VLFLDelaunayVLEL
by Tim C. Lueth, SG-Lib Toolbox: SolidGeometry 5.6 - SG/Solids
Introduced first in SolidGeometry 1.0, Creation date: 2012-08-11, Last change: 2025-09-14
closes a surface by tesselation of triangles using Delaunay
Description
uses matlab function DelaunayTri
Example Illustration
Syntax
[VLA,FLA,CLA,VLB,FLB]=VLFLDelaunayVLEL(p1,p2,p3,OVL,OEL)
Input Parameter
p1: | | Point 1 of outer triangle |
p2: | | Point 2 of outer triangle |
p3: | | Point 3 of outer triangle |
OVL: | | Vertex list |
OEL: | | Edge list of contour and constraints |
Output Parameter
VLA: | | Vertex list of closed surface |
FLA: | | Facet list of closed surface |
CLA: | | Constraint list |
VLB: | | Vertex list of removed surface, wrt convex hull |
FLB: | | Vertex list of removed surface, wrt convex hull |
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 algorithm is designed to close a surface by tessellating triangles using the Delaunay triangulation method. It is part of the VLFL-Library and was created by Tim Lueth on August 11, 2012. The function is named VLFLDelaunayVLEL and it utilizes the MATLAB procedure DelaunayTri.
Input Parameters
- p1, p2, p3: These are the three points that define the outer triangle of the surface to be closed.
- OVL: This is the vertex list, which contains the vertices of the surface.
- OEL: This is the edge list, which includes the edges of the contour and any constraints.
Output Results
- VLA: The vertex list of the closed surface.
- FLA: The facet list of the closed surface.
- CLA: The constraint list.
- VLB: The vertex list of the removed surface, with respect to the convex hull.
- FLB: The facet list of the removed surface, with respect to the convex hull.
Algorithm Steps
- Check if the edge list
OEL is empty. If it is, return empty lists for all outputs.
- Convert the vertex list
OVL from Cartesian to barycentric coordinates using the function carttobaryVL with respect to the points p1, p2, p3.
- Perform Delaunay triangulation on the barycentric coordinates using
DelaunayTri, with OEL as constraints.
- Determine the in-out status of the triangulation using
inOutStatus.
- Convert the triangulated vertices back to Cartesian coordinates using
barytocartUVL.
- Assign the converted vertices to
VLA and VLB.
- Assign the facets of the triangulation to
FLA and FLB, based on the in-out status.
- Shorten the vertex and facet lists using
VLFLshort and swap facets using FLswap for VLA and FLA.
- Shorten the vertex and facet lists for
VLB and FLB using VLFLshort.
- Assign the constraints from the Delaunay triangulation to
CLA.
- Warnings are turned off at the beginning and restored at the end of the function. The last warning message and ID are captured using
lastwarn.
Algorithm explaination created using ChatGPT on 2025-08-19 01:44. (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