# trilinear interpolation

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## trilinear interpolation

A texture mapping technique that produces the most realistic images and requires the most computations. This technique is used in conjunction with MIP mapping, which provides texture maps in different depths.

An algorithm is used to map a screen pixel location to a corresponding point on the two nearest texture maps (MIP maps). A weighted average of the attributes (color, alpha, etc.) of the four surrounding texels on each MIP map is computed (bilinear interpolation). Then the weighted average of the two results is applied to the screen pixel. This process is repeated for each pixel forming the object being textured.

The term trilinear refers to the performing of interpolations in three dimensions (horizontal, vertical and depth). See texture map, MIP mapping, bilinear interpolation and point sampling.
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(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 [33] 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 [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

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