Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

In a three-dimensional space, given a cylinder of radius $R$ and height $L$ with the axis forming a couple of angles $\{\phi,\theta\}$ with respect to the $z$ axis of the $\{x,y,z\}$ reference frame, a gaussian function: $$G=\frac{1}{2\pi\sigma^2}\exp\left(-\frac{1}{2}\frac{x^2+y^2}{\sigma^2}\right)$$ intersects the surface of the cylinder. What is the equation of the shape of the figure formed by this intersection? We can assume the center of the axis of the cylinder to be coincident with the origin of the cartesian coordinates. Thanks.

share|cite|improve this question
Do you mean the surface $z=G(x,y)$? – joriki Oct 10 '12 at 11:19
@joriki: yes, $z=G(x,y)$ – Riccardo.Alestra Oct 10 '12 at 11:22
You can write the cylindrical surface as $(\vec a\cdot\vec r)^2+(\vec b\cdot\vec r)^2=R^2$ and substitute $z=G(x,y)$ to get a relationship between $x$ and $y$ on the curve, but since that results in a transcendental equation I doubt you'll find a closed-form solution. – joriki Oct 10 '12 at 11:30

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.