Before revision:  In this paper, we present an algorithm for reconstructing embedded graphs in R^d (plane graphs in R^2) with n vertices from n^2 - n + d + 1 directional PDs. Lastly , we empirically validate the correctness and time-complexity of our algorithm in R^2 on randomly generated plane graphs using our implementation, and explain the numerical limitations of implementing our algorithm.
After revision:  In this paper, we present an algorithm for reconstructing embedded graphs in R^d (plane graphs in R^2) with n vertices from n^2 - n + d + 1 directional (augmented) PDs. Additionally , we empirically validate the correctness and time-complexity of our algorithm in R^2 on randomly generated plane graphs using our implementation, and explain the numerical limitations of implementing our algorithm.