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Item Automatic Step Size Relaxation in Sphere Tracing(The Eurographics Association, 2023) Bán, Róbert; Valasek, Gábor; Babaei, Vahid; Skouras, MelinaWe 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.Item Area Lights in Signed Distance Function Scenes(The Eurographics Association, 2019) Bán, Róbert; Bálint, Csaba; Valasek, Gábor; Cignoni, Paolo and Miguel, EderThis paper presents two algorithms to incorporate spherical and general area lights into scenes defined by signed distance functions. The first algorithm employs an efficient approximation to the contribution of spherical lights to direct illumination and renders them at real-time rates. The second algorithm is of superior quality at a higher computational cost which is better suited for interactive rates. Our results are compared to both real-time soft shadow algorithms and a ground truth obtained by Monte Carlo integration. We show in these comparisons that our real-time solution computes more accurate shadows while the more demanding variant outperforms Monte Carlo integration at the expense of accuracy.Item Tetrahedral Interpolation on Regular Grids(The Eurographics Association, 2021) Bán, Róbert; Valasek, Gábor; Bittner, Jirí and Waldner, ManuelaThis 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.Item 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.Item First Order Signed Distance Fields(The Eurographics Association, 2020) Bán, Róbert; Valasek, Gábor; Wilkie, Alexander and Banterle, FrancescoThis paper investigates a first order generalization of signed distance fields. We show that we can improve accuracy and storage efficiency by incorporating the spatial derivatives of the signed distance function into the distance field samples. We show that a representation in power basis remains invariant under barycentric combination, as such, it is interpolated exactly by the GPU. Our construction is applicable in any geometric setting where point-surface distances can be queried. To emphasize the practical advantages of this approach, we apply our results to signed distance field generation from triangular meshes. We propose storage optimization approaches and offer a theoretical and empirical accuracy analysis of our proposed distance field type in relation to traditional, zero order distance fields. We show that the proposed representation may offer an order of magnitude improvement in storage while retaining the same precision as a higher resolution distance field.Item Hermite Interpolation of Heightmaps(The Eurographics Association, 2022) Bán, Róbert; Valasek, Gábor; Sauvage, Basile; Hasic-Telalovic, JasminkaHeightmaps 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.Item Quick Cone Map Generation on the GPU(The Eurographics Association, 2022) Valasek, Gábor; Bán, Róbert; Pelechano, Nuria; Vanderhaeghe, DavidWe 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.