This paper analyzes the applicability of the task-programming model to the parallelization of the wavefront pattern. Computations for this type of problem are characterized by a data dependency pattern across a data space. This pattern can produce a variable number of independent tasks through traversing this space. Different implementations of this pattern are studied based on the current state-of-the-art threading frameworks that support tasks. For each implementation, the specific issues are discussed from a programmer's point of view, highlighting any advantageous features in each case. In addition, several experiments are carried out, and the factors that can limit performance in each implementation are identified. Moreover, some optimizations that the programmer can exploit to reduce overheads (task recycling, prioritization of tasks based on locality hints and tiling) are proposed and assessed.