WignerSeitzCell.h

/* Copyright 2016 Kristofer Björnson
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 *     http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */
 
 
#ifndef COM_DAFER45_TBTK_WIGNER_SEITZ_CELL
#define COM_DAFER45_TBTK_WIGNER_SEITZ_CELL
 
#include "TBTK/Index.h"
#include "TBTK/ParallelepipedCell.h"
#include "TBTK/Vector3d.h"
 
#include <cmath>
#include <vector>
 
namespace TBTK{
 
class WignerSeitzCell : public ParallelepipedCell{
public:
    WignerSeitzCell();
 
    WignerSeitzCell(
        const std::vector<std::vector<double>> &basisVectors,
        MeshType meshType
    );
 
    virtual ~WignerSeitzCell();
 
    virtual Index getMajorCellIndex(
        const std::vector<double> &coordinates
    ) const;
 
    virtual Index getMinorCellIndex(
        const std::vector<double> &coordinates,
        const std::vector<unsigned int> &numMeshPoints
    ) const;
 
    virtual std::vector<std::vector<double>> getMajorMesh(
        const std::vector<unsigned int> &numMeshPoints
    ) const;
 
    virtual std::vector<std::vector<double>> getMinorMesh(
        const std::vector<unsigned int> &numMeshPoints
    ) const;
 
    virtual std::vector<double> getMinorMeshPoint(
        const std::vector<unsigned int> &meshPoint,
        const std::vector<unsigned int> &numMeshPoints
    ) const;
private:
//  static constexpr double ROUNDOFF_MARGIN_MULTIPLIER = 1.000001;
 
    unsigned int getMajorCellIndexInternal(Vector3d coordinates) const;
 
    Vector3d getFirstCellCoordinates(Vector3d coordinate) const;
};
 
inline unsigned int WignerSeitzCell::getMajorCellIndexInternal(
    Vector3d coordinates
) const{
    const std::vector<Vector3d> &basisVectors = getBasisVectors();
    double coordinatesNorm = coordinates.norm();
 
    unsigned int cellIndex = 0;
    switch(getNumDimensions()){
    case 1:
    {
        const Vector3d &basisVector = basisVectors.at(0);
        double relativeMagnitude = std::abs(
            coordinates.norm()/basisVector.norm()
        );
        while(relativeMagnitude > 0.5){
            cellIndex++;
            relativeMagnitude -= 0.5;
        }
 
        break;
    }
    case 2:
    {
        const Vector3d &b0 = basisVectors.at(0);
        const Vector3d &b1 = basisVectors.at(1);
        Vector3d b2 = (b0*b1).unit();
 
        double minDistanceLine0 = Vector3d::dotProduct(b0, (b1*b2).unit());
        double minDistanceLine1 = Vector3d::dotProduct(b1, (b2*b0).unit());
        double X = abs(2*coordinatesNorm/minDistanceLine0);
        double Y = abs(2*coordinatesNorm/minDistanceLine1);
 
        for(int x = -X-1; x < X+1; x++){
            for(int y = -Y-1; y < Y+1; y++){
                if(x == 0 && y == 0)
                    continue;
 
                Vector3d latticePoint
                    = x*basisVectors.at(0)
                    + y*basisVectors.at(1);
 
                if(
                    Vector3d::dotProduct(
                        latticePoint,
                        coordinates
                    )/Vector3d::dotProduct(
                        latticePoint,
                        latticePoint
                    ) > 1/2.
                ){
                    cellIndex++;
                }
            }
        }
 
        break;
    }
    case 3:
    {
        const Vector3d &b0 = basisVectors.at(0);
        const Vector3d &b1 = basisVectors.at(1);
        const Vector3d &b2 = basisVectors.at(2);
 
        double minDistancePlane0 = Vector3d::dotProduct(b0, (b1*b2).unit());
        double minDistancePlane1 = Vector3d::dotProduct(b1, (b2*b0).unit());
        double minDistancePlane2 = Vector3d::dotProduct(b2, (b0*b1).unit());
        double X = abs(2*coordinatesNorm/minDistancePlane0);
        double Y = abs(2*coordinatesNorm/minDistancePlane1);
        double Z = abs(2*coordinatesNorm/minDistancePlane2);
 
        for(int x = -X-1; x < X+1; x++){
            for(int y = -Y-1; y < Y+1; y++){
                for(int z = -Z-1; z < Z+1; z++){
                    if(x == 0 && y == 0 && z == 0)
                        continue;
 
                    Vector3d latticePoint
                        = x*basisVectors.at(0)
                        + y*basisVectors.at(1)
                        + z*basisVectors.at(2);
 
                    if(
                        Vector3d::dotProduct(
                            latticePoint,
                            coordinates
                        )/Vector3d::dotProduct(
                            latticePoint,
                            latticePoint
                        ) > 1/2.
                    ){
                        cellIndex++;
                    }
                }
            }
        }
 
        break;
    }
    default:
        TBTKExit(
            "WignerSeitzCell::getCellIndex()",
            "Only coordinates with 1-3 componenents supported.",
            ""
        );
    }
 
    return cellIndex;
}
 
inline Vector3d WignerSeitzCell::getFirstCellCoordinates(Vector3d coordinates) const{
    const std::vector<Vector3d> &basisVectors = getBasisVectors();
    Vector3d b[3];
    for(unsigned int n = 0; n < 3; n++)
        b[n] = basisVectors.at(n);
 
    for(unsigned int n = 0; n < getNumDimensions(); n++){
        double coordinatesProjection = Vector3d::dotProduct(
            coordinates,
            (b[(n+1)%3]*b[(n+2)%3]).unit()
        );
        double bProjection = Vector3d::dotProduct(
            b[n],
            (b[(n+1)%3]*b[(n+2)%3]).unit()
        );
 
        coordinates = coordinates - ((int)((coordinatesProjection - bProjection)/bProjection + 3/2.))*b[n];
    }
 
    bool done = false;
    while(!done){
        done = true;
        for(int x = -1; x <= 1; x++){
            for(int y = -1; y <= 1; y++){
                for(int z = -1; z <= 1; z++){
                    const Vector3d v = x*b[0] + y*b[1] + z*b[2];
 
                    if((coordinates + v).norm() < coordinates.norm()){
                        coordinates = coordinates + v;
                        done = false;
                    }
                }
            }
        }
    }
 
    return coordinates;
}
 
};  //End namespace TBTK
 
#endif