(2003) Marching Cube Algorithm: Review and Trilinear Interpolation
Adaptation for Image-Based Dosimetric Models.
Additionally, the kernel also can be cubic; for example, Gobbi and Peters  introduced the pixel trilinear interpolation (PTL) that made each pixel smeared into a 2x2x 2 kernel and then compounded or alpha-blended into the resulting volume at an appropriate location.
The sampled voxels get opacities and colors through trilinear interpolation using the eight nearest voxels in the original volume grid and then the resampled opacities and colors are merged with each other and with the background by compositing to yield the final colors for the rays and since only one ray is cast per image pixel, for the corresponding pixels of the image plane.
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 .
In mathematics, there are various kinds of interpolation approaches such as linear interpolation, polynomial interpolation, spline interpolation, trilinear interpolation
, and Gaussian interpolation .
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
Trilinear interpolation is a common way to define a function inside each cell.
* topology preserving tetrahedral decomposition of a cube with trilinear interpolation