We present Design-by-Morphing (DbM), a novel design methodology applicable to creating a search space for topology optimization of 2D airfoils. Most design techniques impose geometric constraints and sometimes designers' bias on the design space itself, thus restricting the novelty of the designs created, and only allowing for small local changes. We show that DbM methodology does not impose any such restrictions on the design space and allows for extrapolation from the search space, thus granti...