10
Chapter 2
Tri-Iinear Representation of Segmented Volumes
2.1 Multi-material Contouring
2.1.1 Classification method
Our approach for multi-material contouring is to replace a signed grid of scalars with
a grid whose vertices have an associated scalar and material. In the two material
case, our method should reproduce the standard +/— interpretation using normal
contouring. In the case of three or more materials, the contouring method should
generate piecewise tri-l∙inear contours that join continuously along the faces of the
grid.
Given a grid cell whose corners have associated non-negative scalars si and ma-
terial indices mi, the following method can be used to determine the material index
of a point x inside the cell. The index i ranges from 0 to 7, representing the eight
corners of a cell.
Material Classification Method
• For each distinct material index present in the cell, construct a set of scalars tk
associated with the corners of the cell via the following rule:
tk — Si if к = mi
tkl = 0 otherwise
• Compute the values of the tri-linear interpolant tfc(τ) for each distinct index k.
The tri-linear coefficients are tk for i = 0,1,... 7.