intersectionquadrature.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    intersection.hh
 * @brief   
 */

#ifndef INTERSECTION_HH_
#define INTERSECTION_HH_

/*!
 *
 * Copyright (C) 2007 Technical University of Liberec.  All rights reserved.
 *
 * Please make a following refer to Flow123d on your project site if you use the program for any purpose,
 * especially for academic research:
 * Flow123d, Research Centre: Advanced Remedial Technologies, Technical University of Liberec, Czech Republic
 *
 * 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.
 *
 * 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.
 *
 * You should have received a copy of the GNU General Public License along with this program; if not,
 * write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 021110-1307, USA.
 *
 *
 * $Id: neighbours.h 1055 2011-04-21 13:43:54Z jan.brezina $
 * $Revision: 1055 $
 * $LastChangedBy: jan.brezina $
 * $LastChangedDate: 2011-04-21 15:43:54 +0200 (Thu, 21 Apr 2011) $
 *
 * @file
 * @brief ???
 *
 */


#include "mesh/mesh_types.hh"
#include <armadillo>

#include "mesh/ngh/include/intersectionLocal.h"



/**
 * Navrh algoritmu pro hledani pruniku elementu dvou siti (libovlnych dimenzi)
 * algoritmus postupuje od bodu pruniku pres usecky a polygony k mnohostenum
 *
 * Vstup: Sit1 dimenze d1 a Sit2 dimenze d2
 * predpoladam d1<=d2
 *
 * 1) hladam body na hranici pruniku tj.
 *    Intersection<d> <d_e1,d_e2> .. prunik ma dimenzi d a pronikaji se simplexy dimenze d_e1, a d_e2
 *
 *    Intersection<0><0,0>  .. totozne vrcholy El<0>
 *    Intersection<0><0,1> a <1,0> .. vrchol jedne site lezi na hrane druhe site
 *    Intersection<0><0,n> a <n,0> .. vrchol lezi na El<n> druhe site
 *
 *    Intersection<0><1,1> .. bodovy prusecik dvou usecek v rovine
 *    Intersection<0><1,2> a <2,1> ... prusecik hrany a trojuhelnika
 *    ... dalsi zvlastni pripady vcetne <0><3,3> .. tetrahedrony s vrcholem na povrchu druheho
 *
 * 2) liniove pruniky Intersection<1>:
 *    Intersection<1><1,1> .. usecky na spolecne primce
 *    Intersection<1><1,2> a <2,1>.. usecka v rovine trojuhelnika
 *    Intersection<1><1,3> a <3,1> .. usecka a tetrahedron
 *    Intersection<1><2,2> .. prusecik dvou trojuhelniku
 *    Intersection<1><2,3> a <3,2> .. trojuhelnik a hrana tetrahedronu
 *    ..
 *
 * ... doprcic je to fakt hodne moznosti a je otazka, zda je nutne je vsechny rozlisovat
 *
 * Algoritmus by mel probuhat takto:
 *
 * 1) Najdu vrchol V site 1 a element E site 2 aby V byl v E
 *    (to neni tak trivialni, pokud site nepokryvaji stejnou oblast ale snad by to slo hledat v
 *     pruniku obalovych boxu)
 * 2) najdu pruseciky P_i hran z vrcholu V s povrchem E,
 *    konstruuju vsechny potrebne pruniky elementu majici vrchol V s elementem E
 *
 *    Sousedni elementy spolu s hranami ktere do nich vedou ulozim do prioritni fronty.
 *
 * 3) Vyberu z prioritni fronty novy E, pricemz vyuzivam spositane pruseciky psislusne steny a okoli vrcholu V
 *    tj. jdu po hranach po kterych jsem do noveho lementu prisel a najdu vsechny hranove pruniky, pak konstuuju slozitejsi pruniky
 *    az mam vsechny pruniky s novym elementem ...
 *
 *    ...
 *
 *    Prioritni fronta by preferovala elementy do kterych jsem se nejvicekrat dostal, tim se snazim minimalizovat povrch projite oblasti.
 *    Je ale mozne, ze to algoritmus naopak zpomali, pokud je prioritni fronta log(n).
