An Attempt of Adaptive Heightfield Rendering with Complex Interpolants Using Ray Casting

Abstract: 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.