OrientedBox.hpp

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/*
 * MOAB, a Mesh-Oriented datABase, is a software component for creating,
 * storing and accessing finite element mesh data.
 *
 * Copyright 2004 Sandia Corporation.  Under the terms of Contract
 * DE-AC04-94AL85000 with Sandia Corporation, the U.S. Government
 * retains certain rights in this software.
 *
 * This library is free software; you can redistribute it and/or
 * modify it under the terms of the GNU Lesser General Public
 * License as published by the Free Software Foundation; either
 * version 2.1 of the License, or (at your option) any later version.
 *
 */
 
/**\file OrientedBox.hpp
 *\author Jason Kraftcheck ([email protected])
 *\date 2006-07-18
 */
 
#ifndef MB_ORIENTED_BOX_HPP
#define MB_ORIENTED_BOX_HPP
 
#include "moab/Forward.hpp"
#include "moab/CartVect.hpp"
#include "moab/Matrix3.hpp"
 
#include <iosfwd>
 
namespace moab
{
 
#define MB_ORIENTED_BOX_UNIT_VECTORS 1
#define MB_ORIENTED_BOX_OUTER_RADIUS 1
 
class Range;
 
/**\brief Oriented bounding box
 */
class OrientedBox
{
  private:
    void order_axes_by_length( double ax1_len,
                               double ax2_len,
                               double ax3_len );  //!< orders the box axes by the given lengths for each axis
 
  public:
    CartVect center;  //!< Box center
    Matrix3 axes;     //!< Box axes, unit vectors sorted by extent of box along axis
#if MB_ORIENTED_BOX_UNIT_VECTORS
    CartVect length;  //!< distance from center to plane along each axis
#endif
#if MB_ORIENTED_BOX_OUTER_RADIUS
    double radius;  //!< outer radius (1/2 diagonal length) of box
#endif
 
    inline OrientedBox() : radius( 0.0 ) {}
 
    OrientedBox( const Matrix3& axes_mat, const CartVect& center );
    OrientedBox( const CartVect axes_in[3], const CartVect& center );
 
    inline double inner_radius() const;  //!< radius of inscribed sphere
    inline double outer_radius() const;  //!< radius of circumscribed sphere
    inline double outer_radius_squared(
        const double reps ) const;  //!< square of (radius+at least epsilon) of circumsphere
    inline double inner_radius_squared( const double reps ) const;  //!< square of (radius-epsilon) of inscribed sphere
    inline double volume() const;                                   //!< volume of box
    inline CartVect dimensions() const;                             //!< number of dimensions for which box is not flat
    inline double area() const;                                     //!< largest side area
    inline CartVect axis( int index ) const;                        //!< get unit vector in direction of axis
    inline CartVect scaled_axis( int index ) const;  //!< get vector in direction of axis, scaled to its true length
 
    /** Test if point is contained in box */
    bool contained( const CartVect& point, double tolerance ) const;
 
    // bool contained( const OrientedBox& other, double tolerance ) const;
 
    /**\brief get tag handle for storing oriented box
     *
     * Get the handle for the tag with the specified name and
     * check that the tag is appropriate for storing instances
     * of OrientedBox.  The resulting tag may be used to store
     * instances of OrientedBox directly.
     *
     *\param handle_out  The TagHandle, passed back to caller
     *\param name        The tag name
     *\param create      If true, tag will be created if it does not exist
     */
    static ErrorCode tag_handle( Tag& handle_out, Interface* instance, const char* name );
 
    /**\brief Calculate an oriented box from a set of vertices */
    static ErrorCode compute_from_vertices( OrientedBox& result, Interface* instance, const Range& vertices );
 
    /**\brief Calculate an oriented box from a set of 2D elements */
    static ErrorCode compute_from_2d_cells( OrientedBox& result, Interface* instance, const Range& elements );
 
    /** Structure to hold temporary accumulated triangle data for
     *  calculating box orientation.  See box_from_covariance_data
     *  to see how this is used to calculate the final covariance matrix
     *  and resulting box orientation.
     */
    struct CovarienceData
    {
        CovarienceData() : area( 0.0 ) {}
        CovarienceData( const Matrix3& m, const CartVect& c, double a ) : matrix( m ), center( c ), area( a ) {}
        Matrix3 matrix;   //!< Running sum for covariance matrix
        CartVect center;  //!< Sum of triangle centroids weighted by 2*triangle area
        double area;      //!< 2x the sum of the triangle areas
    };
 
    /** Calculate a CovarienceData struct from a list of triangles */
    static ErrorCode covariance_data_from_tris( CovarienceData& result,
                                                Interface* moab_instance,
                                                const Range& elements );
 
