(2003) Marching Cube Algorithm: Review and
Trilinear Interpolation Adaptation for Image-Based Dosimetric Models.
Inspired by what is done to obtain (24), the function x([xi], [eta], [zeta]), which describes the brick, is obtained as (1) the sum of the three linear interpolations between opposite faces, minus (2) the sum of three bilinear interpolations through three sets of four "parallel" edges, plus (3) a trilinear interpolation through the eight vertices.
and is the contribution from the trilinear interpolation through the eight vertices.
He solves the problem by
trilinear interpolation of diagonal of voxel unit [8].
In mathematics, there are various kinds of interpolation approaches such as linear interpolation, polynomial interpolation, spline interpolation,
trilinear interpolation, and Gaussian interpolation [75].
11-(a) and (b) show isosurfaces for an isovalue of 0.5, and the vertices of the surfaces were generated from
trilinear interpolation on [32.sup.3] and [128.sup.3] grids respectively.
In the second step, values of n are determined at the internal points of the approximated grid cells by means of polynomial
trilinear interpolation. Polynomial structure of n enables to compute refraction and 3D refraction gradient at a trajectory point that belongs to such a cell and to determine the next trajectory point according to system (4).
To obtain the times in a finer grid (necessary for accurate location), we use the
trilinear interpolation described below.
Trilinear interpolation is a common way to define a function inside each cell.
* topology preserving tetrahedral decomposition of a cube with trilinear interpolation