Wire arc additive manufacturing (WAAM) is emerging as the main additive manufacturing (AM) technology used to produce medium-to-large-sized thin-walled parts (order of magnitude: 1 m) at lower cost. To manufacture a part with this technology, the path planning strategy used is the 2.5D. This strategy consists in slicing a 3D model into different planar layers parallel to each other. The use of this strategy limits the complexity of the topologies achievable in WAAM, especially those with large variations in curvature. It also involves several start/stops of the arc as it passes from one layer to another, which induces transient phenomena in which the control of the supply of energy and matter is complex. In this article, a new manufacturing strategy to minimize the start/stop phases of the arc to one unique cycle is presented. The goal of this strategy, called "Continuous Three-dimensional Path Planning" (CTPP) is to generate a continuous trajectory in spiral form for closed-loop thin parts. An adaptive wire speed coupled with a constant travel speed allow a modulation of the deposition geometry that ensures a continuous supply of energy and material throughout the manufacturing process. Using the 5-axis strategy coupled with CTPP allows the manufacture of closed parts with a procedure to determine the optimum closing area and parts on non-planar substrates useful for adding functionalities to an existing structure. Two geometries based on continuous manufacturing with WAAM technology are presented to validate this approach. The manufacturing of these parts with CTPP and several numerical evaluations have shown the reliability of this strategy and its capacity to produce complex new shapes with a good geometrical restitution, difficult or impossible to reach today using 2.5D with WAAM technology.