intersect will have already used it. For a piercing
    // intersection, the normal of all tris must have the same orientation.
    int sign = 0;
    for( unsigned i = 0; i < adj_tris.size(); ++i )
    {
        const EntityHandle* con = NULL;
        rval                    = MBI->get_connectivity( adj_tris[i], con, len );MB_CHK_ERR_RET_VAL( rval, false );
        if( 3 != len ) return false;

        CartVect coords[3];
        rval = MBI->get_coords( con, len, coords[0].array() );MB_CHK_ERR_RET_VAL( rval, false );

        // get normal of triangle
        CartVect v0     = coords[1] - coords[0];
        CartVect v1     = coords[2] - coords[0];
        CartVect norm   = adj_senses[i] * ( v0 * v1 );
        double dot_prod = norm % ray_dir;

        // if the sign has not yet been decided, choose it
        if( 0 == sign && 0 != dot_prod )
        {
            if( 0 < dot_prod )
                sign = 1;
            else
                sign = -1;
        }

        // intersection is glancing if tri and ray do not point in same direction
        // for every triangle
        if( 0 != sign && 0 > sign * dot_prod ) return false;
    }
    return true;
}

ErrorCode GQT_IntRegCtxt::register_intersection( EntityHandle set,
                                                 EntityHandle t,
                                                 double int_dist,
                                                 OrientedBoxTreeTool::IntersectSearchWindow& search_win,
                                                 GeomUtil::intersection_type int_type )
{
    ErrorCode rval;

    // Do not accept intersections if they are in the vector of previously intersected
    // facets.
    if( in_prevFacets( t ) ) return MB_SUCCESS;

    // Do not accept intersections if they are in the neighborhood of previous
    // intersections.
    if( in_neighborhoods( t ) ) return MB_SUCCESS;

    neighborhood.clear();

    // Handle special case of edge/node intersection. Accept piercing
    // intersections and reject glancing intersections.
    // The edge_node_intersection function needs to know surface sense wrt volume.
    // A less-robust implementation could work without sense information.
    // Would it ever be useful to accept a glancing intersection?
    if( GeomUtil::INTERIOR != int_type && rootSet && geomVol && senseTag )
    {
        // get triangles in the proximity of the intersection
        std::vector< EntityHandle > close_tris;
        std::vector< int > close_senses;
        rval = tool->get_close_tris( ray_origin + int_dist * ray_direction, tol, rootSet, geomVol, senseTag, close_tris,
                                     close_senses );

        if( MB_SUCCESS != rval ) return rval;

        if( !edge_node_piercing_intersect( t, ray_direction, int_type, close_tris, close_senses,
                                           tool->get_moab_instance(), &neighborhood ) )
            return MB_SUCCESS;
    }
    else
    {
        neighborhood.push_back( t );
    }

    // NOTE: add_intersection may modify the 'neg_ray_len' and 'nonneg_ray_len'
    //       members, which will affect subsequent calls to ray_tri_intersect
    //       in this loop.
    add_intersection( set, t, int_dist, search_win );

    return MB_SUCCESS;
}

void GQT_IntRegCtxt::append_intersection( EntityHandle set, EntityHandle facet, double dist )
{
    intersections.push_back( dist );
    sets.push_back( set );
    facets.push_back( facet );
    neighborhoods.push_back( neighborhood );
    return;
}

void GQT_IntRegCtxt::set_intersection( int len_idx, EntityHandle set, EntityHandle facet, double dist )
{
    intersections[len_idx] = dist;
    sets[len_idx]          = set;
    facets[len_idx]        = facet;
    return;
}

/* Mode 1: Used if neg_ray_len and nonneg_ray_len are specified
   variables used:     nonneg_ray_len, neg_ray_len
   variables not used: min_tol_int, tol
   1) keep the closest nonneg intersection and one negative intersection, if closer
*/
void GQT_IntRegCtxt::add_mode1_intersection( EntityHandle set,
                                             EntityHandle facet,
                                             double dist,
                                             OrientedBoxTreeTool::IntersectSearchWindow& search_win )
{
    if( 2 != intersections.size() )
    {
        intersections.resize( 2, 0 );
        sets.resize( 2, 0 );
        facets.resize( 2, 0 );
        // must initialize this for comparison below
        intersections[0] = -std::numeric_limits< double >::max();
    }

    // negative case
    if( 0.0 > dist )
    {
        set_intersection( 0, set, facet, dist );
        search_win.second = &intersections[0];
        // nonnegative case
    }
    else
    {
        set_intersection( 1, set, facet, dist );
        search_win.first = &intersections[1];
        // if the intersection is closer than the negative one, remove the negative one
        if( dist < -*( search_win.second ) )
        {
            set_intersection( 0, 0, 0, -intersections[1] );
            search_win.second = &intersections[0];
        }
    }
    //    std::cout << "add_intersection: dist = " << dist << " search_win.second=" <<
    //    *search_win.second
    //          << " search_win.first=" << *search_win.first << std::endl;
    return;
}

void GQT_IntRegCtxt::add_intersection( EntityHandle set,
                                       EntityHandle facet,
                                       double dist,
                                       OrientedBoxTreeTool::IntersectSearchWindow& search_win )
{

    // Mode 1, detected by non-null neg_ray_len pointer
    // keep the closest nonneg intersection and one negative intersection, if closer
    if( search_win.second && search_win.first )
    {
        return add_mode1_intersection( set, facet, dist, search_win );
    }

