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We present DreamSketch, a novel 3D design interface that combines the free-form and expressive qualities of sketching with the computational power of generative design algorithms. In DreamSketch, a user coarsely defines the problem by sketching the design context. Then, a generative design algorithm produces multiple solutions that are augmented as 3D objects in the sketched context. The user can interact with the scene to navigate through the generated solutions. The combination of sketching and generative algorithms enables designers to explore multiple ideas and make better informed design decisions during the early stages of design. Design study sessions with designers and mechanical engineers demonstrate the expressive nature and creative possibilities of DreamSketch.