FLfreeboundaryTR4FL
by Tim C. Lueth, SG-Lib Toolbox: SolidGeometry 5.6 - TR/Tetrahedrons
Introduced first in SolidGeometry 2.4, Creation date: 2015-08-07, Last change: 2025-09-14
returns the freeBoundary facets of a tetrahedron
Description
This function is tricky to use. Use only if you complete understand what you want to do.
This function processes a FL list that contains all surface facets of a tetrahedron delaunay triangulation (ConnectivityList), created for instance by
FL=[TL(:,[2 3 4]); TL(:,[2 4 1]); TL(:,[4 3 1]); TL(:,[2 1 3])].
It analyzes which surface has no attached corresponding facet. Those have to be the outside facets of the tetrahedron delaunay triangulation, i.e. the freeBoundary.
There exist in Matlab already a method freeBoundary for a tetrahedron triangulation (nx4) which returns a facet list. There exist also a method freeBoundary for a triangle triangulation (nx3) which returns an edge list.
Example Illustration
Syntax
fb=FLfreeboundaryTR4FL(TR4FL)
Input Parameter
TR4FL: | | Facet List of a tetrahedron triangulation (FLofTL) |
Output Parameter
fb: | | outside, free boundary facet index list |
Examples
TR4=delaunayTriangulation([0 0 0;100 0 0; 0 100 0; 25 25 100]);
SGfigure; TRplot(TR4)
FL=FLfreeboundaryTR4FL(FLofTL(TR4.ConnectivityList))
Copyright 2015-2025 Tim C. Lueth. All rights reserved. The code is the property of Tim C. Lueth and may not be redistributed or modified without explicit written permission. This software may be used free of charge for academic research and teaching purposes only. Commercial use, redistribution, modification, or reverse engineering is strictly prohibited. Access to source code is restricted and granted only under specific agreements. For licensing inquiries or commercial use, please contact: Tim C. Lueth
Algorithm (Workflow)
This function, FLfreeboundaryTR4FL, identifies the free boundary facets of a tetrahedron triangulation. It processes a facet list (TR4FL) and determines which facets are on the outer boundary of the triangulation.
Input Parameters
- TR4FL: A facet list of a tetrahedron triangulation. This is a matrix where each row represents a facet of the tetrahedron, typically derived from a Delaunay triangulation.
Output
- fb: A logical index list indicating which facets are free boundaries. A value of
true means the facet is a free boundary.
Algorithm Steps
- Initialize a logical array
fb with the same number of rows as TR4FL, all set to false.
- Iterate over each facet in
TR4FL using a loop.
- For each facet, check how many other facets share the same vertices. This is done by checking if the sum of vertices that are members of the current facet equals 3.
- If fewer than two facets share the same vertices, mark the current facet as a free boundary by setting the corresponding index in
fb to true.
Example Usage
To use this function, you can create a Delaunay triangulation and then pass its connectivity list to the function:
TR4 = delaunayTriangulation([0 0 0; 100 0 0; 0 100 0; 25 25 100]);
SGfigure; TRplot(TR4);
FL = FLfreeboundaryTR4FL(FLofTL(TR4.ConnectivityList));
This example creates a tetrahedron and plots it, then calculates the free boundary facets.
Algorithm explaination created using ChatGPT on 2025-08-19 07:33. (Please note: No guarantee for the correctness of this explanation)
Last html export of this page out of FM database by TL: 2025-09-21