The safety and longevity of civil infrastructure rely on robust structural health monitoring (SHM), yet conventional methods are often constrained by the high cost and impracticality of contact-based sensors. On the other hand, existing non-contact technologies typically specialize in either static geometric mapping or spatially limited dynamic vibration analysis, leading to fragmented data and complex post-processing. This research presents a unified non-contact methodology that addresses this challenge by simultaneously acquiring high-resolution 3D geometry time-series vibrational data using a single Light Detection and Ranging (LiDAR) device. For this purpose, we compare point-based measurements using a total station, an iPhone along with a profile-based LiDAR and 3D LiDAR point clouds for an experimental analysis. Sensor observations are recorded and analyzed at the same location on the experimental surface showing flexibility in input dimensionality as well as robustness in resulting scalograms. The core of the analysis is our developed method, a directional wavelet transform, a signal processing technique uniquely suited handling non-stationary signals as multidimensional unstructured data. This method enables the characterization of oscillations across the unstructured 3D surface, a capability beyond traditional modal analysis with one-dimensional time-frequency localization, but using LiDAR point cloud time series. The result is a richer and more integrated understanding of structural behavior, capable of revealing vibration behavior in high spatial detail. The study demonstrates that spatio-temporal LiDAR data contains embedded dynamic information, offering a more comprehensive and efficient way to assess the health and integrity of a structure in the future.