Sequence of smooth functions approximating a 2d cylinder step function Let $f(x,y)=1$ if $(x,y)$ is in the unit disk and $f=0$ otherwise. I would like to approximate $f$ by a sequence of smooth functions. The function...--prophetes.ai

Sequence of smooth functions approximating a 2d cylinder step function Let $f(x,y)=1$ if $(x,y)$ is in the unit disk and $f=0$ otherwise. I would like to approximate $f$ by a sequence of smooth functions. The functions need to be evaluated quickly so the results I'm getting from mollification are to awkward to deal with... Thanks in advance..

You might want to try any of formulae 17 to 27 in the MathWorld page for the unit step function, since the function you're interested in is expressible as

$$1-H(x^2+y^2-1)$$