Volume-Preserving Parameterizations via Preconditioned Nonlinear Conjugate Gradient Method
This page provides the MATLAB demo and the data format for computing ball-shaped volume-preserving mappings of tetrahedral meshes via a preconditioned nonlinear conjugate gradient method for isovolumetric energy minimization.
Input tetrahedral mesh
Ball-shaped mapping result
Data Format
The tetrahedral mesh \((T,V)\) are stored in a MATLAB .mat file, where \(T\) records tetrahedral connectivity, \(V\) stores the original vertex coordinates, and \(S\) stores the mapped vertex coordinates.
Each data item is arranged as follows:
$$ T = \begin{bmatrix} i_1 & j_1 & k_1 & \ell_1 \\ \vdots & \vdots & \vdots & \vdots \\ i_m & j_m & k_m & \ell_m \end{bmatrix}\in\mathbb{N}^{m\times 4} ~\text{, }~ V = \begin{bmatrix} v_1^1 & v_1^2 & v_1^3 \\ \vdots & \vdots & \vdots \\ v_n^1 & v_n^2 & v_n^3 \end{bmatrix} ~\text{ and }~ S = \begin{bmatrix} s_1^1 & s_1^2 & s_1^3 \\ \vdots & \vdots & \vdots \\ s_n^1 & s_n^2 & s_n^3 \end{bmatrix} \in\mathbb{R}^{n\times 3}. $$