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Efficient color transformation implementation
Published in Sharma Gaurav, Digital Color Imaging Handbook, 2017
Trilinear interpolation uses all eight nodes and is the natural extension of linear interpolation to three dimensions. This is shown in Figure 11.6. To compute the interpolant at fractions t, u, and v along three respective dimensions, first compute four intermediate points (n00, n01, n10, and n11) that are t of the way along the edges varying in the first dimension. Then use those four points to define a square and perform bilinear interpolation as described in the previous section. From the square, two more points are computed (n0and n1); these are used to compute the final point n.
Large eddy simulation of flow field and particle dispersion in a ventilated model room using a parallel lattice Boltzmann method
Published in Aerosol Science and Technology, 2023
Farzad Bazdidi-Tehrani, Mohammad Saleh Sargazizadeh
The backward Eulerian method based on the following update rule (Equation (20)) is employed, with the initial condition in which is the flow velocity. This does not lead to an implicit nonlinear system of equations, since substituting the forces on the particle in Equation (19), will be obtained, as follows: where and is fluid viscosity and density, respectively; is Cunningham correction factor coefficient; is particle diameter and is the gravitational acceleration (Gao and Niu 2007). For computing the fluid velocity anywhere in the computational domain and since its information can only be computed on the lattice nodes, interpolation of the fluid velocity is necessary in every step. For this purpose, the trilinear interpolation by three successive linear interpolations in the x, y, and z directions, respectively (see Figure 3), can be executed. First, interpolation along the x-axis is carried out, as follows: where is the lattice length. followed by interpolation along the y-axis: and, finally, with applying in the direction of the z-axis, the particle velocity anywhere in the computational domain can be obtained:
Medical image interpolation based on 3D Lanczos filtering
Published in Computer Methods in Biomechanics and Biomedical Engineering: Imaging & Visualization, 2020
Thiago Moraes, Paulo Amorim, Jorge Vicente Da Silva, Helio Pedrini
The trilinear interpolation (Rajon and Bolch 2003) is a multivariate technique that operates on a three-dimensional regular grid, which approximates the value of an intermediate data point . The method employs the eight nearest points on the grid along , and directions to linearly approximate the value of the data point.