    // ---------------------------------------------------------------------------
    /*   Mode 2: Used if neg_ray_len is not specified
         variables used:     min_tol_int, tol, search_win.first
         variables not used: neg_ray_len
         1) if(min_tol_int<0) return all intersections
         2) otherwise return all inside tolerance and unless there are >min_tol_int
         inside of tolerance, return the closest outside of tolerance */
    // Mode 2
    // If minTolInt is less than zero, return all intersections
    if( minTolInt < 0 && dist > -tol )
    {
        append_intersection( set, facet, dist );
        neighborhoods.push_back( neighborhood );
        return;
    }

    // Check if the 'len' pointer is pointing into the intersection
    // list.  If this is the case, then the list contains, at that
    // location, an intersection greater than the tolerance away from
    // the base point of the ray.
    int len_idx = -1;
    if( search_win.first && search_win.first >= &intersections[0] &&
        search_win.first < &intersections[0] + intersections.size() )
        len_idx = search_win.first - &intersections[0];

    // If the intersection is within tol of the ray base point, we
    // always add it to the list.
    if( dist <= tol )
    {
        // If the list contains an intersection outside the tolerance...
        if( len_idx >= 0 )
        {
            // If we no longer want an intersection outside the tolerance,
            // remove it.
            if( (int)intersections.size() >= minTolInt )
            {
                set_intersection( len_idx, set, facet, dist );
                // From now on, we want only intersections within the tolerance,
                // so update length accordingly
                search_win.first = &tol;
            }
            // Otherwise appended to the list and update pointer
            else
            {
                append_intersection( set, facet, dist );
                search_win.first = &intersections[len_idx];
            }
        }
        // Otherwise just append it
        else
        {
            append_intersection( set, facet, dist );
            // If we have all the intersections we want, set
            // length such that we will only find further intersections
            // within the tolerance
            if( (int)intersections.size() >= minTolInt ) search_win.first = &tol;
        }
    }
    // Otherwise the intersection is outside the tolerance
    // If we already have an intersection outside the tolerance and
    // this one is closer, replace the existing one with this one.
    else if( len_idx >= 0 )
    {
        if( dist <= *search_win.first )
        {
            set_intersection( len_idx, set, facet, dist );
        }
    }
    // Otherwise if we want an intersection outside the tolerance
    // and don'thave one yet, add it.
    else if( (int)intersections.size() < minTolInt )
    {
        append_intersection( set, facet, dist );
        // update length.  this is currently the closest intersection, so
        // only want further intersections that are closer than this one.
        search_win.first = &intersections.back();
    }
}

GeomQueryTool::GeomQueryTool( Interface* impl,
                              bool find_geomsets,
                              EntityHandle modelRootSet,
                              bool p_rootSets_vector,
                              bool restore_rootSets,
                              bool trace_counting,
                              double overlap_thickness,
                              double numerical_precision )
    : verbose( false ), owns_gtt( true )
{
    geomTopoTool = new GeomTopoTool( impl, find_geomsets, modelRootSet, p_rootSets_vector, restore_rootSets );

    senseTag = geomTopoTool->get_sense_tag();

    obbTreeTool = geomTopoTool->obb_tree();
    MBI         = geomTopoTool->get_moab_instance();

    counting           = trace_counting;
    overlapThickness   = overlap_thickness;
    numericalPrecision = numerical_precision;

    // reset query counters
    n_pt_in_vol_calls = 0;
    n_ray_fire_calls  = 0;
}

GeomQueryTool::GeomQueryTool( GeomTopoTool* geomtopotool,
                              bool trace_counting,
                              double overlap_thickness,
                              double numerical_precision )
    : verbose( false ), owns_gtt( false )
{

    geomTopoTool = geomtopotool;

    senseTag = geomTopoTool->get_sense_tag();

    obbTreeTool = geomTopoTool->obb_tree();
    MBI         = geomTopoTool->get_moab_instance();

    counting           = trace_counting;
    overlapThickness   = overlap_thickness;
    numericalPrecision = numerical_precision;

    // reset query counters
    n_pt_in_vol_calls = 0;
    n_ray_fire_calls  = 0;
}

GeomQueryTool::~GeomQueryTool()
{
    if( owns_gtt )
    {
        delete geomTopoTool;
    }
}

ErrorCode GeomQueryTool::initialize()
{

    ErrorCode rval;

    rval = geomTopoTool->find_geomsets();MB_CHK_SET_ERR( rval, "Failed to find geometry sets" );

    rval = geomTopoTool->setup_implicit_complement();MB_CHK_SET_ERR( rval, "Couldn't setup the implicit complement" );

    rval = geomTopoTool->construct_obb_trees();MB_CHK_SET_ERR( rval, "Failed to construct OBB trees" );

    return MB_SUCCESS;
}

void GeomQueryTool::RayHistory::reset()
{
    prev_facets.clear();
}

void GeomQueryTool::RayHistory::reset_to_last_intersection()
{

    if( prev_facets.size() > 1 )
    {
        prev_facets[0] = prev_facets.back();
        prev_facets.resize( 1 );
    }
}

void GeomQueryTool::RayHistory::rollback_last_intersection()
{
    if( prev_facets.size() ) prev_facets.pop_back();
}

ErrorCode GeomQueryTool::RayHistory::get_last_intersection( EntityHandle& last_facet_hit ) const
{
    if( prev_facets.size() > 0 )
    {
        last_facet_hit = prev_facets.back();
        return MB_SUCCESS;
    }
    else
    {
        return MB_ENTITY_NOT_FOUND;
    }
}

bool GeomQueryTool::RayHistory::in_history( EntityHandle ent ) const
{
    return std::find( prev_facets.begin(), prev_facets.end(), ent ) != prev_facets.end();
}

void GeomQueryTool::RayHistory::add_entity( EntityHandle ent )
{
    prev_facets.push_back( ent );
}

