1. A method for establishing new sampling points with respect to previously established sampling points which determines said new sampling points for compressing character data on a character outline comprising: a distance computing part for computing a distance L between adjacent sampling points, respectively, in respect of said sampling points which have been previously established on the outline; an area computing part for computing area S enclosed by respective outline segments cut out by said adjacent sampling points as well as an approximate curve obtained by connecting said respective sampling points which have previously been established on said outline with each other; an appreciation quantity computing part for computing appreciation quantity .xi. being a ratio S/L in respect of each segment on the basis of said distance L computed in said distance computing part and said area S determined in said area computing part; a computing part for comparing magnitude of the maximum value .xi..sub.max of the appreciation quantity determined by said appreciation quantity computing part with that of a predetermined allowable value .xi.'; and a newly-established sampling point computing part for computing further new sampling points on the basis of a prescribed relationship in the case when the result compared in said comparing part is in .xi..sub.max &gt;.xi.'; all the newly-established sampling points computed successively until the compared result turns to a relationship of .xi..sub.max .ltoreq..xi.' being established each time on said outline as desired sampling points.