1. A process for determining values of new pixels which are to be interpolated in a unit area which is determined by four pixel centers of an original image on a display screen, and which has the four pixel centers at four corners thereof, respectively, for magnifying an image consisting of original pixels on the display screen, comprising the steps of: (a) storing, in a plurality of registers, coordinates of a set of division lines uniquely defining a plurality of modes of division of the unit area, respectively, where, in each of the modes, the unit area is divided into sections by one of the division lines corresponding to each of the modes; (b) detecting an angle of an original line image on the display screen in a predetermined vicinity of the unit area by comparing values of a combination of original pixels in the predetermined vicinity of the unit area with each of a plurality of predetermined patterns of an arrangement of pixel values, where the detected angle is digitized to one of a plurality of original line angles; (c) selecting one of a plurality of predetermined modes of division of the unit area so that an angle of one of the division lines of the selected mode of division conforms to the original line angle detected in step (b); (d) determining a value for each of the new pixels by assigning a value, determined based on the values of the original pixels in the predetermined vicinity, to all of the new pixels having centers in one of the sections of the unit area generated by the mode of division selected in step (c); and (e) modifying the original image on the display screen to produce a picture image using the values of the original pixels and the values of the new pixels generated in steps (a)-(d), the predetermined patterns including patterns which respectively correspond to a plurality of different portions of line images in a plurality of predetermined angles, the plurality of original line angles including 0 degrees, 90 degrees, .+-.tan.sup.-1 1, .+-..theta., and .+-.(.pi./2-.theta.), .theta. being one of (tan.sup.-1 1&lt;.theta.&lt;tan.sup.-1 2) and (tan.sup.-1 1/2&lt;.theta.&lt;tan.sup.-1 1), each of the plurality of predetermined modes of division including division lines for dividing the unit area into sections, and said selecting in step (c) selecting one of the plurality of predetermined modes of division including: a first mode having the division lines determined by x=0, y=0, x.+-.y=1/2, and x.+-.y=-1/2; a second mode having the division lines determined by x=0, y=0, y=.+-.(tan .theta.) (x-1/2), and y=.+-.(tan .theta.) (x+1/2); a third mode having the division lines determined by x=0, y=0, y-1/2=.+-.(tan .theta.)x, and y+1/2=.+-.(tan .theta.)x; a fourth mode having the division lines determined by x=0, y=0, and y+1-(1/2)tan .theta.=+(tan .theta.)x.ltoreq.0; a fifth mode having the division lines determined by x=0, y=0, and y-1+(1/2)tan .theta.=-(tan .theta.)x.gtoreq.0; a sixth mode having the division lines determined by x=0, y=0, and y-1+(1/2)tan .theta.=+(tan .theta.)x.gtoreq.0; a seventh mode having the division lines determined by x=0, y=0, and y+1-(1/2)tan .theta.=-(tan .theta.)x.ltoreq.0; an eighth mode having the division lines determined by x=0, y=0, and x-(1/2)cot .theta.+1=+(cot .theta.)y.ltoreq.0; a ninth mode having the division lines determined by x=0, y=0, and x-(1/2)cot .theta.+1=-(cot .theta.)y.ltoreq.0; a tenth mode having the division lines determined by x=0, y=0, and x+(1/2)cot .theta.-1=+(cot .theta.)y.gtoreq.0; and an eleventh mode having the division lines determined by x=0, y=0, and x+(1/2)cot .theta.-1=-(cot .theta.)y.gtoreq.0; where x=0 corresponds to a vertical line, y=0 corresponds to a horizontal line, and x=.+-.1/2 and y=.+-.1/2 determine the boundary of the unit area.