Quantifying damage in nonlinear systems remains challenging. Existing methods using chaotic interrogation are limited because they are based on algorithms designed for time series prediction and have difficulty determining damage type or location. To address this shortcoming, we propose analysis based on exciting a structure with a chaotic signal and then measuring changes in the outer boundary of the chaotic attractor associated with the structural response. Sampling the boundaries of attractors associated with both the undamaged and damaged structures allows boundary transformation vectors (BTVs) to be drawn between the boundaries that encode information about how the system has changed. Certain regions of the boundary will deform proportionally to damage level, but these regions may be situated differently or deform in different directions for different damage types or locations, allowing this additional information to be inferred. If a library of BTVs for known damage cases are recorded, then future, unknown damage can be quantified using interpolation or extrapolation of the library. A simulated mass-spring-damper system is used to demonstrate how both damage level and type/location can be determined using chaotic interrogation in combination with boundary transformation analysis.