negative angle between vectors / planes

Hello,

I would like to ask a simple question: Is there a way to somehow compute and angle between two vectors / planes that is nor only positive??

I will be very thankful for a solution to this problem!!! Thank you.

Answer 1

[Moe_2015]

In order to determine if the angle between two vectors is positive or not, there would have to be a reference normal plane vector (vn). If so, yes you can. There is a way to check if the angle between those two vectors should be negative. First take the cross product of the two vectors (v1 x v2) to get the normal of the plane (v3). Then, find the dot product of v3 and vn. If this dot product is negative, then the theta (angle between v1 and v2) should be negative

[Leo Müller]

Do you mean the code should look like this? Thanks!

angle = sign(dot(cross(v1,v2),vn))* acos( dot(v1,v2) /... ( norm(v1) * norm(v2) ) );

[Moe_2015]

No problem. Yes, that is right.

[Leo Müller]

I have another question:

If I would like to find the angle between two planes, how would I do that?

Thanks!

[Moe_2015]

The angle between two planes is the same as the angle of the normal vectors of the two planes. So just use the dot product method where vn1 is the normal vector of one plane and vn2 is the normal vector of the other.

acos(dot(vn1,vn2) /( norm(vn1) * norm(vn2) )

If you don't have the normal vector and just the equation of the plane, the normal vector is just the coefficients of x y and z. For example if your plane is 3x+y-10z=5 then your normal vector to that plane is [3,1,-10].