bounding_box.hh

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/*!
 *
 * Copyright (C) 2015 Technical University of Liberec.  All rights reserved.
 * 
 * This program is free software; you can redistribute it and/or modify it under
 * the terms of the GNU General Public License version 3 as published by the
 * Free Software Foundation. (http://www.gnu.org/licenses/gpl-3.0.en.html)
 * 
 * This program is distributed in the hope that it will be useful, but WITHOUT
 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
 * FOR A PARTICULAR PURPOSE.  See the GNU General Public License for more details.
 *
 * 
 * @file    bounding_box.hh
 * @brief   
 */

#ifndef BOX_ELEMENT_HH_
#define BOX_ELEMENT_HH_

#include "system/system.hh"
#include "system/global_defs.h"
#include "mesh/point.hh"

#include <vector>
#include <armadillo>

/**
 * @brief Bounding box in 3d ambient space.
 *
 * Primary intention is usage in BIHTree and various speedups of non-compatible
 * intersections.
 *
 * Copy constructor and assignment are default provided by compiler.
 * These can be used to set bounds latter on without particular method
 * to this end:
 *
 * @code
 * BoundingBox box;         // non-initialized box
 * box=BoundingBox( arma::vec3("0 1 2"), arma::vec3("4 5 6") );
 * @endcode
 *
 * Don;t worry about performance, all is inlined.
 */
class BoundingBox {
public:
    TYPEDEF_ERR_INFO( EI_split_point, double);
    TYPEDEF_ERR_INFO( EI_interval_left, double);
    TYPEDEF_ERR_INFO( EI_interval_right, double);
    DECLARE_EXCEPTION(ExcSplitting, << "Split point " << EI_split_point::val
                                    << "out of bounds: <" << EI_interval_left::val
                                    << ", " << EI_interval_right::val << ">\n");

    /// Currently we set dimension to 3.
    static const unsigned int dimension = 3;
    /// stabilization parameter
    static const double epsilon;
    /// Currently we assume
    typedef Space<dimension>::Point Point;


    /**
     * Default constructor.
     * No initialization of vertices. Be very careful using this.
     * One necessary usage is vector of BoundigBox.
     */
    BoundingBox() {}

    /**
     * Constructor for point box.
     */
    BoundingBox(const Point &min)
    : min_vertex_(min), max_vertex_(min)
    {};

    /**
     * Constructor.
     *
     * From given minimal and maximal vertex.
     */
    BoundingBox(const Point &min, const Point &max)
    : min_vertex_(min), max_vertex_(max)
    {
        OLD_ASSERT( arma::min( min <= max ) , "Wrong coordinates in constructor.");
    };

    /**
     * Constructor.
     *
     * Make bounding box for set of points.
     */
    BoundingBox(const vector<Point> &points);

    /**
     * Set maximum in given axis.
     */
    void set_max(unsigned int axis, double max) {
        OLD_ASSERT_LESS(axis , dimension);
        OLD_ASSERT_LE( min(axis) , max);
        max_vertex_[axis] = max;
    }

    /**
     * Set minimum on given axis.
     */
    void set_min(unsigned int axis, double min) {
        OLD_ASSERT_LESS(axis, dimension);
        OLD_ASSERT_LE(min , max(axis));
        min_vertex_[axis] = min;
    }

    /**
     *  Return minimal vertex of the bounding box.
     */
    const Point &min() const {
        return min_vertex_;
    }

    /**
     *  Return maximal vertex of the bounding box.
     */
    const Point &max() const {
        return max_vertex_;
    }

    /**
     *  Return minimal value on given axis.
     */
    double min(unsigned int axis) const {
        return min()[axis];
    }

    /**
     *  Return maximal value on given axis.
     */
    double max(unsigned int axis) const {
        return max()[axis];
    }


    /**
     *  Return size of the box in given axis.
     */
    double size(unsigned int axis) const {
        return max()[axis] - min()[axis];
    }


    /**
     *  Return center of the bounding box.
     */
    Point center() const {
        return (max_vertex_ + min_vertex_) / 2.0;
    }

