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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 s_i and ma-
terial indices m_i, 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 t^k
associated with the corners of the cell via the following rule:

t^k — Si if к = m_i
t^k_l = 0 otherwise

• Compute the values of the tri-linear interpolant t^fc(τ) for each distinct index k.
The tri-linear coefficients are t^k for i = 0,1,... 7.

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