Caustics rendering remains a long-standing challenge in Monte Carlo rendering because high-energy specular paths occupy only a small region of path space, making them difficult to sample effectively. Recent work such as Specular Manifold Sampling (SMS) [Zeltner et al. 2020] can stochastically sample these specular paths and estimate their unbiased weights using Bernoulli trials. However, applying SMS in interactive rendering is non-trivial because it is slow and delivers noisy images given a very limited time budget.

Abstract We introduce Arches, a hardware simulation framework designed to explore and evaluate massively parallel ray‐tracing architectures. Operating at the cycle level, Arches captures detailed performance metrics, including computational throughput, on‐chip data movement across processors, caches, and off‐chip communication via an accurate memory system model. The framework is modular, allowing flexible configuration and interconnection of processor cores, caches, and custom hardware units, enabling easy exploration of diverse hardware architectures. Arches supports high‐performance parallel execution, simulating complex ray tracing workloads to image completion. It leverages the GNU toolchain, allowing users to write C++ software targeting both the simulated architecture and native execution for debugging, including support for custom instructions to control specialized hardware components. The framework provides comprehensive performance instrumentation, offering insights into time‐varying statistics across all modules and identifying performance bottlenecks. Our evaluations demonstrate that Arches delivers performance estimates closely matching real hardware, offering faster and more accurate simulations than existing open‐source hardware simulators. Its modularity also makes it a valuable tool for exploring alternative parallel computing strategies for high‐performance ray tracing, and its extensibility enables adaptation for other workloads or general‐purpose computation.

Finding valid light paths that involve specular vertices in Monte Carlo rendering requires solving many non-linear, transcendental equations in high-dimensional space. Existing approaches heavily rely on Newton iterations in path space, which are limited to obtaining at most a single solution each time and easily diverge when initialized with improper seeds. We propose specular polynomials , a Newton iteration-free methodology for finding a complete set of admissible specular paths connecting two arbitrary endpoints in a scene. The core is a reformulation of specular constraints into polynomial systems, which makes it possible to reduce the task to a univariate root-finding problem. We first derive bivariate systems utilizing rational coordinate mapping between the coordinates of consecutive vertices. Subsequently, we adopt the hidden variable resultant method for variable elimination, converting the problem into finding zeros of the determinant of univariate matrix polynomials. This can be effectively solved through Laplacian expansion for one bounce and a bisection solver for more bounces. Our solution is generic, completely deterministic, accurate for the case of one bounce, and GPU-friendly. We develop efficient CPU and GPU implementations and apply them to challenging glints and caustic rendering. Experiments on various scenarios demonstrate the superiority of specular polynomial-based solutions compared to Newton iteration-based counterparts. Our implementation is available at https://github.com/mollnn/spoly.

Complex visual effects such as caustics are often produced by light paths containing multiple consecutive specular vertices (dubbed specular chains) , which pose a challenge to unbiased estimation in Monte Carlo rendering. In this work, we study the light transport behavior within a sub-path that is comprised of a specular chain and two non-specular separators. We show that the specular manifolds formed by all the sub-paths could be exploited to provide coherence among sub-paths. By reconstructing continuous energy distributions from historical and coherent sub-paths, seed chains can be generated in the context of importance sampling and converge to admissible chains through manifold walks. We verify that importance sampling the seed chain in the continuous space reaches the goal of importance sampling the discrete admissible specular chain. Based on these observations and theoretical analyses, a progressive pipeline, manifold path guiding , is designed and implemented to importance sample challenging paths featuring long specular chains. To our best knowledge, this is the first general framework for importance sampling discrete specular chains in regular Monte Carlo rendering. Extensive experiments demonstrate that our method outperforms state-of-the-art unbiased solutions with up to 40 × variance reduction, especially in typical scenes containing long specular chains and complex visibility.