Probably the right curve was a circle's involute.
"...Its successive turns are parallel curves with constant separation distance..."
Not sure how this can be proven, but this seems to fit well with the concept of stroked path -as parallel curves at it's edges-.
Mathematical functions for the parametric curve is
x=a*(cos(t)+t*sin(t))
y=a*(sin(t)-t*cos(t))
More info here:
http://en.wikipedia.org/wiki/Involute 漸開線的圓圈 2014、circle、clipartrequest 203115、curve、evolvent、function、gear、geometry、involute、Lazur、math、parametric、spiral、tooth profile、URH 2014、圈、clipartrequest 203115、曲線、漸、功能、齒輪、幾何、漸開線、天藍、數學、參數、螺旋、牙齒輪廓、URH 資料來源:openclipart ( https://openclipart.org/ )