# Measurement-Driven Synthesis of Female Digital Mannequin Using Convex Sub-Volumes
## 3 Materials and Methods
### Synthesis of Mannequins from Tailor Measurements
In order to build each \(f_{i}\in F\), radial basis functions and inverse distance weighting (IDW) were tested. The resulting nature of the synthesized mannequins using the former method was unstable due to the need for tuning inherent parameters. The latter rendered the best results with a polynomial degree of 2 (\(p\)). Consequently, the IDW method that defines each \(f_{i}\in F\) is expressed in Equation (1). Equation (1) is presented for a particular ellipsoid \(E_{i}\) and a particular geometrical property (e.g., \(D\) or \(S\)), following the segmented interpolation scheme. The same process is repeated for other ellipsoids and each geometrical property. Furthermore, consider the following inputs and output for Equation (1). **Inputs (variables):**  
1. \(me_{f}:\) point in \(\mathbb{R}^{l}\) that describes the \(l\) measurements of \(Me_{f}\) that influence \(E_{i}\in B_{f}\), with \(B_{f}\) the synthesized model; \(me_{f}\subset Me_{f}\). **Inputs (parameters):**  
1. \(me_{j}:\) point in \(\mathbb{R}^{l}\) that describes the \(l\) measurements of \(Me_{j}\) that influence \(E_{i}\in B_{j}\), with \(B_{j}\in RM\); \(me_{j}\subset Me_{j}\). 2. \(Q_{j}:\) known geometric property (i.e., \(D_{j}\) or \(S_{j}\)) of \(E_{i}\in B_{j}\) with \(B_{j}\in RM\)
3. \(d_{j}=||me_{j}-me_{f}||:\) euclidean distance between \(me_{f}\) and \(me_{j}\). 4. \(p:\) degree of the interpolation polynomial; \(p=2\). **Output:**  
1. \(Q_{f}:\) interpolated property (i.e., \(D_{k}\) or \(S_{k}\)) of \(E_{i}\in B_{f}\); \(Q_{f}=f(me_{j},me_{f},Q_{j})\) with \(j=1,2,\ldots,5\). \[Q_{f}=f(me)=\frac{\sum_{j=1}^{n}(\frac{Q_{j}}{d_{j}^{\prime}})}{\sum_{j=1}^{n} (\frac{1}{d_{j}^{\prime}})} \tag{1}\]  
**Example of Neighborhood Synthesis**  
An example of the synthesis of the lower body neighborhood (subset of ellipsoids) is presented in Figure 17. This example exhibits the changes of geometric properties (shape) as a function of the dependent measurements (see Figure 16a) by following the segmented interpolation scheme. The synthesized neighborhood is only dependent on measurements \(He\) and \(Hi\) given that none of the other tailor measurements in \(Me\) influence its geometry. Furthermore, note that from Figure 17, the geometry of the synthesized neighborhoods (transparent) partially resembles that of the closest Reference Mannequins (\(RM_{i}\)). The mentioned proximity corresponds to the distance in the bidimensional space defined by \(He\) and \(Hi\) between the points that represents the measurements of the particular synthesized model and of  
Figure 16: Body subsets of ellipsoids for segmented interpolation scheme. Each subset is interpolated with different subsets of the input measurements \(Me\). (**a**) Measurement dependency for body neighborhoods (subsets of ellipsoids). (**b**) Example of subsets of ellipsoids influenced by different measurements. each \(RM_{i}\). Take into account that the average mannequin in \(RM\) is omitted **only** in this particular example for the sake of simplicity.