VLtrans

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

return similar to PLtrans or SGtrans a transformed VL

Description

Function that analyzes the transfer argument for translation. Slower than VLtransT etc.
Usage of T
0 Center around origin
1 Only 1st quadrant
[nx3] Translation vector
[3x3] Rotation matrix
[3x4] Rotation plus translation matrix
[4x4] Fully homogenous transformation matrix

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

Example Illustration

Syntax

VL=VLtrans(VLA,T)

Input Parameter

`VLA`:		Vertex list
`T`:		Transformation vector

Output Parameter

VL: tranformed vertex list

Examples

close all; SGfigure(-30,30);  view(-30,30)
VLtrans(VLaddz(PLcircle(10,8)),0)
VLtrans(VLaddz(PLcircle(10,8)),1)
VLtrans(VLaddz(PLcircle(10,8)),[0 0 40])
VLtrans(VLaddz(PLcircle(10,8)),rot([pi/3,pi/3,pi/3]))

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)

The function VLtrans is designed to transform a vertex list (VLA) using a specified transformation (T). It is part of the SG-Library and is used for spatial transformations.

Input Parameters

VLA: A vertex list, which is a matrix where each row represents a vertex in 3D space. If the vertex list has fewer than 3 columns, a z-coordinate of 0 is added.
T: The transformation parameter, which can take several forms:
- 0: Centers the vertices around the origin.
- 1: Transforms the vertices to the first quadrant.
- [nx3]: A translation vector that shifts the vertices by the specified amounts in x, y, and z directions.
- [3x3]: A rotation matrix that rotates the vertices around the origin.
- [3x4]: A matrix that combines rotation and translation.
- [4x4]: A fully homogeneous transformation matrix that includes rotation, translation, and scaling.

Output

VL: The transformed vertex list, which is the result of applying the transformation T to VLA.

Algorithm Steps

Check if the vertex list VLA has fewer than 3 columns. If so, add a z-coordinate of 0 using the function VLaddz.
Create a structure SG with fields VL (set to VLA) and FL (an empty array).
Call the function SGtrans with the structure SG and the transformation T to perform the transformation.
Extract the transformed vertex list from SG.VL and assign it to VL.
If no output is requested (i.e., nargout==0), plot the original and transformed vertex lists using SGfigure and VLplot.

Example Usage

The function can be used in various ways, as shown in the examples:

VLtrans(VLaddz(PLcircle(10,8)),0): Centers a circle around the origin.
VLtrans(VLaddz(PLcircle(10,8)),1): Transforms a circle to the first quadrant.
VLtrans(VLaddz(PLcircle(10,8)),[0 0 40]): Translates a circle 40 units in the z-direction.
VLtrans(VLaddz(PLcircle(10,8)),rot([pi/3,pi/3,pi/3])): Rotates a circle by pi/3 radians around each axis.

Algorithm explaination created using ChatGPT on 2025-08-19 01:40. (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