# 3D bend equation derivation.

This is how the bend work: (The number is the angle)

I was searching for an equation to bend an object in a specific axis and I found one,It worked pretty well,but unfortunately I don't know why it works.

The equation is :

$$x'= (x-\frac { 1 }{ z\theta } )\times\cos ({ z\theta })+\frac { 1 }{ z\theta } \\ y'= y\\ z'= -(x-\frac { 1 }{ z\theta } )\times\sin ({ z\theta })$$

I want to know how they got this equation,or at least a simple explanation. and if it is already a known equation,what is its name?

• you are using a non clear reference system and notation: please explain better – G Cab Apr 27 '16 at 14:44
• @GCab you mean the equations? – Omar Ahmad Apr 27 '16 at 14:47
• yes, in the equations, how are the axes orientated with respect to the "bar" ? , why 3D ? derivative vs. $\theta$ or what ? – G Cab Apr 27 '16 at 18:55
• @GCab the Y axis is the axis that is going inward or perpendicular to the screen plane. 3D because it can take place in the 3 axis by 2 other equations similar to this. By derivation,I mean how did this equation came from,how to prove it? – Omar Ahmad Apr 28 '16 at 12:19
• What is x? Is it the height? – N.S.JOHN Apr 29 '16 at 3:46