  This paper presents a new method to generate tool paths for machining
freeform surfaces represented either as parametric surfaces or as triangular
meshes. This method allows for the optimal tradeoff between the preferred feed
direction field and the constant scallop height, and yields a minimized overall
path length. The optimality is achieved by formulating tool path planning as a
Poisson problem that minimizes a simple, quadratic energy. This Poisson
formulation considers all tool paths at once, without resorting to any
heuristic sampling or initial tool path choosing as in existing methods, and is
thus a globally optimal solution. Finding the optimal tool paths amounts to
solving a well-conditioned sparse linear system, which is computationally
convenient and efficient. Tool paths are represented with an implicit scheme
that can completely avoid the challenging topological issues of path
singularities and self-intersections seen in previous methods. The presented
method has been validated with a series of examples and comparisons.
