We present a fast, parallel GPU algorithm for construction of uniform grids for ray tracing, which we implement in CUDA. The algorithm performance does not depend on the primitive distribution, because we reduce the problem to sorting pairs of primitives and cell indices. Our implementation is able to take full advantage of the parallel architecture of the GPU, and construction speed is faster than CPU algorithms running on multiple cores. Its scalability and robustness make it superior to alternative approaches, especially for scenes with complex primitive distributions.
We investigate the use of two-level nested grids as acceleration structure for ray tracing of dynamic scenes. We propose a massively parallel, sort-based construction algorithm and show that the two-level grid is one of the structures that is fastest to construct on modern graphics processors. The structure handles non-uniform primitive distributions more robustly than the uniform grid and its traversal performance is comparable to those of other high quality acceleration structures used for dynamic scenes. We propose a cost model to determine the grid resolution and improve SIMD utilization during ray-triangle intersection by employing a hybrid packetization strategy. The build times and ray traversal acceleration provide overall rendering performance superior to previous approaches for real time rendering of animated scenes on GPUs.
In this paper, we develop a theoretical framework for characterizing shapes by building blocks. We address two questions: First, how do shape correspondences induce building blocks? For this, we introduce a new representation for structuring partial symmetries (partial self-correspondences), which we call "microtiles". Starting from input correspondences that form point-wise equivalence relations, microtiles are obtained by grouping connected components of points that share the same set of symmetry transformations. The decomposition is unique, requires no parameters beyond the input correspondences, and encodes the partial symmetries of all subsets of the input. The second question is: What is the class of shapes that can be assembled from these building blocks? Here, we specifically consider r-similarity as correspondence model, i.e., matching of local r-neighborhoods. Our main result is that the microtiles of the partial r-symmetries of an object S can build all objects that are (r + ε)-similar to S for any ε > 0. Again, the construction is unique. Furthermore, we give necessary conditions for a set of assembly rules for the pairwise connection of tiles. We describe a practical algorithm for computing microtile decompositions under rigid motions, a corresponding prototype implementation, and conduct a number of experiments to visualize the structural properties in practice.
Figure 1: We present a system for the fabrication of construction sets from example geometry. Pipeline overview: (1) input geometry (2) symmetry-based tiling grammar (3) optimized grammar (4) pieces that can be manufactured and assembled to (5) produce shape variations. AbstractThis paper poses the problem of fabricating physical construction sets from example geometry: A construction set provides a small number of different types of building blocks from which the example model as well as many similar variants can be reassembled. This process is formalized by tiling grammars. Our core contribution is an approach for simplifying tiling grammars such that we obtain physically manufacturable building blocks of controllable granularity while retaining variability, i.e., the ability to construct many different, related shapes. Simplification is performed by sequences of two types of elementary operations: non-local joint edge collapses in the tile graphs reduce the granularity of the decomposition and approximate replacement operations reduce redundancy. We evaluate our method on abstract graph grammars in addition to computing several physical construction sets, which are manufactured using a commodity 3D printer.
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