ErrorCode GeomQueryTool::ray_fire( const EntityHandle volume,
                                   const double point[3],
                                   const double dir[3],
                                   EntityHandle& next_surf,
                                   double& next_surf_dist,
                                   RayHistory* history,
                                   double user_dist_limit,
                                   int ray_orientation,
                                   OrientedBoxTreeTool::TrvStats* stats )
{

    // take some stats that are independent of nps
    if( counting )
    {
        ++n_ray_fire_calls;
        if( 0 == n_ray_fire_calls % 10000000 )
        {
            std::cout << "n_ray_fires=" << n_ray_fire_calls << " n_pt_in_vols=" << n_pt_in_vol_calls << std::endl;
        }
    }

#ifdef MB_GQT_DEBUG
    std::cout << "ray_fire:"
              << " xyz=" << point[0] << " " << point[1] << " " << point[2] << " uvw=" << dir[0] << " " << dir[1] << " "
              << dir[2] << " entity_handle=" << volume << std::endl;
#endif

    const double huge_val = std::numeric_limits< double >::max();
    double dist_limit     = huge_val;
    if( user_dist_limit > 0 ) dist_limit = user_dist_limit;

    // don't recreate these every call
    std::vector< double > dists;
    std::vector< EntityHandle > surfs;
    std::vector< EntityHandle > facets;

    EntityHandle root;
    ErrorCode rval = geomTopoTool->get_root( volume, root );MB_CHK_SET_ERR( rval, "Failed to get the obb tree root of the volume" );

    // check behind the ray origin for intersections
    double neg_ray_len;
    if( 0 == overlapThickness )
    {
        neg_ray_len = -numericalPrecision;
    }
    else
    {
        neg_ray_len = -overlapThickness;
    }

    // optionally, limit the nonneg_ray_len with the distance to next collision.
    double nonneg_ray_len = dist_limit;

    // the nonneg_ray_len should not be less than -neg_ray_len, or an overlap
    // may be missed due to optimization within ray_intersect_sets
    if( nonneg_ray_len < -neg_ray_len ) nonneg_ray_len = -neg_ray_len;
    if( 0 > nonneg_ray_len || 0 <= neg_ray_len )
    {
        MB_SET_ERR( MB_FAILURE, "Incorrect ray length provided" );
    }

    // min_tolerance_intersections is passed but not used in this call
    const int min_tolerance_intersections = 0;

    // numericalPrecision is used for box.intersect_ray and find triangles in the
    // neighborhood of edge/node intersections.
    GQT_IntRegCtxt int_reg_ctxt( geomTopoTool->obb_tree(), point, dir, numericalPrecision, min_tolerance_intersections,
                                 &root, &volume, &senseTag, &ray_orientation,
                                 history ? &( history->prev_facets ) : NULL );

    OrientedBoxTreeTool::IntersectSearchWindow search_win( &nonneg_ray_len, &neg_ray_len );
    rval = geomTopoTool->obb_tree()->ray_intersect_sets( dists, surfs, facets, root, numericalPrecision, point, dir,
                                                         search_win, int_reg_ctxt, stats );

    MB_CHK_SET_ERR( rval, "Ray query failed" );

    // If no distances are returned, the particle is lost unless the physics limit
    // is being used. If the physics limit is being used, there is no way to tell
    // if the particle is lost. To avoid ambiguity, DO NOT use the distance limit
    // unless you know lost particles do not occur.
    if( dists.empty() )
    {
        next_surf = 0;
#ifdef MB_GQT_DEBUG
        std::cout << "          next_surf=0 dist=(undef)" << std::endl;
#endif
        return MB_SUCCESS;
    }

    // Assume that a (neg, nonneg) pair of RTIs could be returned,
    // however, only one or the other may exist. dists[] may be populated, but
    // intersections are ONLY indicated by nonzero surfs[] and facets[].
    if( 2 != dists.size() || 2 != facets.size() )
    {
        MB_SET_ERR( MB_FAILURE, "Incorrect number of facets/distances" );
    }
    if( 0.0 < dists[0] || 0.0 > dists[1] )
    {
        MB_SET_ERR( MB_FAILURE, "Invalid intersection distance signs" );
    }

    // If both negative and nonnegative RTIs are returned, the negative RTI must
    // closer to the origin.
    if( ( 0 != facets[0] && 0 != facets[1] ) && ( -dists[0] > dists[1] ) )
    {
        MB_SET_ERR( MB_FAILURE, "Invalid intersection distance values" );
    }

    // If an RTI is found at negative distance, perform a PMT to see if the
    // particle is inside an overlap.
    int exit_idx = -1;
    if( 0 != facets[0] )
    {
        // get the next volume
        std::vector< EntityHandle > vols;
        EntityHandle nx_vol;
        rval = MBI->get_parent_meshsets( surfs[0], vols );MB_CHK_SET_ERR( rval, "Failed to get the parent meshsets" );
        if( 2 != vols.size() )
        {
            MB_SET_ERR( MB_FAILURE, "Invaid number of parent volumes found" );
        }
        if( vols.front() == volume )
        {
            nx_vol = vols.back();
        }
        else
        {
            nx_vol = vols.front();
        }
        // Check to see if the point is actually in the next volume.
        // The list of previous facets is used to topologically identify the
        // "on_boundary" result of the PMT. This avoids a test that uses proximity
        // (a tolerance).
        int result;
        rval = point_in_volume( nx_vol, point, result, dir, history );MB_CHK_SET_ERR( rval, "Point in volume query failed" );
        if( 1 == result ) exit_idx = 0;
    }

