Generation of Random Triangular Digital Curves Using Combinatorial Techniques

This work presents an algorithm to generate simple closed random triangular digital curves of finite length imposed on a background triangular grid. A novel timestamp-based combinatorial technique is incorporated to allow the curve to grow freely without intersecting itself. The algorithm runs in linear time as a fixed set of vertices are consulted to find the next direction and since it does not require backtracking. The proposed algorithm is implemented and tested exhaustively.