CODEWITHSUNDEEP
rgeometry
P. Vauclin
P. Vauclin

Reputation: 387

Angle between 2 planes

I have the equation of a plane. I would like to obtain the angle between this plane and the plane formed by the x and y axes.

Here is an illustration:

enter image description here

Upvotes: 1

Views: 579

Answers (3)

Stéphane Laurent
Stéphane Laurent

Reputation: 84599

The angle between two planes is the same as the angle between the normals of these planes.

If ax + by + cz + d = 0 is the plane equation then (a,b,c) is a normal of this plane.

Then use the dot product:

dot_product(normal1, normal2) = cos(the_angle) * norm(normal1) * norm(normal2)

Then acos to get the angle.

Upvotes: 0

blunova
blunova

Reputation: 2532

Given the equations of the two planes:

A1x + B1y + C1z + D1 = 0
A2x + B2y + C2z + D2 = 0

where A, B, C and D are the plane coefficients, then the angle between the two planes is given by the following formula:

enter image description here

The equation of the second plane will be much simpler, i.e. z = 0.

Upvotes: 1

Mohamed Desouky
Mohamed Desouky

Reputation: 4425

If your equation of the plane is in form of

 ax + by + cz + d = 0

hence the equation of x-y plane is

z = 0

then by using this function it will return the angle in degree

ang_degree <- function(a , b , c){
    acos(abs(c)/sqrt(a^2 + b^2 + c^2))*180/pi
}

if you want it in radian remove *180/pi

Upvotes: 1

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