How to buffer a polygon by area

On Wed, May 28, 2014 at 3:36 PM, ONKELINX, Thierry

    while(abs(achieved.precision) > precision & steps < maxsteps){
      buffered.perimeter <- gLength(buffered.spgeom)
      buffer.width <- buffer.width - achieved.precision * spgeom.area /
buffered.perimeter
      buffered.spgeom <- gBuffer(spgeom, width = buffer.width)
      achieved.precision <- gArea(buffered.spgeom) / spgeom.area - ratio
      steps <- steps + 1
    }

Is this guaranteed to converge? Could there be some polygon for which
the buffer width updating step bounces between two values like the
bistable state of an iterated function? Could a concave polygon have a
smaller perimeter for a larger buffer size? I think yes, but I'm not
sure if that would cause this method to not converge anyway...

My binary search is guaranteed to converge since buffer area is
strictly increasing with increasing buffer width...

Barry