Design process that performs geometry synthesis on a 3D model of a product based on a design problem statement and manufacturing constraints associated with a manufacturing machine intended to manufacture the product. The manufacturing constraints may include dimensions for a tool bit, dimensions for a tool head, a set of machining directions of the manufacturing machine, or any combination thereof. For a 5-axis manufacturing machine, the set of machining directions may be determined by a “NormalSearch” algorithm and/or a “HeatSearch” algorithm. The geometry synthesis produces a design solution comprising a final 3D model of the product, whereby each point on the boundary of the final 3D model is determined to be accessible by a tool bit and/or tool head in at least one machining direction of the manufacturing machine. Thus, the design solution for the product is more easily and directly manufacturable by the manufacturing machine.