类的函数表

给所有有限元基函数做了一个函数表。就是把类的成员函数的指针封装进一个容器里。

基函数的函数类型为basis_type

typedef double(BasisFunction::* basis_type)(double, double);

函数表为basis

std::vector<std::map<std::string, basis_type>> basis;

使用时只要这样就行了：basis[1]["dx"]

#BasisFunction.h
#pragma once
#include <functional>
#include <map>
#include <string>
#include <vector>
#include "MeshElement.h"

class BasisFunction;
typedef double(BasisFunction::* basis_type)(double, double);


class BasisFunction {
public:
    std::vector<std::map<std::string, basis_type>> basis;
    BasisFunction(const MeshElement& e) {
        auto c = e.coordinates;
        x1 = c[0][0]; y1 = c[0][1];
        x2 = c[1][0]; y2 = c[1][1];
        x3 = c[2][0]; y3 = c[2][1];
        _j = (x2 - x1) * (y3 - y1) - (x3 - x1) * (y2 - y1);
        /// this part is ugly.
        /// "bind" can be used to replace these lines.
        std::map<std::string, basis_type> basis_map; 
        basis_map.erase(basis_map.begin(), basis_map.end());
        basis_map["original"] = &BasisFunction::basis_1;
        basis_map["dx"]       = &BasisFunction::basis_1_dx;
        basis_map["dy"]       = &BasisFunction::basis_1_dy;
        basis.push_back(basis_map);
        basis_map.erase(basis_map.begin(), basis_map.end());
        basis_map["original"] = &BasisFunction::basis_2;
        basis_map["dx"]       = &BasisFunction::basis_2_dx;
        basis_map["dy"]       = &BasisFunction::basis_2_dy;
        basis.push_back(basis_map);
        basis_map.erase(basis_map.begin(), basis_map.end());
        basis_map["original"] = &BasisFunction::basis_3;
        basis_map["dx"]       = &BasisFunction::basis_3_dx;
        basis_map["dy"]       = &BasisFunction::basis_3_dy;
        basis.push_back(basis_map);
    }


    double get_jacobian_determian() {
        return _j;
    }

    double basis_1(double x, double y) {
        return -x_reference(x, y) - y_reference(x, y) + 1;
    }
    double basis_1_dx(double x, double y) {
        return -(y3 - y1) / _j - (y1 - y2) / _j;
    }
    double basis_1_dy(double x, double y) {
        return -(x1 - x3) / _j - (x2 - x1) / _j;
    }

    double basis_2(double x, double y) {
        return x_reference(x, y);
    }
    double basis_2_dx(double x, double y) {
        return (y3 - y1) / _j;
    }
    double basis_2_dy(double x, double y) {
        return (x1 - x3) / _j;
    }

    double basis_3(double x, double y) {
        auto z = y_reference(x, y);
        return z;
    }
    double basis_3_dx(double x, double y) {
        return (y1 - y2) / _j;
    }
    double basis_3_dy(double x, double y) {
        return (x2 - x1) / _j;
    }


private:

    // the determinant of jacobian matrix.
    double _j;
    // coordinates
    double x1, x2, x3, y1, y2, y3;

    // reference coordinates.
    double x_reference(double x, double y) {
        return ((y3 - y1) * (x - x1) - (x3 - x1) * (y - y1)) / _j;
    };
    double y_reference(double x, double y) {
        return (-(y2 - y1) * (x - x1) + (x2 - x1) * (y - y1)) / _j;
    };
};