 *
 *    Zpracovani jednoho elementu tedy zahrnuje
 *    1) trasovani hran:
 *       pro hranu H: testuju hledam prusecik se ctyrstenem:
 *         ANO -> pamatuju si hranovy prunik a ke stene (resp. sousednimu elementu) kde hrana vychazi pridam vychozi hranu
 *         NE -> konci ve vrcholu, dalsi hrany vychazejici z vrcholu pridam na seznam hran vchazejicich do elementu
 *
 *    2) po nalezeni pruniku vsech hran, hledam pruniky vsech vchazejicich ploch:
 *       jedna plocha ma se vstupni stenou useckovy prunik na jehoz konci jsou:
 *        *vstupni hrana
 *        * okraj steny
 *       kazdopadne trasuju okraj plosneho pruniku pres povrch elementu, nebo po vstupnich hranach,
 *       pokud prunikova plocha obsahuje vrchol tvorim nove vstupni plochy ...
 *
 *    3) Podobne trasuju vchazejici objemy
 *
 *    ?? lze nejak vyuzit pokud ma element vice vstupnich sten
 *       minimalne se da kontrolovat ...
 *
 *
 *  Struktura systemu pruniku do budoucna:
 *  1) trida IntersectionManager, ma matici vektoru. Na poli A(i,j) je vektor lokalnich souradnic na elementu dimenze i (chodi od 1 do 3)
 *     pruniku dimenze j (chodi od 0 do 3 resp do 2 pokud nebudu chtit prekryvy siti stejne dimenze)
 *
 *  2) Jeden intersection objekt je pak iterator dvou elementu a dva indexy lokalnich souradnic v prislusnych vektorech.
 *
 *  Prozatim to zjednodusime tak, ze vektory lokalnich souradnic budu alokovat zvlast a nebudu je zdruzovat
 *
 *
 *  Nakonec potrebuju pocitat integral pres prunik z nejake funkce f(phi_a(x), phi_b(x)), kde phi_a je bazova funkce na jednom elementu a phi_b na druhem.
 *  To budu delat numerickou kvadraturou, takze potrebuji zobrazit prunik na jednotkovy simplex. Pro uzel kvardatury x_i musim najit body a_i a b_i na
 *  referencnich elementech A a B. Tj potrebuju lokalni souradnice (to jsou souradnice na referencnich elementech) kvadraturnich bodu. V nic pak umim spocitat hodnotu bazovych funkci
 *  a pak i hodnotu funkce f.
 *
 *  K tomu staci mit matici transformace pruniku na referencni element. Takze bych pro jednotlive dvojice element - prunik mel matici + posouvaci vektor z armadila.
 *
 *
 *
 */

#include <iostream>

class Intersection {
public:
    Intersection(const ElementFullIter ele_master, const ElementFullIter ele_slave,
                 const IntersectionLocal *isec);

    /// dimension of the master element
    unsigned int master_dim();

    /// dimension of the slave element
    unsigned int slave_dim();

    const Element * master_iter() const
        {return const_cast<Element *>( (Element *)(master) );}
    const Element * slave_iter() const
        {return const_cast<Element *>( (Element *)(slave) );}

    arma::vec map_to_master(const arma::vec &point) const;
    arma::vec map_to_slave(const arma::vec &point) const;
    double intersection_true_size() const;

    ElementFullIter master, slave; // master lower dimension

private:
    /// dimenze pruniku
    unsigned int dim;

    /// matrix part of linear transform from reference element of intersection to reference element of master or slave
    arma::Mat<double> master_map, slave_map;
    /// shift vector of the linear transform
    arma::vec master_shift, slave_shift;
    void intersection_point_to_vectors(const IntersectionPoint *point, arma::vec &vec1, arma::vec &vec2);
};


#endif /* INTERSECTION_HH_ */