Algorithm (Workflow)

This algorithm is a simple procedure that utilizes MATLAB's Delaunay triangulation to generate a tetrahedron list from a given vertex list. Below is a detailed explanation of the algorithm and its parameters:

Input Parameters

• VL: This is the vertex list, which is a matrix where each row represents a vertex in 3D space. Each vertex is defined by three coordinates (x, y, z).

Output Results

• THL: This is the tetrahedron list, which is the output of the function. It contains indices of the vertices that form each tetrahedron in the triangulation.

Algorithm Steps

1. The function begins by calling MATLAB's DelaunayTri function with the x, y, and z coordinates of the vertices from the input vertex list VL.
2. The DelaunayTri function performs Delaunay triangulation on the given set of points in 3D space. This process divides the convex hull of the points into tetrahedra such that no point is inside the circumsphere of any tetrahedron.
3. The result of the DelaunayTri function is stored in the variable dt, which is a Delaunay triangulation object.
4. The tetrahedron list THL is then extracted from the Triangulation property of the dt object. This list contains the indices of the vertices that form each tetrahedron.
5. The function returns the tetrahedron list THL as the output.

This algorithm is straightforward and relies on MATLAB's built-in Delaunay triangulation capabilities to efficiently compute the tetrahedral mesh from a set of 3D points.