Actuated shape output provides novel opportunities for experiencing, creating and manipulating 3D content in the physical world. While various shape displays have been proposed, a common approach utilizes an array of linear actuators to form 2.5D surfaces. Through identifying a set of common interactions for viewing and manipulating content on shape displays, we argue why input modalities beyond direct touch are required. The combination of freehand gestures and direct touch provides additional degrees of freedom and resolves input ambiguities, while keeping the locus of interaction on the shape output. To demonstrate the proposed combination of input modalities and explore applications for 2.5D shape displays, two example scenarios are implemented on a prototype system.