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Pythagorean Hodograph Curves - Quaternion Representation (Quintics)

version 1.1.0.0 (153 KB) by Duccio Mugnaini
Implementation in c++ of Spatial PH Quintic is provided.

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Updated 22 Jun 2016

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.: Pythagorean Hodograph Quintic Curves by Quaternion Representation (PHQCQR) Package :.
The package comprises a library of routine written in C++ to build a PH Quintic. Here you can find C++ methods that can help you to manage:
- basic operation between arrays such as V1+V2, V1-V2, dotProd(V1, V2), crossProd(V1, V2), dirCos(V1), norm(V)
- basic quaternion algebra ( Q+Q, Q*Q, Q-Q, conj(Q), magn(Q))
- constructor to build Spatial Ph Quintic Curves;
- constructor to build General Helical Spatial Ph Quintic Curves;
- constructor to build Spatial Ph Quintic Curves which satisfies Hermite Interpolant Conditions.
The main ideas, behind this code, is use C++ to generate all numerical values related to Spatial Ph Quintic Curve, then read and visualize all datas through Matlab.
The code has been developed using XCode 7.3 and Matlab 2014b on Mac OSX El Capitan 10.11.5 (June 2016).
The code is widely commented and easy to use.
.: Hint :.
To have a better and deeply idea about the function that you can find I suggest you to take a look to the following header files:
- quaternion.hpp
- sptPhQuintic.hpp
- readWriteLib.hpp

.: Coding (Matlab):.
From a programmers' perspective, this example illustrates how to use:
- OOP (https://www.mathworks.com/help/pdf_doc/matlab/matlab_oop.pdf);
- Advance use of plot properties (http://it.mathworks.com/help/matlab/ref/plot.html);

.: Coding (C++):.
From a programmers' perspective, this example illustrates how to use:
- OOP (http://www.cplusplus.com/doc/tutorial/classes/);
- Advance Operator Overloading:
http://www.tutorialspoint.com/cplusplus/cpp_overloading.htm
http://www.learncpp.com/cpp-tutorial/92-overloading-the-arithmetic-operators-using-friend-functions/
- I/O writing on file to produce readable numerical results.

.: References :.
[1] Rida T. Farouki, Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable,
http://www.springer.com/us/book/9783540733973

.: Other :.
If you consider to use this library in your work you are kindly requested to mention this repository in your work.
If you find any kind of error or simply you have some questions, please contact me immediately at: duccio.mugnaini[at]gmail.com
Many thanks in advance,
Duccio Mugnaini.

.: Demo :.
https://www.youtube.com/watch?v=A06aMBZIvzM

.: Quaternions :.
https://www.youtube.com/watch?v=dVCZs7vedWE

Cite As

Duccio Mugnaini (2021). Pythagorean Hodograph Curves - Quaternion Representation (Quintics) (https://www.mathworks.com/matlabcentral/fileexchange/57804-pythagorean-hodograph-curves-quaternion-representation-quintics), MATLAB Central File Exchange. Retrieved .

Comments and Ratings (3)

Leonardo Montecchi

Nice work!

Mauro Maccioni

Very good!

Niccolò Rogai

It works

MATLAB Release Compatibility
Created with R2014b
Compatible with any release
Platform Compatibility
Windows macOS Linux

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