    /** Calculate an OrientedBox given an array of CovarienceData and
     *  the list  of vertices the box is to bound.
     */
    static ErrorCode compute_from_covariance_data( OrientedBox& result,
                                                   Interface* moab_instance,
                                                   const CovarienceData* orient_array,
                                                   unsigned orient_array_length,
                                                   const Range& vertices );
 
    /** Test for intersection of a ray (or line segment) with this box.
     *  Ray length limits are used to optimize Monte Carlo particle tracking.
     *\param ray_start_point     The base point of the ray
     *\param ray_unit_direction  The direction of the ray (must be unit length)
     *\param distance_tolerance  Tolerance to use in intersection checks
     *\param nonnegative_ray_len Optional length of ray in forward direction
     *\param negative_ray_len    Optional length of ray in reverse direction
     */
    bool intersect_ray( const CartVect& ray_start_point,
                        const CartVect& ray_unit_direction,
                        const double distance_tolerance,
                        const double* nonnegatve_ray_len = 0,
                        const double* negative_ray_len   = 0 ) const;
 
    /**\brief Find closest position on/within box to input position.
     *
     * Find the closest position in the solid box to the input position.
     * If the input position is on or within the box, then the output
     * position will be the same as the input position.  If the input
     * position is outside the box, the outside position will be the
     * closest point on the box boundary to the input position.
     */
    void closest_location_in_box( const CartVect& input_position, CartVect& output_position ) const;
 
    //! Construct a hexahedral element with the same shape as this box.
    ErrorCode make_hex( EntityHandle& hex, Interface* instance );
 
    /** Calculate an OrientedBox given a CovarienceData struct and
     *  the list of points the box is to bound.
     */
    static ErrorCode compute_from_covariance_data( OrientedBox& result,
                                                   Interface* moab_instance,
                                                   CovarienceData& orientation_data,
                                                   const Range& vertices );
};
 
std::ostream& operator<<( std::ostream&, const OrientedBox& );
 
double OrientedBox::inner_radius() const
{
#if MB_ORIENTED_BOX_UNIT_VECTORS
    return length[0];
#else
    return axes.col( 0 ).length();
#endif
}
 
double OrientedBox::outer_radius() const
{
#if MB_ORIENTED_BOX_OUTER_RADIUS
    return radius;
#elif MB_ORIENTED_BOX_UNIT_VECTORS
    return length.length();
#else
    return ( axes.col( 0 ) + axes.col( 1 ) + axes.col( 2 ) ).length();
#endif
}
 
// Add at least epsilon to the radius, before squaring it.
double OrientedBox::outer_radius_squared( const double reps ) const
{
#if MB_ORIENTED_BOX_OUTER_RADIUS
    return ( radius + reps ) * ( radius + reps );
#elif MB_ORIENTED_BOX_UNIT_VECTORS
    CartVect tmp( length[0] + reps, length[1] + reps, length[2] + reps );
    return tmp % tmp;
#else
    CartVect half_diag = axes.col( 0 ) + axes.col( 1 ) + axes.col( 2 );
    half_diag += CartVect( reps, reps, reps );
    return half_diag % half_diag;
#endif
}
 
// Subtract epsilon from the length of the shortest axis, before squaring it.
double OrientedBox::inner_radius_squared( const double reps ) const
{
#if MB_ORIENTED_BOX_UNIT_VECTORS
    return ( length[0] - reps ) * ( length[0] - reps );
#else
    CartVect tmp = axes.col( 0 );
    tmp -= CartVect( reps, reps, reps );
    return ( tmp % tmp );
#endif
}
 
double OrientedBox::volume() const
{
#if MB_ORIENTED_BOX_UNIT_VECTORS
    return 8 * length[0] * length[1] * length[2];
#else
    return fabs( 8 * axes.col( 0 ) % ( axes.col( 1 ) * axes.col( 2 ) ) );
#endif
}
 
CartVect OrientedBox::dimensions() const
{
#if MB_ORIENTED_BOX_UNIT_VECTORS
    return 2.0 * length;
#else
    return 2.0 * CartVect( axes.col( 0 ).length(), axes.col( 1 ).length(), axes.col( 2 ).length() );
#endif
}
 
double OrientedBox::area() const
{
#if MB_ORIENTED_BOX_UNIT_VECTORS
    return 4 * length[1] * length[2];
#else
    return 4 * ( axes.col( 1 ) * axes.col( 2 ) ).length();
#endif
}
 
CartVect OrientedBox::axis( int index ) const
{
    return axes.col( index );
}
 
CartVect OrientedBox::scaled_axis( int index ) const
{
#if MB_ORIENTED_BOX_UNIT_VECTORS
    return length[index] * axes.col( index );
#else
    return axes.col( index );
#endif
}
 
}  // namespace moab
 
#endif