What Is the Purpose of the 2skew Function in Barbic's Paper?

[datahead8888]

Hello,

Background:
I was going to implement an implicit approach to 3d tetrahedra deformations (first in Matlab then in C++).
I need the Jacobian for the partial derivative of force wrt position to do this.
I found this paper that gives a method for computing it:
http://www-bcf.usc.edu/~jbarbic/BarbicExactCorotationalFEMStiffnessMatrix.pdf

The Question:
In the report, he defines a 2skew function (to the right of the page). I'm pretty confused on what it means. I think I forgot what skew means from linear algebra - that's probably part of my problem. It sounds like skew symmetric means that a negated matrix is equal to its transpose. What exactly is this 2skew function for?

 

[jvicens]

Hello,

Thank you for sharing your findings and question. The 2skew function mentioned in the paper is used to compute the skew symmetric matrix of a given matrix. In linear algebra, a skew symmetric matrix is a square matrix where the elements below the main diagonal are the negative of the corresponding elements above the main diagonal. This means that a skew symmetric matrix is equal to its own transpose multiplied by -1.

The 2skew function is used in the paper to compute the skew symmetric matrix of the rotation matrix. This is important because the rotation matrix is used to calculate the Jacobian in the deformable tetrahedra model. By using the 2skew function, the authors are able to efficiently calculate the Jacobian without having to manually compute the skew symmetric matrix.

I hope this explanation helps clarify the use of the 2skew function in the paper. Let me know if you have any further questions or concerns. Good luck with your implementation!