Generating automatically tuned bitmaps from outlines

Abstract

Consider the problem of generating bitmaps from character shapes given as outlines. The obvious scan-conversion process does not produce acceptable results unless important features such as stem widths are carefully controlled during the scan-conversion process. This paper describes a method for automatically extracting the necessary feature information and generating high-quality bitmaps without resorting to hand editing. Almost all of the work is done in a preprocessing step, the result of which is an intermediate form that can be quickly converted into bitmaps once the font size and device resolution are known. A heuristically defined system of linear equations describes how the ideal outlines should be distorted in order to produce the best possible results when scan converted in a straightforward manner. The Lova´sz basis reduction algorithm then reduces the system of equations to a form that makes it easy to find an approximate solution subject to the constraint that some variables must be integers. The heuristic information is of such a general nature that it applies equally well to Roman fonts and Japanese Kanji.

A natural lattice basis problem with applications

“…The application described in [10] deals with adjusting outline fonts so that they can be converted to bitmap form without introducing undesirable artifacts. This is important because printers and computer terminals require bitmaps, while character shapes are most naturally described via outlines.…”

“…The quadratic function minimized in [10] is a heuristic estimate of the distortion in important features when a given set of outlines is scan-converted. The main variables are the coordinates of control points that describe the outlines.…”

“…The paper [10] proceeds by finding certain features of the original outlines and deciding what relationships need to hold in order for the features to be preserved after scan-conversion. Each new relation to be preserved generates a new row of a matrix which we can callĀ.…”

“…There are no provisions in [10] for linear constraints on x, but they easily fit into the framework outlined above. When a relation is very important, [10] multiplies the corresponding row ofĀ by a large constant.…”

“…Lenstra [13] uses the algorithms from [1,12] for integer programming; Shamir [17], Odlyzko [14], Hastad [9] use them for cryptographic applications; Sugihara [18] uses them for representing geometrical objects; Hobby [10] uses them for font generation. Other applications appear in Frieze et al [5], Grosse and Hobby [7], and Hastad et al [8].…”