Automatic Step Size Relaxation in Sphere Tracing

Abstract

We propose a robust auto-relaxed sphere tracing method that automatically scales its step sizes based on data from previous iterations. It possesses a scalar hyperparemeter that is used similarly to the learning rate of gradient descent methods. We show empirically that this scalar degree of freedom has a smaller effect on performance than the step-scale hyperparameters of concurrent sphere tracing variants. Additionally, we compare the performance of our algorithm to these both on procedural and discrete signed distance input and show that it outperforms or performs up to par to the most efficient method, depending on the limit on iteration counts. We also verify that our method takes significantly fewer robustness-preserving sphere trace fallback steps, as it generates fewer invalid, over-relaxed step sizes.