A smoother version of a polygon Â¿ is defined as a polygon which approximates Â¿ according to a given criterion and which simultaneously has no more edges than Â¿ itself. In this paper, a scale preserving smoothing algorithm is presented. The input to the algorithm is a polygon Â¿ and the output is its smoothed version Â¿. Â¿, which contains all the scale information that Â¿ contains, is called the linear minimum perimeter polygon (LMPP) of Â¿ within a tolerance of. Using the quantity the degree of with Â¿ approximates Â¿ can be controlled. From the LMPP a representation for a polygon approximating Â¿ can be procured, which is invariant to scale and translation changes. Examples of smoothing maps and characters have been presented.