plucker.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    plucker.hh
 * @brief   Plucker coordinates class.
 * @author  Viktor Fris, Pavel Exner
 *
 */

#include <armadillo>
#include <iostream>
#include "system/system.hh"
#include "system/armor.hh"
#include "mesh/point.hh"

#ifndef _PLUCKER_H
#define _PLUCKER_H

/** @brief Plucker coordinates representing line given by points A,B.
 * 
 * Plucker class represents a line by 6 dimensional vector.
 * After inserting a three-dimensional points A and B, which represents the line,
 * class creates plucker coordinates of the line.
 *
 * Class also can compute a product of two plucker coordinates.
 * 
 * Description of Plücker Coordinates:
 * https://en.wikipedia.org/wiki/Pl%C3%BCcker_coordinates
 *
 * Empty constructor is used for passing object to pointers from different places
 * coordinates data are filled after calling method "compute"
 * a flag "computed" is for comparison if coordinates data are filled
 *
 */
class Plucker{
private:

    arma::vec6 coordinates_; ///< Plucker coordinates.
    double scale_;
    bool computed_;          ///< True, if Plucker coordinates are computed; false otherwise.
    Armor::Array<double> points_;

public:
    typedef typename Space<3>::Point Point;
    /** Default constructor.
     * Creates empty object, cannot call compute later!
     */
    Plucker();
    /** @brief Creates Plucker coordinates object for a line AB.
     * Does NOT compute Plucker coordinates.
     * Does set end points and computes direction vector.
     * @param a - A point from AB line
     * @param b - B point from AB line
     */
    Plucker(Point a, Point b);
    /** @brief The same as above constructor,
     * but can compute Pl. coordinates immediately if @p compute_pc.
     */
    Plucker(Point a, const Point b, bool compute_pc);
    
    /// Destructor.
    ~Plucker(){};

    double scale() const
    { return scale_; }

    /// Returns Plucker coordinate of @p index.
    double operator[](const unsigned int index) const;

    /// Compute product of two Plucker coordinates.
    double operator*(const Plucker &b);

    /// Sets the flag computed on false.
    void clear();

    /// Return true if Plucker coordinates have been computed already.
    bool is_computed() const;
    
    /// Gets coordinates of point.
    arma::vec3 point(unsigned int idx) const;

    /** @brief Compute Plucker coordinates and set computed to true.
     */
    void compute();

    /// Gets directional vector U.
    arma::vec3 get_u_vector() const;

    /// Gets cross product vector UxA.
    arma::vec3 get_ua_vector() const;

    /// Gets Plucker coordinates.
    arma::vec6 get_plucker_coords() const;
    
    /// Friend output operator.
    friend std::ostream& operator<< (std::ostream& os, const Plucker& p);
};

/// Operator for printing Plucker coordinates.
std::ostream& operator<<(std::ostream& os, const Plucker& p);

/****************** inline implementation *****************************/
inline double Plucker::operator[](const unsigned int index) const
{   ASSERT_DBG(computed_);
    return coordinates_[index]; }

inline void Plucker::clear()
{   computed_ = false; }

inline bool Plucker::is_computed() const
{   return computed_; }

inline arma::vec3 Plucker::point(unsigned int idx) const
{   return points_.vec<3>(idx); }

inline arma::vec3 Plucker::get_u_vector() const
{   //ASSERT_DBG(computed_);
    return coordinates_(arma::span(0,2)); }

inline arma::vec3 Plucker::get_ua_vector() const
{   ASSERT_DBG(computed_);
    return coordinates_(arma::span(3,5)); }

inline arma::vec6 Plucker::get_plucker_coords() const
{   ASSERT_DBG(computed_);
    return coordinates_; }

#endif