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With the present concept, a comprehensive synthesis from theoretical tensor notation and traditional matrix calculus to new classes of matrices and object-oriented algorithms for mechanics and engineering problems was accomplished. This integral approach to the elementary tensor calculus of tensor bases has been realized with the tensor class BASIS, and was tested using the function METRIC. In this context, also graphical methods for the perspective representation of basis vectors and tensor quantities play a significant role in illustrating the correlation of these quantities in three-dimensional space. For this purpose, the graphic classes PERSPEKTIVE and PyPLOT were created and utilized with the function BASES_3D for three-dimensional stereo vision.

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Conclusion

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  • 发表日期：

    2025年

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  • Udo F. Meissner

摘要

With the present concept, a comprehensive synthesis from theoretical tensor notation and traditional matrix calculus to new classes of matrices and object-oriented algorithms for mechanics and engineering problems was accomplished. This integral approach to the elementary tensor calculus of tensor bases has been realized with the tensor class BASIS, and was tested using the function METRIC. In this context, also graphical methods for the perspective representation of basis vectors and tensor quantities play a significant role in illustrating the correlation of these quantities in three-dimensional space. For this purpose, the graphic classes PERSPEKTIVE and PyPLOT were created and utilized with the function BASES_3D for three-dimensional stereo vision.