VLFLDelaunayVL
by Tim C. Lueth, SG-Lib Toolbox: SolidGeometry 5.6 - Auxiliary function
Introduced first in SolidGeometry 1.1, Creation date: 2014-01-10, Last change: 2025-09-14
Converts or Displays the Tetrahedrons of a Vertex List
Example Illustration
Syntax
[VL,FL]=VLFLDelaunayVL(VL)
Input Parameter
Output Parameter
VL: | | Vertex list |
FL: | | Facet List |
Examples
Displays the tetrahedrons of a cube:
VLFLfigure; VLFLDelaunayVL(VLFLbox(30,20,10))
Copyright 2014-2025 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 algorithm is designed to convert or display the tetrahedrons of a vertex list using Delaunay triangulation. It is part of the SG-Library and was created by Tim Lueth in 2014.
Input Parameters
- VL: The original vertex list, which is a matrix where each row represents a vertex in 3D space with x, y, and z coordinates.
Output Results
- VL: The updated vertex list after Delaunay triangulation.
- FL: The facet list, which represents the free boundary of the triangulation.
Algorithm Steps
- Create a Delaunay triangulation object
dt using the input vertex list VL. This is done by calling DelaunayTri with the x, y, and z coordinates of the vertices.
- Update the vertex list
VL with the vertices from the Delaunay triangulation object dt using dt.X.
- Extract the free boundary of the triangulation using
freeBoundary(dt) and store it in FL.
- Check if the number of output arguments is zero using
nargout==0. If true, proceed to display the tetrahedrons:
- Determine the number of tetrahedrons
n using size(dt.Triangulation).
- Iterate over each tetrahedron using a for loop
for i=1:n.
- For each tetrahedron, calculate its facet list
FLT using FLofTetrahedron(dt(i,:)).
- Plot the vertex list and facet list for the current tetrahedron using
VLFLplot(VL,FL,i).
Algorithm explaination created using ChatGPT on 2025-08-18 22:02. (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