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Now showing 1 - 5 of 5
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    Automatic Step Size Relaxation in Sphere Tracing
    (The Eurographics Association, 2023) Bán, Róbert; Valasek, Gábor; Babaei, Vahid; Skouras, Melina
    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.
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    Tetrahedral Interpolation on Regular Grids
    (The Eurographics Association, 2021) Bán, Róbert; Valasek, Gábor; Bittner, Jirí and Waldner, Manuela
    This work proposes the use of barycentric interpolation on enclosing simplices of sample points to infer a reconstructed function from discrete data. In particular, we compare the results of trilinear and tetrahedral interpolation over regular 3D grids of second order spherical harmonics (SH) light probes. In general, tetrahedral interpolation only requires four data samples per query in contrast to the 8 samples necessary for trilinear interpolation, at the expense of a more expensive weight computation. Our tetrahedral implementation subdivides the cubical cells into six tetrahedra and uses the barycentric coordinates of the query position as weights to blend the probe data. We show that barycentric coordinates can be calculated efficiently in shaders for our particular tetrahedral decomposition of the cube, resulting only in simple arithmetic and conditional move operations.
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    Sparse Ferguson-Hermite Signed Distance Fields
    (The Eurographics Association, 2023) Bán, Róbert; Valasek, Gábor; Singh, Gurprit; Chu, Mengyu (Rachel)
    We investigate Hermite interpolation in the context of discrete signed distance field filtering. Our method uses tricubic Hermite interpolation to generate a C1 continuous approximation to the signed distance function of the input scene. Our representation is kept purely first order by setting the mixed partial derivatives to zero, similarly to how Ferguson constructed bicubic Hermite patches. Our scheme stores four scalars at each sample, the value of the signed distance function and its first three partial derivatives. We optimize storage by only storing voxels that enclose a volume boundary. We show that this provides both a significant reduction in storage and render times compared to a dense grid of Ferguson-Hermite samples. Moreover, our construct requires smaller storage than traditional zero order trilinearly filtered fields of the same visual quality, at the expense of performance.
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    Hermite Interpolation of Heightmaps
    (The Eurographics Association, 2022) Bán, Róbert; Valasek, Gábor; Sauvage, Basile; Hasic-Telalovic, Jasminka
    Heightmaps are ubiquitous in real-time computer graphics. They are used to describe geometric detail over an underlying coarser surface. Various techniques, such as parallax occlusion mapping and relief mapping, use heightmap textures to impose mesostructural details over macrostructural elements without increasing the actual complexity of the rendered geometries. We aim to improve the quality of the fine resolution surface by incorporating the gradient of the original function into the sampling procedure. The traditional representation consists of simple height values stored on a regular grid. During rendering, bilinear filtering is applied. We propose to store the partial derivatives with the height values and use Hermite interpolation between the samples. This guarantees a globally C1 continuous heightfield instead of the C0 -continuity of bilinear filtering. Moreover, incorporating higher order information via partial derivatives allows us to use lower resolution heightmaps while retaining the appearance of a higher resolution map. In parallax mapping, surface normals are often stored alongside the height values, as such, our method does not require additional storage, since normals and partial derivatives can be calculated from one another. The exact normals of the reconstructed cubic Hermite surface can also be calculated, resulting in a storage efficient replacement for normal mapping with richer visual appearance.
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    Quick Cone Map Generation on the GPU
    (The Eurographics Association, 2022) Valasek, Gábor; Bán, Róbert; Pelechano, Nuria; Vanderhaeghe, David
    We propose an efficient conservative cone map generation algorithm that has T(N^2 logN) complexity for textures of dimension N ×N in contrast to the T(N^4) complexity of brute-force approaches. This is achieved by using a maximum mip texture of a heightmap to process all texels during the search for cone apertures, resulting in real-time generation times. Furthermore, we show that discarding already visited regions of neighboring mip texels widens the obtained cones considerably while still being conservative. Finally, we present a method to increase cone aperture tangents further at the expense of conservativeness. We compare our methods to brute-force and relaxed cone maps in generation and rendering performance.