Lipschitz-agnostic, efficient and accurate rendering of implicit surfaces

In this paper, we propose an accurate and controllable rendering process for implicit surfaces with no or unknown analytic Lipschitz constants. Our process is built upon a ray-casting approach where we construct an adaptive Chebyshev proxy along each ray to perform an accurate intersection test via a robust and multi-stage searching method. By taking into account approximation errors and numerical conditions, our methods comprise several pre-conditioning and post-processing stages to improve the numerical accuracy, which potentially applied recursively. The intersection search is performed by evaluating a QR decomposition on the Chebyshev proxy function, which can be done in a numerically accurate way. Our process achieves comparable accuracy to other techniques that impose more constraints on the surface, e.g., knowledge of Lipschitz constants, and higher accuracy compared to approaches that impose similar constraints as our approach.