    // if the negative distance is not the exit, try the nonnegative distance
    if( -1 == exit_idx && 0 != facets[1] ) exit_idx = 1;

    // if the exit index is still unknown, the particle is lost
    if( -1 == exit_idx )
    {
        next_surf = 0;
#ifdef MB_GQT_DEBUG
        std::cout << "next surf hit = 0, dist = (undef)" << std::endl;
#endif
        return MB_SUCCESS;
    }

    // return the intersection
    next_surf      = surfs[exit_idx];
    next_surf_dist = ( 0 > dists[exit_idx] ? 0 : dists[exit_idx] );

    if( history )
    {
        history->prev_facets.push_back( facets[exit_idx] );
    }

#ifdef MB_GQT_DEBUG
    if( 0 > dists[exit_idx] )
    {
        std::cout << "          OVERLAP track length=" << dists[exit_idx] << std::endl;
    }
    std::cout << "          next_surf = " << next_surf  // todo: use geomtopotool to get id by entity handle
              << ", dist = " << next_surf_dist << " new_pt=";
    for( int i = 0; i < 3; ++i )
    {
        std::cout << point[i] + dir[i] * next_surf_dist << " ";
    }
    std::cout << std::endl;
#endif

    return MB_SUCCESS;
}

ErrorCode GeomQueryTool::point_in_volume( const EntityHandle volume,
                                          const double xyz[3],
                                          int& result,
                                          const double* uvw,
                                          const RayHistory* history )
{
    // take some stats that are independent of nps
    if( counting ) ++n_pt_in_vol_calls;

    // early fail for piv - see if point inside the root level obb
    // if its not even in the box dont bother doing anything else
    ErrorCode rval = point_in_box( volume, xyz, result );
    if( !result )
    {
        result = 0;
        return MB_SUCCESS;
    }

    // get OBB Tree for volume
    EntityHandle root;
    rval = geomTopoTool->get_root( volume, root );MB_CHK_SET_ERR( rval, "Failed to find the volume's obb tree root" );

    // Don't recreate these every call. These cannot be the same as the ray_fire
    // vectors because both are used simultaneously.
    std::vector< double > dists;
    std::vector< EntityHandle > surfs;
    std::vector< EntityHandle > facets;
    std::vector< int > dirs;

    // if uvw is not given or is full of zeros, use a random direction
    double u = 0, v = 0, w = 0;

    if( uvw )
    {
        u = uvw[0];
        v = uvw[1], w = uvw[2];
    }

    if( u == 0 && v == 0 && w == 0 )
    {
        u                      = rand();
        v                      = rand();
        w                      = rand();
        const double magnitude = sqrt( u * u + v * v + w * w );
        u /= magnitude;
        v /= magnitude;
        w /= magnitude;
    }

    const double ray_direction[] = { u, v, w };

    // if overlaps, ray must be cast to infinity and all RTIs must be returned
    const double large = 1e15;
    double ray_length  = large;

    // If overlaps occur, the pt is inside if traveling along the ray from the
    // origin, there are ever more exits than entrances. In lieu of implementing
    // that, all intersections to infinity are required if overlaps occur (expensive)
    int min_tolerance_intersections;
    if( 0 != overlapThickness )
    {
        min_tolerance_intersections = -1;
        // only the first intersection is needed if overlaps do not occur (cheap)
    }
    else
    {
        min_tolerance_intersections = 1;
    }

    // Get intersection(s) of forward and reverse orientation. Do not return
    // glancing intersections or previous facets.
    GQT_IntRegCtxt int_reg_ctxt( geomTopoTool->obb_tree(), xyz, ray_direction, numericalPrecision,
                                 min_tolerance_intersections, &root, &volume, &senseTag, NULL,
                                 history ? &( history->prev_facets ) : NULL );

    OrientedBoxTreeTool::IntersectSearchWindow search_win( &ray_length, (double*)NULL );
    rval = geomTopoTool->obb_tree()->ray_intersect_sets( dists, surfs, facets, root, numericalPrecision, xyz,
                                                         ray_direction, search_win, int_reg_ctxt );MB_CHK_SET_ERR( rval, "Ray fire query failed" );

    // determine orientation of all intersections
    // 1 for entering, 0 for leaving, -1 for tangent
    // Tangent intersections are not returned from ray_tri_intersect.
    dirs.resize( dists.size() );
    for( unsigned i = 0; i < dists.size(); ++i )
    {
        rval = boundary_case( volume, dirs[i], u, v, w, facets[i], surfs[i] );MB_CHK_SET_ERR( rval, "Failed to resolve boundary case" );
    }

    // count all crossings
    if( 0 != overlapThickness )
    {
        int sum = 0;
        for( unsigned i = 0; i < dirs.size(); ++i )
        {
            if( 1 == dirs[i] )
                sum += 1;  // +1 for entering
            else if( 0 == dirs[i] )
                sum -= 1;  // -1 for leaving
            else if( -1 == dirs[i] )
            {  //  0 for tangent
                std::cout << "direction==tangent" << std::endl;
                sum += 0;
            }
            else
            {
                MB_SET_ERR( MB_FAILURE, "Error: unknown direction" );
            }
        }

        // inside/outside depends on the sum
        if( 0 < sum )
            result = 0;  // pt is outside (for all vols)
        else if( 0 > sum )
            result = 1;  // pt is inside  (for all vols)
        else if( geomTopoTool->is_implicit_complement( volume ) )
            result = 1;  // pt is inside  (for impl_compl_vol)
        else
            result = 0;  // pt is outside (for all other vols)

