We describe a new technique that works from a set of concept sketches to support the exploration and engineering of products. Our approach allows the capture and reuse of geometric shape information contained in concept sketches, as a means to generate solutions that can concurrently satisfy aesthetic and functional requirements. At the heart of our approach is a graph-based representation of sketches that allows the determination of topological and geometric similarities in the input sketches. This analysis, when combined with a geometric deformation analysis, results in a design space from which new shapes can be synthesized, or a developing design can be optimized to satisfy prescribed objectives. Moreover, it facilitates a sketch-based, interactive editing of existing designs that preserves the shape characteristics captured in the design space. A key advantage of the proposed method is that shape features common to all sketches as well as those unique to each sketch can be separately identified, thus allowing a mixing of different sketches to generate a topologically and geometrically rich set of conceptual alternatives. We demonstrate our technique with 2D and 3D examples.