Converting 2D points into 3D then connect 3D lines together

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Hi All, I'm trying to convert 2D points using camera matrix then I find the 3D lines using cv::fitLine, then I try to project them back into 2D to visualize the lines. but I get only two points and all the projected points are just in one place.

//Generate a camera intrinsic matrix
            Mat K = (Mat_<double>(3, 3)
                << 1600, 0,src.cols/2,
                0, 1600,src.rows/2,
                0, 0, 1);



            Mat invCameraIntrinsics = K.inv();
            cout << "inv" << invCameraIntrinsics;
            std::vector<cv::Vec3d> pointsTransformed3D;

            std::vector<cv::Vec3d> points3D;
            for (int i = 0; i < corners.size(); i++)
            {
                cv::Vec3d pt;

                pt[2] = 1.0f;

                pt[0] = (corners[i].x );
                pt[1] = (corners[i].y );

                points3D.push_back(pt);
            }

            cv::transform(points3D, pointsTransformed3D, invCameraIntrinsics);


            std::vector<Vec6f> outputlines;
            for (int i = 0; i < pointsTransformed3D.size(); i++)
            {   
                cv::Vec3f p1;
                p1[0] = pointsTransformed3D[i][0];
                p1[1] = pointsTransformed3D[i][1];
                p1[2] = pointsTransformed3D[i][2];
                for (int j = i + 1; j < pointsTransformed3D.size(); j++)
                {

                    cv::Vec3f p2;
                    p2[0] = pointsTransformed3D[j][0];
                    p2[1] = pointsTransformed3D[j][1];
                    p2[2] = pointsTransformed3D[j][2];

                    for (int b = j + 1; b < pointsTransformed3D.size(); b++)
                    {
                        cv::Vec3f p3;
                        p3[0] = pointsTransformed3D[b][0];
                        p3[1] = pointsTransformed3D[b][1];
                        p3[2] = pointsTransformed3D[b][2];

                        std::vector<cv::Vec3f> lines;

                        lines.push_back(p1);
                        lines.push_back(p2);
                        lines.push_back(p3);

                        Vec6f lineOutput;
                        cv::fitLine(lines, lineOutput, CV_DIST_L2, 0, 0.01, 0.01);

                        outputlines.push_back(lineOutput);

                    }
                }
            }

Mat rvec = (Mat_<double>(3, 3) << 1, 0, 0, 0, 1, 0, 0, 0, 1);
            Mat tvec = (Mat_<double>(3, 1) << 0, 0, 0);


            //Project the 3D Point onto 2D plane
            std::vector<cv::Point2d> points_2d;
            std::vector<cv::Point3d> points_3d;

            for (int i = 0; i < pointsTransformed3D.size(); i++)
            {
                cv::Point3d pt; 
                pt.x = (outputlines[i][0]);
                pt.y = (outputlines[i][1]);
                pt.z = (outputlines[i][2]);
                points_3d.push_back(pt);
            }

            projectPoints(points_3d, rvec, tvec, K, Mat(), points_2d);

            for (size_t i = 0; i < points_2d.size(); i++)
            {
                cv::Point2d pt;

                pt.x = points_2d[i].x;
                pt.y = points_2d[i].y;

                cv::circle(src, pt, 10, cv::Scalar(255, 0, 255), -1);
            }