Given a polygon of N vertices, you need only N steps to draw the similar shape of any ratio.
I would like to confirm that given a 2D shape which is non-polygonal and not circumscribed by a circle, let's say, the contour of a patato, it's impossible to precisely (in mathematical/ geometrical terms) draw its similar shape (of scaled size)? My argument is that doing so will require infinite number of steps. Such method as approximation/interpolation is not considered to be mathematically/geometrically precise.
If the above assumption is wrong, what is the method to draw such a scaled shape?
Let us take the leaf of a tree whose contour may not admit mathematical definition.(ie irregular) One can paste that leaf on a transparent sheet and pass light through that sheet and capture the image (shadow) on a screen at a distance suitably calculated to produce magnification at a desired level. (Of course ensure that light falls perpendicularly onto the sheet and that the screen and the sheet are parallel).