VLtransN

by Tim C. Lueth, SG-Lib Toolbox: SolidGeometry 5.6 - Spatial Relations
Introduced first in SolidGeometry 2.4, Creation date: 2015-08-19, Last change: 2025-09-14

returns a relative to normal vectors transformed vertex list

See Also: VLtransT , VLtransP , VLtrans1 , VLtrans0 , VLtransR , VLtransT , VLtrans

Example Illustration

Syntax

[VL,EL,EOL,FL,VNL]=VLtransN(VLO,FLO,[s,d])

Input Parameter

`VLO`:		Vertex list of a planar surface
`FLO`:		Facet list of a planar surface
`s`:		shrink factor
`d`:		distance factor

Output Parameter

`VL`:		Vertex list [nx3]
`EL`:		Edge list [nx2]
`EOL`:		Edge orthogonal list [nx3]
`FL`:		Facet list [nx3]
`VNL`:		Vertex normal list [nx3]

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, VLtransN, transforms a vertex list of a planar surface by applying a relative transformation to normal vectors. It is part of the SG-Library and was developed by Tim Lueth.

Input Parameters

VLO: Vertex list of a planar surface.
FLO: Facet list of a planar surface.
s: Shrink factor (optional, default is 0).
d: Distance factor (optional, default is 0).
T: Transformation matrix (optional, default is the identity matrix).

Output Results

VL: Transformed vertex list [nx3].
EL: Edge list [nx2].
EOL: Edge orthogonal list [nx3].
FL: Facet list [nx3].
VNL: Vertex normal list [nx3].

Algorithm Steps

Initialize s and d to 0 if not provided.
Initialize T to the identity matrix if not provided.
Use VLFLselect to select vertices and facets from VLO and FLO.
Create a triangulation object TRA using FL and VL.
Compute vertex normals VNL using vertexNormal function.
Determine the free boundary edges EL using freeBoundary.
Calculate edge normals EOL and indices c using edgeNormal.
Move border vertices outwards by s * EOL.
Move vertices towards the normal vector by d * VNL.
If T is not the identity matrix, apply transformation VLtransT to VL.
If no output is requested, plot the original and transformed surfaces using SGfigure and VLFLplot.

Algorithm explaination created using ChatGPT on 2025-08-19 07:53. (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