## 3 Meshless Approach Overview
### Methodology
#### 3.1.3 Algorithm
The data presented in this study are available on request from the corresponding author. We appreciate the support of Australian Research Council (arc) through a Discovery Project (DP) Grant No. DP17010 2324. We would like to extend our appreciation to the respective user-access programs of j-parc and ansto (j-parc Long Term Proposal No. 2017L0101 and ansto Program Proposal) for providing access to the radon and kowari instruments and The University of Newcastle for funding R.A's scholarship. There are no conflicts of interest to declare. ## Appendix A

The LRT measurements for Bragg-edge neutron transmission with respect the sample geometry and coordinate system Figure 1 is shown below:

Table 1.9

where \(\textbf{x_{a}}=(x_{a},y_{a})\) is the entry points of the ray to the sample. Figure 4:0

Now, substituting radial basis function expression for \(\epsilon_{11},\epsilon_{12},\ \text{and}\ \epsilon_{22}\) determined previously in Equation (4) in terms of linear combination of \(R_{i}\) and \(P_{j}\) we get a closed form of line integral as: assuming, \(R_{i}\) as the Gaussian function and \(P_{j}\) as the second order polynomial written as

Figure 4:1

Figure 4:2

Hence,

Figure 4:3

where

Figure 4:4

Figure 4:5Figure 4:6

Figure 4:7

Figure 4:8

### Polynomial Basis Functions

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