Fourier Error Analysis of Ray Tracing on a Geospatial Polygonal Model

This paper demonstrates that the error associated with ray tracing photorealistic polygonal models of Light Detection and Ranging (LIDAR) scan data is negligible for many applications. In some cases, the standard deviation of error is actually reduced by ray tracing to points on a polygonal model between LIDAR data rather than capturing more data from a scanner. Numerical analyses on the sources of error were performed using Fourier analysis, Taylor expansion, and a statistical model of LIDAR data. Ray tracing was then used to calculate the intersection of each polygon at a point of interest, allowing 3D data to be quantified at any location in between LIDAR points. Actual acquired from a LIDAR scanner and modeled data are then compared to the ray traced values. Results show that many data types have sufficiently low spectral content, allowing accurate representation of 3D data acquired from a LIDAR scanner as a polygonal model.