        // Only use the first crossing
    }
    else
    {
        if( dirs.empty() )
        {
            result = 0;  // pt is outside
        }
        else
        {
            int smallest = std::min_element( dists.begin(), dists.end() ) - dists.begin();
            if( 1 == dirs[smallest] )
                result = 0;  // pt is outside
            else if( 0 == dirs[smallest] )
                result = 1;  // pt is inside
            else if( -1 == dirs[smallest] )
            {
                // Should not be here because Plucker ray-triangle test does not
                // return coplanar rays as intersections.
                std::cerr << "direction==tangent" << std::endl;
                result = -1;
            }
            else
            {
                MB_SET_ERR( MB_FAILURE, "Error: unknown direction" );
            }
        }
    }

#ifdef MB_GQT_DEBUG
    std::cout << "pt_in_vol: result=" << result << " xyz=" << xyz[0] << " " << xyz[1] << " " << xyz[2] << " uvw=" << u
              << " " << v << " " << w << " vol_id=" << volume
              << std::endl;  // todo: use geomtopotool to get id by entity handle
#endif

    return MB_SUCCESS;
}

/**
 *  \brief For the volume pointed to and the point wished to be tested, returns
 *   whether the point is inside or outside the bounding box of the volume.
 * inside = 0, not inside, inside = 1, inside
 */
ErrorCode GeomQueryTool::point_in_box( EntityHandle volume, const double point[3], int& inside )
{
    double minpt[3];
    double maxpt[3];
    ErrorCode rval = geomTopoTool->get_bounding_coords( volume, minpt, maxpt );MB_CHK_SET_ERR( rval, "Failed to get the bounding coordinates of the volume" );

    // early exits
    if( point[0] > maxpt[0] || point[0] < minpt[0] )
    {
        inside = 0;
        return rval;
    }
    if( point[1] > maxpt[1] || point[1] < minpt[1] )
    {
        inside = 0;
        return rval;
    }
    if( point[2] > maxpt[2] || point[2] < minpt[2] )
    {
        inside = 0;
        return rval;
    }
    inside = 1;
    return rval;
}

ErrorCode GeomQueryTool::test_volume_boundary( const EntityHandle volume,
                                               const EntityHandle surface,
                                               const double xyz[3],
                                               const double uvw[3],
                                               int& result,
                                               const RayHistory* history )
{
    ErrorCode rval;
    int dir;

    if( history && history->prev_facets.size() )
    {
        // the current facet is already available
        rval = boundary_case( volume, dir, uvw[0], uvw[1], uvw[2], history->prev_facets.back(), surface );MB_CHK_SET_ERR( rval, "Failed to resolve the boundary case" );
    }
    else
    {
        // look up nearest facet

        // Get OBB Tree for surface
        EntityHandle root;
        rval = geomTopoTool->get_root( volume, root );MB_CHK_SET_ERR( rval, "Failed to get the volume's OBB tree root" );

        // Get closest triangle on surface
        const CartVect point( xyz );
        CartVect nearest;
        EntityHandle facet_out;
        rval = geomTopoTool->obb_tree()->closest_to_location( point.array(), root, nearest.array(), facet_out );MB_CHK_SET_ERR( rval, "Failed to find the closest point to location" );

        rval = boundary_case( volume, dir, uvw[0], uvw[1], uvw[2], facet_out, surface );MB_CHK_SET_ERR( rval, "Failed to resolve the boundary case" );
    }

    result = dir;

    return MB_SUCCESS;
}

// use spherical area test to determine inside/outside of a polyhedron.
ErrorCode GeomQueryTool::point_in_volume_slow( EntityHandle volume, const double xyz[3], int& result )
{
    ErrorCode rval;
    Range faces;
    std::vector< EntityHandle > surfs;
    std::vector< int > senses;
    double sum = 0.0;
    const CartVect point( xyz );

    rval = MBI->get_child_meshsets( volume, surfs );MB_CHK_SET_ERR( rval, "Failed to get the volume's child surfaces" );

    senses.resize( surfs.size() );
    rval = geomTopoTool->get_surface_senses( volume, surfs.size(), &surfs[0], &senses[0] );MB_CHK_SET_ERR( rval, "Failed to get the volume's surface senses" );

    for( unsigned i = 0; i < surfs.size(); ++i )
    {
        if( !senses[i] )  // skip non-manifold surfaces
            continue;

        double surf_area = 0.0, face_area;
        faces.clear();
        rval = MBI->get_entities_by_dimension( surfs[i], 2, faces );MB_CHK_SET_ERR( rval, "Failed to get the surface entities by dimension" );

        for( Range::iterator j = faces.begin(); j != faces.end(); ++j )
        {
            rval = poly_solid_angle( *j, point, face_area );MB_CHK_SET_ERR( rval, "Failed to determin the polygon's solid angle" );

            surf_area += face_area;
        }

        sum += senses[i] * surf_area;
    }

    result = fabs( sum ) > 2.0 * M_PI;
    return MB_SUCCESS;
}

ErrorCode GeomQueryTool::find_volume( const double xyz[3], EntityHandle& volume, const double* dir )
{
    ErrorCode rval;
    volume = 0;

    EntityHandle global_surf_tree_root = geomTopoTool->get_one_vol_root();

    // fast check - make sure point is in the implicit complement bounding box
    int ic_result;
    EntityHandle ic_handle;
    rval = geomTopoTool->get_implicit_complement( ic_handle );MB_CHK_SET_ERR( rval, "Failed to get the implicit complement handle" );

    rval = point_in_box( ic_handle, xyz, ic_result );MB_CHK_SET_ERR( rval, "Failed to check implicit complement for containment" );
    if( ic_result == 0 )
    {
        volume = 0;
        return MB_ENTITY_NOT_FOUND;
    }

