Algorithm (Workflow)

This algorithm is designed to generate facets for a closed contour using a vertex list (VL) as input. It is a part of the SG-Library and was created by Tim Lueth in 2012.

Input Parameters

• VL: A vertex list or point list containing four or more points. It is expected to be a matrix where each row represents a point in 3D space.

Output Results

• VL: The vertex list, potentially resorted.
• FL: The facet list, which contains the indices of the vertices that form each facet.

Algorithm Steps

1. Check if the input vertex list (VL) has more than three columns. If so, transpose it to ensure it is in the correct format.
2. Find the starting point for the contour. This is done using the VLGraham function, which likely implements the Graham scan algorithm to find the convex hull of the points.
3. Determine the index of the starting point in the original vertex list and shift the list so that this point is the first.
4. Initialize indices k0, k1, and k2 to represent the first three points in the list. Initialize an empty facet list FL.
5. Enter a loop that continues until k0 equals k2, indicating the contour is closed.
6. Calculate the cross product of vectors formed by the points at indices k0, k1, and k2 to determine the orientation of the turn.
7. If the cross product S is positive, it indicates a counter-clockwise turn, and a facet is formed with these points. Update the facet list FL and move to the next point by incrementing k1 and k2.
8. If S is not positive, it indicates a clockwise turn, and the algorithm backtracks by adjusting the indices k0, k1, and k2 to consider previous points.
9. Repeat the process until the contour is closed, and all facets are generated.

The algorithm efficiently generates a set of facets for a closed contour by iteratively checking the orientation of turns and adjusting the indices of the points accordingly.