Abstract. The DRAT-trim tool is a satisfiability proof checker based on the new DRAT proof format. Unlike its predecessor, DRUP-trim, all presently known SAT solving and preprocessing techniques can be validated using DRAT-trim. Checking time of a proof is comparable to the running time of the proof-producing solver. Memory usage is also similar to solving memory consumption, which overcomes a major hurdle of resolution-based proof checkers. The DRAT-trim tool can emit trimmed formulas, optimized proofs, and new TraceCheck + dependency graphs. We describe the output that is produced, what optimizations have been made to check RAT clauses, and potential applications of the tool.

Ray tracing has long been a method of choice for off-line rendering, but traditionally was too slow for interactive use. With faster hardware and algorithmic improvements this has recently changed, and real-time ray tracing is finally within reach. However, real-time capability also opens up new problems that do not exist in an off-line environment. In particular real-time ray tracing offers the opportunity to interactively ray trace moving/animated scene content. This presents a challenge to the data structures that have been developed for ray tracing over the past few decades. Spatial data structures crucial for fast ray tracing must be rebuilt or updated as the scene changes, and this can become a bottleneck for the speed of ray tracing. This bottleneck has recently received much attention by researchers and that has resulted in a multitude of different algorithms, data structures and strategies for handling animated scenes. The effectiveness of techniques for ray tracing dynamic scenes vary dramatically depending on details such as scene complexity, model structure, type of motion and the coherency of the rays. Consequently, there is so far no approach that is best in all cases, and determining the best technique for a particular problem can be a challenge. In this State of the Art Report (STAR), we aim to survey the different approaches to ray tracing animated scenes, discussing their strengths and weaknesses, and their relationship to other approaches. The overall goal is to help the reader choose the best approach depending on the situation, and to expose promising areas where there is potential for algorithmic improvements.

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Clausal proofs have become a popular approach to validate the results of SAT solvers. However, validating clausal proofs in the most widely supported format (DRAT) is expensive even in highly optimized implementations. We present a new format, called LRAT, which extends the DRAT format with hints that facilitate a simple and fast validation algorithm. Checking validity of LRAT proofs can be implemented using trusted systems such as the languages supported by theorem provers. We demonstrate this by implementing two certified LRAT checkers, one in Coq and one in ACL2.

Construction of effective acceleration structures for ray tracing is a well studied problem. The highest quality acceleration structures are generally agreed to be those built using greedy cost optimization based on a surface area heuristic (SAH). This technique is most often applied to the construction of kd-trees, as in this work, but is equally applicable to the construction of other hierarchical acceleration structures. Unfortunately, SAH-optimized data structure construction has previously been too slow to allow per-frame rebuilding for interactive ray tracing of dynamic scenes, leading to the use of lower-quality acceleration structures for this application. The goal of this paper is to demonstrate that high-quality SAH based acceleration structures can be constructed quickly enough to make them a viable option for interactive ray tracing of dynamic scenes.We present a scanning-based algorithm for choosing kd-tree split planes that are close to optimal with respect to the SAH criteria. Our approach approximates the SAH cost function across the spatial domain with a piecewise quadratic function with bounded error and picks minima from this approximation. This algorithm takes full advantage of SIMD operations (e.g., SSE) and has favorable memory access patterns. In practice this algorithm is faster than sorting-based SAH build algorithms with the same asymptotic time complexity, and is competitive with non-SAH build algorithms which produce lower-quality trees. The resulting trees are almost as good as those produced by a sorting-based SAH builder as measured by ray tracing time. For a test scene with 180k polygons our system builds a high-quality kd-tree in 0.26 seconds that only degrades ray tracing time by 3.6% compared to a full quality tree.