Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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

As I know it, a periodic function is a function that repeats its values in regular intervals or period. However Bézier curves can also be periodic which means closed as opposed to non-periodic which means open. How is this related or possible?

share|cite|improve this question
For a closed curve, the Bézier components become periodic if the slopes at the "two" endpoints (actually, now just one point since they are coincident) are matched accordingly. – J. M. Aug 17 '12 at 1:02
up vote 2 down vote accepted

A curve $C$ parameterised over the interval $[a,b]$ is closed if $C(a) = C(b)$. Or, in simpler terms, a curve is closed if its start point coincides with its end-point. A Bézier curve will be closed if its initial and final control points are the same.

A curve $C$ is periodic if $C(t+p) = C(t)$ for all $t$ ($p \ne 0$ is the period). Bézier curves are described by polynomials, so a Bézier curve can not be periodic. Just making its start and end tangents match (as J. M. suggested) does not make it periodic.

A spline (constructed as a string of Bézier curves) can be periodic.

People in the CAD field are sloppy in this area -- they often say "periodic" when they mean "closed".

share|cite|improve this answer
Hmm, I was sloppy there. I should have said that you could make a periodic extension out of your Bézier curve components... – J. M. Aug 18 '12 at 5:50

Your Answer


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

Not the answer you're looking for? Browse other questions tagged or ask your own question.