Meshfree Interpolation of Multidimensional Time-Varying Scattered Data

Interpolating and approximating scattered scalar and vector data is fundamental in resolving numerous engineering challenges. These methodologies predominantly rely on establishing a triangulated structure within the data domain, typically constrained to the dimensions of 2D or 3D. Subsequently, an interpolation or approximation technique is employed to yield a smooth and coherent outcome. This contribution introduces a meshless methodology founded upon radial basis functions (RBFs). This approach exhibits a nearly dimensionless character, facilitating the interpolation of data evolving over time. Specifically, it enables the interpolation of dispersed spatio-temporally varying data, allowing for interpolation within the space-time domain devoid of the conventional "time-frames". Meshless methodologies tailored for scattered spatio-temporal data hold applicability across a spectrum of domains, encompassing the interpolation, approximation, and assessment of data originating from various sources, such as buoys, sensor networks, tsunami monitoring instruments, chemical and radiation detectors, vessel and submarine detection systems, weather forecasting models, as well as the compression and visualization of 3D vector fields, among others.