Study of surface representation methods based on signed distance functions

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Abstract

The paper studies surface rendering methods based on ray tracing for representations based on signed distance functions. The main objects of interest were the rendering algorithm execution time, the amount of memory occupied, and the accuracy of the surface representation estimated by the render using the PSNR metric. Six different representations and four intersection search algorithms were analyzed. In all cases, a bounding volume hierarchy was used as an accelerating structure. The comparison revealed promising representations and algorithms and showed that distance functions in some cases are not inferior to polygonal models in speed, while they can win in terms of memory consumption and represent the surface with a good level of accuracy.

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About the authors

A. R. Garifullin

Keldysh Institute of Applied Mathematics, Russian Academy of Sciences 4 Miusskaya Square

Author for correspondence.
Email: albert.garifullin@gin.keldysh.ru
ORCID iD: 0000-0001-5385-4841
Russian Federation, Moscow, 125047

V. A. Frolov

Institute of Artificial Intelligence, Moscow State University Leninskie Gory; Keldysh Institute of Applied Mathematics, Russian Academy of Sciences 4 Miusskaya Square; Moscow State University Leninskie Gory Faculty of Computational Mathematics and Cybernetics

Email: vladimir.frolov@graphics.cs.msu.ru
ORCID iD: 0000-0001-8829-9884
Russian Federation, Moscow, 119899; Moscow, 125047; Moscow, 119899

A. S. Budak

Institute of Artificial Intelligence, Moscow State University Leninskie Gory; Moscow State University Leninskie Gory Faculty of Computational Mathematics and Cybernetics

Email: s02220347@gse.cs.msu.ru
ORCID iD: 0009-0005-6819-4184
Russian Federation, Moscow, 119899; Moscow, 119899

V. A. Galaktionov

Keldysh Institute of Applied Mathematics, Russian Academy of Sciences

Email: vlgal@gin.keldysh.ru
ORCID iD: 0000-0003-1252-8294
Russian Federation, 4 Miusskaya Square, Moscow, 125047

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Supplementary files

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2. Fig. 1. Schematic representation of the SDF representations considered in the paper. From left to right: regular grid, octree, octree with preserving values in corners (frame_octree), sparse voxel set (SVS), sparse brick set (SBS). The upper diagrams demonstrate the partitioning of the space for each of the representations. The lower diagrams show the leaf nodes of the BVH for each of the representations. Green and red dots are the positions from which the SDF is preserved in this representation. Green ones are outside the object, red ones are inside. The lower diagrams show non-empty (blue) leaf nodes of the BVH for each of the representations.

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3. Fig. 2. Test models.

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4. Fig. 3. The original 3D model (left) and Sparse Voxel Set (sdf_SVS) of different sizes built from it.

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5. Fig. 4. Comparison of SDS with compact surface representation methods (decimation, NGLOD and N-BVH). In the graphs, the x-axis represents the size, and the y-axis represents the PSNR metric value.

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