We present an approach to high-level shape editing that adapts the structure of the shape while maintaining its global characteristics. Our main contribution is a new algebraic model of shape structure that characterizes shapes in terms of linked translational patterns. The space of shapes that conform to this characterization is parameterized by a small set of numerical parameters bounded by a set of linear constraints. This convex space permits a direct exploration of variations of the input shape. We use this representation to develop a robust interactive system that allows shapes to be intuitively manipulated through sparse constraints.