OPTIMAL CALCULATION OF ODF WITH THE CANONICAL NORMAL DISTRIBUTION ON THE ROTATION GROUP

By T. Savyolova, E. A. Davidzhan, T. Ivanova. 1999

Macroscopic physical properties of most polycrystalline materials are controlled by orientation distribution of their grains. The orientation distribution function (ODF) of a polycrystal is seldom if ever determined directly from an experiment. Usually experimental data are represented by a set of pole figures (PFs), these latter are some integral projections of the ODF. The main problem of quantitative texture analysis is to recover ODF from its corresponding PFs. With any set of PFs the solution of this problem is non-unique. That is why some assumptions about ODF structure are necessary. We consider ODF as superposition of the canonical normal distribution (CND) on the rotation group SO(3).

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Citations in the corpus

• DiffDock: Diffusion Steps, Twists, and Turns for Molecular Docking (2022, background): “The diffusion kernel on SO(3) is given by the IGSO(3) distribution [8, 9], which can be sampled in the axis-angle parameterization by sampling a unit vector ω̂ ∈ so(3) uniformly and random angle ω ∈ [0, π] according to”
• Antigen-Specific Antibody Design and Optimization with Diffusion-Based Generative Models for Protein Structures (2022, background): “IGSO(3) denotes the isotropic Gaussian distribution on SO(3) parameterized by a mean rotation and a scalar variance [30, 34, 35].”
• SE(3) diffusion model with application to protein backbone generation (2023, unknown): “3.3 agrees with previous proposed expressions of the law of the Brownian motion (Nikolayev & Savyolov, 1970; Leach et al., 2022) up to a two-fold deceleration of time.”