  Coverage path planning is a fundamental challenge in robotics, with diverse
applications in aerial surveillance, manufacturing, cleaning, inspection,
agriculture, and more. The main objective is to devise a trajectory for an
agent that efficiently covers a given area, while minimizing time or energy
consumption. Existing practical approaches often lack a solid theoretical
foundation, relying on purely heuristic methods, or overly abstracting the
problem to a simple Traveling Salesman Problem in Grid Graphs. Moreover, the
considered cost functions only rarely consider turn cost, prize-collecting
variants for uneven cover demand, or arbitrary geometric regions.
  In this paper, we describe an array of systematic methods for handling
arbitrary meshes derived from intricate, polygonal environments. This
adaptation paves the way to compute efficient coverage paths with a robust
theoretical foundation for real-world robotic applications. Through
comprehensive evaluations, we demonstrate that the algorithm also exhibits low
optimality gaps, while efficiently handling complex environments. Furthermore,
we showcase its versatility in handling partial coverage and accommodating
heterogeneous passage costs, offering the flexibility to trade off coverage
quality and time efficiency.
