Most positive/negative curvature and flexure are among the most useful seismic attributes for detecting faults and fractures in the subsurface based on the geometry of seismic reflections. When applied to fracture characterization and modelling of a fractured reservoir, their magnitude and azimuth help quantify both the intensity and orientation of fracturing, respectively. However, previous efforts focus on estimating only the magnitude of both attributes, whereas their associated azimuth is ignored in three-dimensional (3D) seismic interpretation. This study presents an efficient algorithm for simultaneously evaluating both the magnitude and azimuth of most positive/negative curvature and flexure from 3D seismic data. The approach implemented in this study is analytically more accurate and computationally more efficient compared with the existing approach. The added value of extracting most positive/negative curvature and flexure is demonstrated through the application to a fractured reservoir at Teapot Dome (Wyoming). First, the newly extracted attributes make computer-aided fault/fracture decomposition possible. This allows interpreters to focus on one particular component for fracture characterization at a time, so that a composite fractured reservoir could be partitioned into different components for detailed analysis. Second, curvature/flexure azimuth allows interpreters to plot fracture histogram and/or rose diagram in an automatic and quantitative manner. Compared with the conventional plotting rose diagram based on manual measurements, automatic plotting is more efficient and offers unbiased insights into fracture systems by illuminating the most likely orientations of natural fractures in fractured reservoirs.