The use of inflatable structures in aerospace applications is becoming increasingly widespread. In order to monitor the inflation status and overall health of these inflatables, an accurate means of shape sensing is required. To this end, we investigated two existing methods for measuring simple curvature, or curvature in one-dimension. The first method utilizes a pair of strain sensing Fiber Bragg Gratings (FBGs) separated by a known distance; dividing the difference in strain by the separation distance yields an experimental value for the one-dimensional curvature at a point. The second method makes use of conductive ink-based flex sensors, which give a variable resistance based on curvature. We used the latter was in a design for a Curvature-Based Inflation Controller (CBIC). While the controller successfully inflated a test body, its overall utility is limited by the simplicity of its sensors. To improve the shape sensing capabilities of the controller, we investigated the use of FBGs in a multidimensional array. We fabricated a curvature-sensing FBG pair on an inflatable membrane and tested its accuracy as the membrane was shaped into a known radius of curvature. This work reports on the assembly of three such curvature-sensing FBG pairs into a two-dimensional Curvature-Sensing Rosette (CSR). The goal is to use this rosette to measure the curvature of a surface in multiple directions at a single point. A 3-D printed surface with saddle geometry was used to calibrate the curvature-sensing rosette. Presented will be methods of extracting values for the tensor of curvature for the surface at a point using the curvature-sensing rosette, along with experimental verification. This essentially defines the local geometry about the rosette, measured in real time. By employing an array of such rosettes across the surface of an inflatable structure, the local curvature of the inflatable could be known at every point. Combining these curvature measurements can yield an accurate depiction of the global geometry. Thus, the inflation status of the inflatable space structure could be monitored in real time.