    // if geomTopoTool doesn't have a global tree, use a loop over vols (slow)
    if( !global_surf_tree_root )
    {
        rval = find_volume_slow( xyz, volume, dir );
        return rval;
    }

    moab::CartVect uvw( 0.0 );

    if( dir )
    {
        uvw[0] = dir[0];
        uvw[1] = dir[1];
        uvw[2] = dir[2];
    }

    if( uvw == 0.0 )
    {
        uvw[0] = rand();
        uvw[1] = rand();
        uvw[2] = rand();
    }

    // always normalize direction
    uvw.normalize();

    // fire a ray along dir and get surface
    const double huge_val = std::numeric_limits< double >::max();
    double pos_ray_len    = huge_val;
    double neg_ray_len    = -huge_val;

    // RIS output data
    std::vector< double > dists;
    std::vector< EntityHandle > surfs;
    std::vector< EntityHandle > facets;

    FindVolumeIntRegCtxt find_vol_reg_ctxt;
    OrientedBoxTreeTool::IntersectSearchWindow search_win( &pos_ray_len, &neg_ray_len );
    rval =
        geomTopoTool->obb_tree()->ray_intersect_sets( dists, surfs, facets, global_surf_tree_root, numericalPrecision,
                                                      xyz, uvw.array(), search_win, find_vol_reg_ctxt );MB_CHK_SET_ERR( rval, "Failed in global tree ray fire" );

    // if there was no intersection, no volume is found
    if( surfs.size() == 0 || surfs[0] == 0 )
    {
        volume = 0;
        return MB_ENTITY_NOT_FOUND;
    }

    // get the positive distance facet, surface hit
    EntityHandle facet = facets[0];
    EntityHandle surf  = surfs[0];

    // get these now, we're going to use them no matter what
    EntityHandle fwd_vol, bwd_vol;
    rval = geomTopoTool->get_surface_senses( surf, fwd_vol, bwd_vol );MB_CHK_SET_ERR( rval, "Failed to get sense data" );
    EntityHandle parent_vols[2];
    parent_vols[0] = fwd_vol;
    parent_vols[1] = bwd_vol;

    // get triangle normal
    std::vector< EntityHandle > conn;
    CartVect coords[3];
    rval = MBI->get_connectivity( &facet, 1, conn );MB_CHK_SET_ERR( rval, "Failed to get triangle connectivity" );

    rval = MBI->get_coords( &conn[0], 3, coords[0].array() );MB_CHK_SET_ERR( rval, "Failed to get triangle coordinates" );

    CartVect normal = ( coords[1] - coords[0] ) * ( coords[2] - coords[0] );
    normal.normalize();

    // reverse direction if a hit in the negative direction is found
    if( dists[0] < 0 )
    {
        uvw *= -1;
    }

    // if this is a "forward" intersection return the first sense entity
    // otherwise return the second, "reverse" sense entity
    double dot_prod = uvw % normal;
    int idx         = dot_prod > 0.0 ? 0 : 1;

    if( dot_prod == 0.0 )
    {
        std::cerr << "Tangent dot product in find_volume. Shouldn't be here." << std::endl;
        volume = 0;
        return MB_FAILURE;
    }

    volume = parent_vols[idx];

    return MB_SUCCESS;
}

ErrorCode GeomQueryTool::find_volume_slow( const double xyz[3], EntityHandle& volume, const double* dir )
{
    ErrorCode rval;
    volume = 0;
    // get all volumes
    Range all_vols;
    rval = geomTopoTool->get_gsets_by_dimension( 3, all_vols );MB_CHK_SET_ERR( rval, "Failed to get all volumes in the model" );

    Range::iterator it;
    int result = 0;
    for( it = all_vols.begin(); it != all_vols.end(); it++ )
    {
        rval = point_in_volume( *it, xyz, result, dir );MB_CHK_SET_ERR( rval, "Failed in point in volume loop" );
        if( result )
        {
            volume = *it;
            break;
        }
    }
    return volume ? MB_SUCCESS : MB_ENTITY_NOT_FOUND;
}

// detemine distance to nearest surface
ErrorCode GeomQueryTool::closest_to_location( EntityHandle volume,
                                              const double coords[3],
                                              double& result,
                                              EntityHandle* closest_surface )
{
    // Get OBB Tree for volume
    EntityHandle root;
    ErrorCode rval = geomTopoTool->get_root( volume, root );MB_CHK_SET_ERR( rval, "Failed to get the volume's obb tree root" );

    // Get closest triangles in volume
    const CartVect point( coords );
    CartVect nearest;
    EntityHandle facet_out;

    rval = geomTopoTool->obb_tree()->closest_to_location( point.array(), root, nearest.array(), facet_out,
                                                          closest_surface );MB_CHK_SET_ERR( rval, "Failed to get the closest intersection to location" );
    // calculate distance between point and nearest facet
    result = ( point - nearest ).length();

    return MB_SUCCESS;
}

// calculate volume of polyhedron
ErrorCode GeomQueryTool::measure_volume( EntityHandle volume, double& result )
{
    ErrorCode rval;
    std::vector< EntityHandle > surfaces;
    result = 0.0;

    // don't try to calculate volume of implicit complement
    if( geomTopoTool->is_implicit_complement( volume ) )
    {
        result = 1.0;
        return MB_SUCCESS;
    }

    // get surfaces from volume
    rval = MBI->get_child_meshsets( volume, surfaces );MB_CHK_SET_ERR( rval, "Failed to get the volume's child surfaces" );

