VLFLtetra
by Tim C. Lueth, SG-Lib Toolbox: SolidGeometry 5.6 - SG/Solids
Introduced first in SolidGeometry 1.0, Creation date: 2012-07-15, Last change: 2025-09-14
returns a simple tetrahedron geomatry
Example Illustration
Syntax
[VL,FL]=VLFLtetra([a])
Input Parameter
a: | | side length of the tetrahedron base |
Output Parameter
VL: | | Vertex list of the tetrahedron |
FL: | | Facet list of the tetrahedron |
Copyright 2012-2025 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, VLFLtetra, generates a simple tetrahedron geometry. It is part of the SG-Library and was introduced in SolidGeometry 1.0. The function returns the vertex list (VL) and facet list (FL) of the tetrahedron.
Input Parameters
- a: The side length of the tetrahedron base. If not provided, it defaults to 10 mm.
Output Results
- VL: A matrix containing the coordinates of the vertices of the tetrahedron.
- FL: A matrix containing the indices of the vertices that form each facet of the tetrahedron.
Algorithm Steps
- Initialize the side length
a to 10 mm. If an argument is provided, set a to that value.
- Define the vertex list
VL for the tetrahedron using the side length a. The vertices are positioned in 3D space as follows:
- Vertex 1: (-a/2, -a/2, 0)
- Vertex 2: (+a/2, -a/2, 0)
- Vertex 3: (0, a/2, 0)
- Vertex 4: (0, 0, a)
- Use the
delaunayTriangulation function to create a triangulation of the vertices and extract the free boundary using freeBoundary. This provides the facet list FL and updates VL.
- If no output arguments are specified, visualize the tetrahedron using
SGfigure and VLFLplot with a view angle of (-30, 30).
Algorithm explaination created using ChatGPT on 2025-08-18 22:35. (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