We design and analyze an algorithm with linear complexity to perform projections between 2D and 3D nonmatching grids. This algorithm, named the PANG algorithm, is based on an advancing front technique and neighboring information. Its implementation is surprisingly short, and we give the entire Matlab code. For computing the intersections, we use a direct and numerically robust approach. We show numerical experiments both for 2D and 3D grids, which illustrate the optimal complexity and negligible overhead of the algorithm. An outline of this algorithm has already been presented in a short proceedings paper of the 18th International Conference on Domain Decomposition Methods (see Gander and Japhet [2008]).