    // get surface senses
    std::vector< int > senses( surfaces.size() );
    rval = geomTopoTool->get_surface_senses( volume, surfaces.size(), &surfaces[0], &senses[0] );MB_CHK_SET_ERR( rval, "Failed to retrieve surface-volume sense data. Cannot calculate volume" );

    for( unsigned i = 0; i < surfaces.size(); ++i )
    {
        // skip non-manifold surfaces
        if( !senses[i] ) continue;

        // get triangles in surface
        Range triangles;
        rval = MBI->get_entities_by_dimension( surfaces[i], 2, triangles );MB_CHK_SET_ERR( rval, "Failed to get the surface triangles" );

        if( !triangles.all_of_type( MBTRI ) )
        {
            std::cout << "WARNING: Surface " << surfaces[i]  // todo: use geomtopotool to get id by entity handle
                      << " contains non-triangle elements. Volume calculation may be incorrect." << std::endl;
            triangles.clear();
            rval = MBI->get_entities_by_type( surfaces[i], MBTRI, triangles );MB_CHK_SET_ERR( rval, "Failed to get the surface triangles" );
        }

        // calculate signed volume beneath surface (x 6.0)
        double surf_sum = 0.0;
        const EntityHandle* conn;
        int len;
        CartVect coords[3];
        for( Range::iterator j = triangles.begin(); j != triangles.end(); ++j )
        {
            rval = MBI->get_connectivity( *j, conn, len, true );MB_CHK_SET_ERR( rval, "Failed to get the connectivity of the current triangle" );
            if( 3 != len )
            {
                MB_SET_ERR( MB_FAILURE, "Incorrect connectivity length for triangle" );
            }
            rval = MBI->get_coords( conn, 3, coords[0].array() );MB_CHK_SET_ERR( rval, "Failed to get the coordinates of the current triangle's vertices" );

            coords[1] -= coords[0];
            coords[2] -= coords[0];
            surf_sum += ( coords[0] % ( coords[1] * coords[2] ) );
        }
        result += senses[i] * surf_sum;
    }

    result /= 6.0;
    return MB_SUCCESS;
}

// sum area of elements in surface
ErrorCode GeomQueryTool::measure_area( EntityHandle surface, double& result )
{
    // get triangles in surface
    Range triangles;
    ErrorCode rval = MBI->get_entities_by_dimension( surface, 2, triangles );MB_CHK_SET_ERR( rval, "Failed to get the surface entities" );
    if( !triangles.all_of_type( MBTRI ) )
    {
        std::cout << "WARNING: Surface " << surface  // todo: use geomtopotool to get id by entity handle
                  << " contains non-triangle elements. Area calculation may be incorrect." << std::endl;
        triangles.clear();
        rval = MBI->get_entities_by_type( surface, MBTRI, triangles );MB_CHK_SET_ERR( rval, "Failed to the surface's triangle entities" );
    }

    // calculate sum of area of triangles
    result = 0.0;
    const EntityHandle* conn;
    int len;
    CartVect coords[3];
    for( Range::iterator j = triangles.begin(); j != triangles.end(); ++j )
    {
        rval = MBI->get_connectivity( *j, conn, len, true );MB_CHK_SET_ERR( rval, "Failed to get the current triangle's connectivity" );
        if( 3 != len )
        {
            MB_SET_ERR( MB_FAILURE, "Incorrect connectivity length for triangle" );
        }
        rval = MBI->get_coords( conn, 3, coords[0].array() );MB_CHK_SET_ERR( rval, "Failed to get the current triangle's vertex coordinates" );

        // calculated area using cross product of triangle edges
        CartVect v1 = coords[1] - coords[0];
        CartVect v2 = coords[2] - coords[0];
        CartVect xp = v1 * v2;
        result += xp.length();
    }
    result *= 0.5;
    return MB_SUCCESS;
}

ErrorCode GeomQueryTool::get_normal( EntityHandle surf,
                                     const double in_pt[3],
                                     double angle[3],
                                     const RayHistory* history )
{
    EntityHandle root;
    ErrorCode rval = geomTopoTool->get_root( surf, root );MB_CHK_SET_ERR( rval, "Failed to get the surface's obb tree root" );

    std::vector< EntityHandle > facets;

    // if no history or history empty, use nearby facets
    if( !history || ( history->prev_facets.size() == 0 ) )
    {
        rval = geomTopoTool->obb_tree()->closest_to_location( in_pt, root, numericalPrecision, facets );MB_CHK_SET_ERR( rval, "Failed to get closest intersection to location" );
    }
    // otherwise use most recent facet in history
    else
    {
        facets.push_back( history->prev_facets.back() );
    }

    CartVect coords[3], normal( 0.0 );
    const EntityHandle* conn;
    int len;
    for( unsigned i = 0; i < facets.size(); ++i )
    {
        rval = MBI->get_connectivity( facets[i], conn, len );MB_CHK_SET_ERR( rval, "Failed to get facet connectivity" );
        if( 3 != len )
        {
            MB_SET_ERR( MB_FAILURE, "Incorrect connectivity length for triangle" );
        }

        rval = MBI->get_coords( conn, 3, coords[0].array() );MB_CHK_SET_ERR( rval, "Failed to get vertex coordinates" );

        coords[1] -= coords[0];
        coords[2] -= coords[0];
        normal += coords[1] * coords[2];
    }

    normal.normalize();
    normal.get( angle );

    return MB_SUCCESS;
}

/* SECTION II (private) */

// If point is on boundary, then this function is called to
// discriminate cases in which the ray is entering or leaving.
// result= 1 -> inside volume or entering volume
// result= 0 -> outside volume or leaving volume
// result=-1 -> on boundary with null or tangent uvw
ErrorCode GeomQueryTool::boundary_case( EntityHandle volume,
                                        int& result,
                                        double u,
                                        double v,
                                        double w,
                                        EntityHandle facet,
                                        EntityHandle surface )
{
    ErrorCode rval;

