SGofVLalphaShape
by Tim C. Lueth, SG-Lib Toolbox: SolidGeometry 5.6 - TR/Tetrahedrons
Introduced first in SolidGeometry 4.2, Creation date: 2018-08-14, Last change: 2025-09-14
returns the alphashape of a vertex list
See Also:
Example Illustration
Syntax
SG=SGofVLalphaShape(VL,[al])
Input Parameter
VL: | | Vertex List |
al: | | optional alpha radius |
Output Parameter
SG: | | Solid Geometry of the Alpha Shape |
Examples
[a,b,c,d,e,f]=invkinrplan3(5,10,5); VL=f(e,:); SGfigure; VLplot(VL,'.'); view(-30,30)
SGofVLalphaShape(VL)
Copyright 2018-2025 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, SGofVLalphaShape, computes the alpha shape of a given vertex list (VL) and returns the solid geometry of the alpha shape. It is part of the SG-Library and was introduced in SolidGeometry 4.2.
Input Parameters
- VL: A list of vertices representing points in space.
- al (optional): The alpha radius, which influences the shape of the alpha shape. If not provided, a default value is used.
Output Results
- SG: The solid geometry of the alpha shape, including vertex and face lists.
- ca: The critical alpha value, which is the smallest alpha that captures all points in the shape.
Algorithm Steps
- Initialize
al to an empty array. If an alpha value is provided in varargin, assign it to al.
- Create an alpha shape object
Tas using the vertex list VL. If al is provided, use it; otherwise, use the default.
- Calculate the critical alpha value
ca using the criticalAlpha function with the 'all-points' option.
- Generate the alpha triangulation
TL from Tas.
- Create a triangulation object
TR3 using TL and VL.
- Extract the free boundary
FL from TR3.
- Store the vertex list
VL and free boundary FL in the output structure SG.
- If no output is requested, plot the alpha shape using
VLFLplot and set the plot lighting. Display the critical alpha value.
Algorithm explaination created using ChatGPT on 2025-08-19 00:57. (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