TR3ofTR4
by Tim C. Lueth, SG-Lib Toolbox: SolidGeometry 5.6 - TR/Tetrahedrons
Introduced first in SolidGeometry 2.4, Creation date: 2015-08-02, Last change: 2025-09-14
returns the surface triangulation of a tetrahedron
Description
Single line function:
TR3=triangulation(freeBoundary(TR4),TR4.Points);
The function does not (!) remove unnecessary vertices unless rem=true (default is false)
Example Illustration
Syntax
[TR3,VL,FL,SI]=TR3ofTR4(TR4,[rem])
Input Parameter
TR4: | | tetrahedron triangulation |
rem: | | remove unused (internal) vertices; default is false |
Output Parameter
TR3: | | surface triangulation |
VL: | | Vertex list |
FL: | | Facet list |
SI: | | FL=SI(FL) => maps to TR4.Points |
Examples
TR4=delaunayTriangulation([0 0 0;100 0 0; 0 100 0; 25 25 100]);
TR3ofTR4(TR4)
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, TR3ofTR4, is designed to extract the surface triangulation from a given tetrahedron triangulation. It is part of the SG-Library and was developed by Tim Lueth.
Input Parameters
- TR4: This is the input tetrahedron triangulation. It is expected to be a valid triangulation object.
- rem: This is an optional boolean parameter. If set to true, the function will remove unused (internal) vertices from the triangulation. The default value is false.
Output Results
- TR3: This is the resulting surface triangulation derived from the input tetrahedron.
- VL: This is the vertex list of the surface triangulation.
- FL: This is the facet list of the surface triangulation.
- SI: This is an index mapping such that
FL=SI(FL) maps to TR4.Points.
Algorithm Steps
- Initialize
SI as an empty array and rem as false. If a second argument is provided and is not empty, set rem to this value.
- Extract the points from
TR4 and assign them to VL.
- Determine the free boundary of
TR4 and assign it to FL.
- If
rem is true, call the function VLFLselect to remove unused vertices and update VL, SI, and FL.
- Suppress specific warnings related to points not being in the triangulation.
- Create a new triangulation
TR3 using FL and VL.
- Restore the previous warning state.
- If no output arguments are specified, visualize the triangulation using
VLFLfigure and set the view angle.
Algorithm explaination created using ChatGPT on 2025-08-19 00:25. (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