    // test to see if uvw is provided
    if( u <= 1.0 && v <= 1.0 && w <= 1.0 )
    {

        const CartVect ray_vector( u, v, w );
        CartVect coords[3], normal( 0.0 );
        const EntityHandle* conn;
        int len, sense_out;

        rval = MBI->get_connectivity( facet, conn, len );MB_CHK_SET_ERR( rval, "Failed to get the triangle's connectivity" );
        if( 3 != len )
        {
            MB_SET_ERR( MB_FAILURE, "Incorrect connectivity length for triangle" );
        }

        rval = MBI->get_coords( conn, 3, coords[0].array() );MB_CHK_SET_ERR( rval, "Failed to get vertex coordinates" );

        rval = geomTopoTool->get_sense( surface, volume, sense_out );MB_CHK_SET_ERR( rval, "Failed to get the surface's sense with respect to it's volume" );

        coords[1] -= coords[0];
        coords[2] -= coords[0];
        normal = sense_out * ( coords[1] * coords[2] );

        double sense = ray_vector % normal;

        if( sense < 0.0 )
        {
            result = 1;  // inside or entering
        }
        else if( sense > 0.0 )
        {
            result = 0;  // outside or leaving
        }
        else if( sense == 0.0 )
        {
            result = -1;  // tangent, therefore on boundary
        }
        else
        {
            result = -1;  // failure
            MB_SET_ERR( MB_FAILURE, "Failed to resolve boundary case" );
        }

        // if uvw not provided, return on_boundary.
    }
    else
    {
        result = -1;  // on boundary
        return MB_SUCCESS;
    }

    return MB_SUCCESS;
}

// point_in_volume_slow, including poly_solid_angle helper subroutine
// are adapted from "Point in Polyhedron Testing Using Spherical Polygons", Paulo Cezar
// Pinto Carvalho and Paulo Roma Cavalcanti, _Graphics Gems V_, pg. 42.  Original algorithm
// was described in "An Efficient Point In Polyhedron Algorithm", Jeff Lane, Bob Magedson,
// and Mike Rarick, _Computer Vision, Graphics, and Image Processing 26_, pg. 118-225, 1984.

// helper function for point_in_volume_slow.  calculate area of a polygon
// projected into a unit-sphere space
ErrorCode GeomQueryTool::poly_solid_angle( EntityHandle face, const CartVect& point, double& area )
{
    ErrorCode rval;

    // Get connectivity
    const EntityHandle* conn;
    int len;
    rval = MBI->get_connectivity( face, conn, len, true );MB_CHK_SET_ERR( rval, "Failed to get the connectivity of the polygon" );

    // Allocate space to store vertices
    CartVect coords_static[4];
    std::vector< CartVect > coords_dynamic;
    CartVect* coords = coords_static;
    if( (unsigned)len > ( sizeof( coords_static ) / sizeof( coords_static[0] ) ) )
    {
        coords_dynamic.resize( len );
        coords = &coords_dynamic[0];
    }

    // get coordinates
    rval = MBI->get_coords( conn, len, coords->array() );MB_CHK_SET_ERR( rval, "Failed to get the coordinates of the polygon vertices" );

    // calculate normal
    CartVect norm( 0.0 ), v1, v0 = coords[1] - coords[0];
    for( int i = 2; i < len; ++i )
    {
        v1 = coords[i] - coords[0];
        norm += v0 * v1;
        v0 = v1;
    }

    // calculate area
    double s, ang;
    area = 0.0;
    CartVect r, n1, n2, b, a = coords[len - 1] - coords[0];
    for( int i = 0; i < len; ++i )
    {
        r   = coords[i] - point;
        b   = coords[( i + 1 ) % len] - coords[i];
        n1  = a * r;                                          // = norm1 (magnitude is important)
        n2  = r * b;                                          // = norm2 (magnitude is important)
        s   = ( n1 % n2 ) / ( n1.length() * n2.length() );    // = cos(angle between norm1,norm2)
        ang = s <= -1.0 ? M_PI : s >= 1.0 ? 0.0 : acos( s );  // = acos(s)
        s   = ( b * a ) % norm;                               // =orientation of triangle wrt point
        area += s > 0.0 ? M_PI - ang : M_PI + ang;
        a = -b;
    }

    area -= M_PI * ( len - 2 );
    if( ( norm % r ) > 0 ) area = -area;
    return MB_SUCCESS;
}

void GeomQueryTool::set_overlap_thickness( double new_thickness )
{

    if( new_thickness < 0 || new_thickness > 100 )
    {
        std::cerr << "Invalid overlap_thickness = " << new_thickness << std::endl;
    }
    else
    {
        overlapThickness = new_thickness;
    }
    if( verbose ) std::cout << "Set overlap thickness = " << overlapThickness << std::endl;
}

void GeomQueryTool::set_numerical_precision( double new_precision )
{

    if( new_precision <= 0 || new_precision > 1 )
    {
        std::cerr << "Invalid numerical_precision = " << numericalPrecision << std::endl;
    }
    else
    {
        numericalPrecision = new_precision;
    }
    if( verbose ) std::cout << "Set numerical precision = " << numericalPrecision << std::endl;
}

}  // namespace moab