Hessian-based Robust Ray-Tracing of Implicit Surfaces on GPU

Abstract

In recent years, the Ray Tracing of Implicit Surfaces on a GPU has been studied by many researchers. However, the existing methods have challenges that mainly includes solving for self-intersecting surfaces. General solutions for Ray Tracing suffer from the problem of false roots, and robust solutions are hard to generalize. In this paper, we present a robust algorithm based on Extended Taylor-Test Adaptive Marching Points, which allows a robust rendering of Self-Intersecting Implicit Surfaces on a GPU. We are using the Second Order Taylor Series expansion to alleviate the problem of double-roots in Self-Intersecting Implicit Surfaces. Our approach is simple to implement and is based on the Hessian Matrix of the Implicit Surface that can be attributed to the Hessian Matrix can be used to obtain second-order Taylor Series expansion for the univariate ray-equation. We compare our results using the simulated ground-truth with the smallest step-size possible with the proposed algorithm, and our proposed algorithm gives the best visual results as well as highest SSIM percentage than other approaches.