1. A data converting apparatus for converting a set of outline data representative of an outline of a desired image, such as a character, into a set of dot data representative of a dot image corresponding to the desired image, said apparatus comprising: a memory means for storing at least one set of outline data, each set of outline data representative of an outline of an image; selection means for selecting a set of outline data representative of an outline of a desired image; coordinate defining means for defining the outline of the desired image selected by said selection means relative to a coordinate system where the dot image corresponding to the desired image is to be formed, said coordinate defining means converting the outline data for the desired image selected by said selection means into data of coordinate values indicative of a position of at least one point on the outline of the desired image relative to the coordinate system, picture elements being defined in the coordinate system; straight line segment determining means for determining whether the set of outline data of the desired image selected by said selection means includes at least one straight line segment; direction determining means for determining whether a difference defined between a direction of each straight line segment and a predetermined reference direction falls within a predetermined range by comparing, with the predetermined reference direction, each straight line segment of the outline determined by said straight line segment determining means, when the straight line segment determining means determines that the set of outline data of the desired image includes at least one straight line segment; offset error determining means for determining whether an offset error, which will be produced when a straight line segment that is determined by said direction determining means to have a difference falling within the predetermined range is converted to a dot image, deviates from a predetermined tolerance range, the offset error determining means including maximum calculating means for calculating a maximum value of offset error which would occur dependent on a position of the straight outline segment relative to the coordinate system and maximum offset judging means for judging whether the maximum value of the offset error falls outside from the predetermined tolerance range; correction means for correcting a straight line segment, that is determined by said offset error determining means to produce an offset error deviating from the predetermined tolerance range, so that the offset error of the determined straight line segment may not fall outside the tolerance range, the correction means correcting the coordinate values indicative of a position of at least one point on the corrected straight line segment relative to the coordinate system; and filling-in means for converting the outline data including any straight line segment corrected by said correction means to a dot image and outputting dot data for creation of the dot image, said filling-in means including picture element determining means for determining, based on the coordinate values, picture elements where image dots should be located for substantially reproducing the desired image, and dot data producing means for producing the dot data for an image dot to be formed in each of the determined picture elements.