     /**
     * Return center of projection of the bounding box to given @p axis.
     * Axis coding is: 0 - axis x, 1 - axis y, 2 - axis z.
     */
    double projection_center(unsigned int axis) const {
        OLD_ASSERT_LESS(axis, dimension);
        return (max_vertex_[axis] + min_vertex_[axis])/2;
    }

    /**
     * Returns true is the  box element contains @p point
     *
     * @param point Testing point
     * @return True if box element contains point
     */
    bool contains_point(const Point &point) const
    {
        for (unsigned int i=0; i<dimension; i++) {
            if ((point(i) + epsilon < min_vertex_(i)) ||
                (point(i) > epsilon + max_vertex_(i))) return false;
        }
        return true;
    }

    /**
     * Returns true if two bounding boxes have intersection.
     *
     * This serves as an estimate of intersection of elements.
     * To make it safe (do not exclude possible intersection) for
     * 1d and 2d elements aligned with axes, we use some tolerance.
     * Since this tolerance is fixed, there could be problem with
     * highly refined meshes (get false positive result).
     */
    bool intersect(const BoundingBox &b2) const
    {
        for (unsigned int i=0; i<dimension; i++) {
            if ( (min_vertex_(i) > b2.max_vertex_(i) + epsilon) ||
                 (b2.min_vertex_(i)  > max_vertex_(i) + epsilon ) ) return false;
        }
        return true;
    }

    /**
     * Returns true if projection of the box to @p axis is an interval
     * less then (with tolerance) to given @p value.
     */
    bool projection_lt(unsigned int axis, double value) const
    {
        return max_vertex_(axis) + epsilon < value;
    }

    /**
     * Returns true if projection of the box to @p axis is an interval
     * greater then (with tolerance) to given @p value.
     */
    bool projection_gt(unsigned int axis, double value) const
    {
        return min_vertex_(axis) - epsilon > value;
    }

    /**
     * Split box into two boxes along @p axis by the
     * plane going through @p splitting_point on the axis.
     */
    void split(unsigned int axis, double splitting_point,
            BoundingBox &left, BoundingBox &right ) const
    {
        OLD_ASSERT_LESS(axis , dimension);
        if (min_vertex_[axis] <= splitting_point && splitting_point <= max_vertex_[axis] ) {
            left = *this;
            right = *this;
            left.max_vertex_[axis] = splitting_point;
            right.min_vertex_[axis] = splitting_point;
        } else {
            THROW( ExcSplitting() << EI_interval_left(min_vertex_[axis])
                                  << EI_interval_right(max_vertex_[axis])
                                  << EI_split_point(splitting_point) );
        }
    }

    /**
     * Expand bounding box to contain also given @p point.
     */
    void expand(const Point &point) {
        for(unsigned int j=0; j<dimension; j++) {
            min_vertex_(j) = std::min( min_vertex_[j], point[j] );
            max_vertex_(j) = std::max( max_vertex_[j], point[j] );
        }
    }

    /**
     * Return index of the axis in which the box has longest projection.
     */
    unsigned char longest_axis() const {
       auto diff=max_vertex_ - min_vertex_;
       return (diff[1] > diff[0])
                   ?  ( diff[2] > diff[1] ? 2 : 1 )
                   :  ( diff[2] > diff[0] ? 2 : 0 );
    }

    /**
     * Project point to bounding box.
     *
     * If point is in bounding box, returns its.
     */
    Point project_point(const Point &point) const {
        Point projected_point;
        for (unsigned int i=0; i<dimension; ++i) {
            if ( projection_gt(i, point[i]) ) projected_point[i] = min_vertex_(i);
            else if ( projection_lt(i, point[i]) ) projected_point[i] = max_vertex_(i);
            else projected_point[i] = point[i];
        }

        return projected_point;
    }


private:
    /// minimal coordinates of bounding box
    Point min_vertex_;
    /// maximal coordinates of bounding box
    Point max_vertex_;
};

/// Overloads output operator for box.
inline ostream &operator<<(ostream &stream, const BoundingBox &box) {
    stream << "Box("
           << box.min(0) << " "
           << box.min(1) << " "
           << box.min(2) << "; "
           << box.max(0) << " "
           << box.max(1) << " "
           << box.max(2) << ")";
    return stream;
}

#endif /* BOX_ELEMENT_HH_ */