Hi, my name is Dale and I am new to this forum.

Hopefully, someone will find this problem interesting. It has stumped me for far too long and would really appreciate some help.

Given Local Orthogonal Vectors Xa, Ya, Za and Xb, Yb, Zb

Find the rotation angle theta such that the edges intersect (complex miter joint problem)

Normally miter joint problems are concerned with the saw-cut angle but for my case, I need to know the torsional rotation angle.

I am hope the image explains the problem adequately. If more information is needed, just let me know. Thanks!

Angle of torsion required for complex miter joint-math-problem.jpg