aofR

by Tim C. Lueth, SG-Lib Toolbox: SolidGeometry 5.6 - Experiments
Introduced first in SolidGeometry 1.0, Creation date: 2012-11-11, Last change: 2025-09-14

Experiment to generate radial tubes by radial segment curves

Description

This is a simple experiment to understand that it is not possible to generate tubes simple by surface bezier curves instead of central bezier curves

Example Illustration

Syntax

[wx,wy]=aofR(R)

Input Parameter

R: bending radius

Output Parameter

`wx`:
`wy`:

Examples

Compare different curves
exp_2012_11_10
exp_2012_11_10 (4)
exp_2012_11_10 (4,[1 0 0])

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 function calculates the absolute rotation angles around the x, y, and z axes from a given 3x3 rotation matrix R.

Input Parameters

R: A 3x3 rotation matrix representing a rotation in 3D space.

Output Results

wx: Absolute rotation around the x-axis, ranging from -À to +À. If not defined, returns NaN.
wy: Absolute rotation around the y-axis, ranging from -À to +À.
wz: Absolute rotation around the z-axis, ranging from -À to +À.

Algorithm Steps

Initialize wx, wy, and wz to NaN.
Extract the third column of R as ez, the first column as ex, and the second column as ey.
Calculate wx using the formula: wx = atan2(ez(3), ez(2)) - À/2.
Adjust wx to ensure it falls within the range [-À, À].
Set wx to NaN if both ez(3) and ez(2) are zero.
Calculate wy using the formula: wy = À/2 - atan2(ez(3), ez(1)).
Adjust wy to ensure it falls within the range [-À, À].
Set wy to NaN if both ez(3) and ez(1) are zero.
Calculate wz using the formula: wz = atan2(ex(2), ex(1)).
Adjust wz to ensure it falls within the range [-À, À].

The function returns the calculated angles wx, wy, and wz, which represent the absolute rotations around the respective axes.

Algorithm explaination created using ChatGPT on 2025-08-19 06:42. (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