  In this technical report, we document our attempt to visualize adaptive
heightfields with smooth interpolation using ray casting in real time. The
performance of ray casting depends strongly on the used interpolant and its
efficient evaluation. Unfortunately, analytical solutions for ray-surface
intersections are only given in the literature for very few simple, piece-wise
polynomial surfaces. In our use case, we approximate the heightfield with
radial basis functions defined on an adaptive grid, for which we propose a
two-step solution: First, we reconstruct and discretize the currently visible
portion of the surface with smooth approximation into a set of off-screen
buffers. In a second step, we interpret these off-screen buffers as regular
heightfields that can be rendered efficiently with ray casting using a simple
bilinear interpolant. While our approach works, our quantitative evaluation
shows that the performance depends strongly on the complexity and size of the
heightfield. Real-time performance cannot be achieved for arbitrary
heightfields, which is why we report our findings as a failed attempt to use
ray casting for practical geospatial visualization in real time.
