均值重心坐标Mean Value Coordinates In 2D代码实现

c++实现2维多边形均值重心坐标（代码可能有冗余，未优化代码！）：

关于3维中均值重心坐标的实现可参考我的另一篇博客：均值重心坐标Mean Value Coordinates In 3D代码实现

/*
/// @brief      mean value coordinates in 2D
/// @details    
/// @param[in]  p,postiveity
/// @return     
/// @attention  
*/
VectorXd MyPolygon::meanValueCoordinates(Vector2d &p, bool &postiveity)
{
    postiveity = true;
    int numOfV = this->getNumberOfVertices();
    VectorXd mvc_coor = VectorXd::Zero(numOfV);
    VectorXd tanalpha = VectorXd::Zero(numOfV);
    MatrixXd temp = MatrixXd::Zero(2, numOfV);
    MatrixXd unit_v = MatrixXd::Zero(2, numOfV);
    for (int i = 0; i < numOfV; ++i)
    {
        temp.col(i) = this->vertices.col(i) - p;
        unit_v.col(i) = temp.col(i).normalized();
    }
    for (int i = 0; i < numOfV; ++i)
    {
        //Vector3d cor = Vector3d(unit_v(0, i), unit_v(1, i), 0).cross(Vector3d(unit_v(0, (i + 1) % numOfV), unit_v(1, (i + 1) % numOfV), 0));
        //tanalpha[i] = (1 - unit_v.col(i).dot(unit_v.col((i + 1) % numOfV))) / (cor.norm())*(2 * (cor.dot(Vector3d(0, 0, 1)) < 0) - 1);
        tanalpha[i] = (1 - unit_v(0, (i + 1) % numOfV)*unit_v(0, i) - unit_v(1, (i + 1) % numOfV)*unit_v(1, i)) / (unit_v(0, (i + 1) % numOfV)*unit_v(1, i) - unit_v(0, i)*unit_v(1, (i + 1) % numOfV));
    }
    for (int i = 0; i < numOfV; ++i)
    {
        mvc_coor[i] = (tanalpha[i] + tanalpha[(i - 1 + numOfV) % numOfV]) / temp.col(i).norm();
    }
    mvc_coor /= mvc_coor.sum();
    postiveity = mvc_coor.minCoeff() >= 0;
    cout << mvc_coor << endl;
    return mvc_coor;
}

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