Evolutionary triangulator

This paper describes a new approach to automatic generation of unstructured and irregular triangulations of convex regions. Such triangulations find many applications, including solutions of partial differential equations using the finite element methods. A method that is based on the ideas of genetic algorithms and overcomes some weaknesses of the prior geometric approaches is presented. In general, a genetic algorithm allows a solution to evolve by selecting and promoting better solution candidates over the worse candidates. It is a self-learning algorithm enforced by raising the average fitness value of the population as the generations go by. The method starts with a random population of candidate solution, which admits a low quality of triangles and violation of the conformance criterion. The triangulator then quickly learns to move any ''nonconforming'' points inside the boundary, and continues with focusing on ''teaching'' the population to favor good quality triangular shapes as the generations evolve.