A simplicial approach to the determination of an integer point of a simplex

We propose an algorithm to find an integer point of a simplex. The algorithm is based on an integer labeling rule and a triangulation of the space. Starting at an integer point, the algorithm leaves it along one of n rays and generates a sequence of adjacent simplices of varying dimension. Within a finite number of iterations, the algorithm either yields an integer point of the simplex or proves that no such point exists.