Abstract: A method and apparatus convert font outlines to rasterized bitmaps. The method accesses stored outline data representing an object in a first coordinate space and transforms the outline data to corresponding data representing the object in a second corrdinate space. Regional relationship information is maintained in both corrdinate spaces through a non-linear transformation expressed as a plurality of linear transformation matrices, and a bit map, suitable for displaying the object, is generated as a result of the transformation. The apparatus of the invention analyzes Bezier curves and subdivides them as necessary until each portion is sufficiently flat to be approximated as a straight line, and calculates where line segments cross pixel midlines in order to fill the outline, and then generates the bit map.