- #1

- 402

- 1

## Main Question or Discussion Point

Hello mathematicians,

I'm creating a program and I need in this program to rotate some planes around the origin, while I'm given the coefficients a,b,c and d for this plane, they represent a plane of the form:

a x + b y + c z = d

So these coefficients are given and I want to rotate the plane with Euler angles (alpha, beta and gamma).

What I tried is the following:

As a first step, I need to parametrise this plane, to do that I casted this simple parametrisation:

x = u,

y = v,

z = (d - a u - b v)/c

So now to apply the rotation I just have to use the rotation group, as follows:

x' = u cos(alpha) + v sin(alpha),

y' = -u sin(alpha) + v cos(alpha),

z' = z,

where x',y',z' are the rotated coordinates.

Now the problem appears here. How will I restore this form as coefficients a,b,c and d to be in the first formulation ax'+by'+cz'=d? In other words how will I cancel the parametrisation?

Have I chosen the shortest path? is there a smarter way to do this?

Any effort is highly appreciated,

Thank you

I'm creating a program and I need in this program to rotate some planes around the origin, while I'm given the coefficients a,b,c and d for this plane, they represent a plane of the form:

a x + b y + c z = d

So these coefficients are given and I want to rotate the plane with Euler angles (alpha, beta and gamma).

What I tried is the following:

As a first step, I need to parametrise this plane, to do that I casted this simple parametrisation:

x = u,

y = v,

z = (d - a u - b v)/c

So now to apply the rotation I just have to use the rotation group, as follows:

x' = u cos(alpha) + v sin(alpha),

y' = -u sin(alpha) + v cos(alpha),

z' = z,

where x',y',z' are the rotated coordinates.

Now the problem appears here. How will I restore this form as coefficients a,b,c and d to be in the first formulation ax'+by'+cz'=d? In other words how will I cancel the parametrisation?

Have I chosen the shortest path? is there a smarter way to do this?

Any effort is highly appreciated,

Thank you