I have the following problem. I not only want to calculate the angle between two planes, I would also like to know what's the direction of this angle, basically the yaw angle. So I would set plane A to some angle, then calculate the angle between the direction of plane A and the direction of the highest slope between both planes. I know angle alpha in the image thats no problem

So far I have two planes, defined by their normal vector. Then I can calculate the cross product of these two, which give me the line of intersection. Then I take the normal vector of this line, project it to reference plane A and say plane A has a certain direction vector. Now I calculate the angle between the direction vector of plane A and the projected normal vector of the line of intersection. But then I still don't know if I am going up or down.

I would like to know the angle beta in this picture. Black is a reference vector for the first (reference plane A), which I can assign to this plane, red is the direction of the highest slope. How do I find this vector? Then I could calculate beta.

Maybe there is also another possibility. If I calculate roll and pitch angle (so set the normal component of the reference plane one time to zero for x -> roll angle between both plane, and one time to zero for y - pitch angle) separately, then I could from a combination of these, also calculate the yaw angle between two planes?

Does someone know the solution? I hope I have explained it clearly.


  • $\begingroup$ keyword : "dihedral angle" $\endgroup$ – Jean Marie Jan 29 '20 at 15:33
  • $\begingroup$ Does this answer your question? calculating the dihedral angle of two planes $\endgroup$ – Jean Marie Jan 29 '20 at 15:36
  • $\begingroup$ The highest slope angle is your $\alpha$ in the first picture. Maybe you're confused by thinking ''ok, if I move this vector then the angle will grow and get a higher slope'' but that is not the case (since contradicts definition) but also because in that mindset, there wouldn't be such a highest slope line since by letting your red vector approach the line of intersection then you would get a higher slope but never reaching a maximum since at the intersection line itself it is not defined. I hope this helps, regards. $\endgroup$ – astro Jan 29 '20 at 23:58
  • $\begingroup$ hmm but I would like to calculate alpha (already done) and beta (I don't know how). There must be a way to also calculate beta, or I am really confused? I mean this red vector is also in the reference plane. So if they match the direction is a 0 degree, so if I go forward I get the highest slope. $\endgroup$ – gab Jan 30 '20 at 0:06

If you have the two normal vectors, lets call them $u, v$

then $\frac {u\cdot v}{\|u\|\|v\|} = \cos \theta$

This Theta will be the angle between the normal vectors. But it will also be the angle that you are looking for for the intersection of the planes.

  • $\begingroup$ I am already know how to calculate this angle. I have added two pictures, I hope they make it more clear. $\endgroup$ – gab Jan 29 '20 at 23:19

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.