Abstract: The invention relates to methods, systems, and programming for producing and drawing subpixel-optimized bitmap images of shapes, such as fonts, by using non-linear color balancing. Some embodiments associate a luminosity with each subpixel of such an image as a function of (a) the percent of the subpixel's area covered by the shape and (b) the distribution to nearby subpixels of portions of the subpixel's resulting coverage value that cause color imbalance. Some embodiments distribute a subpixel's coverage value as a function of its difference from coverage values of other subpixels in the same pixel. Some embodiments draw a image comprised of pure foreground and background color pixels, as well as intermediary pixels in which subpixels are determined as a function of both foreground and background colors and color balancing. The intermediary pixels can, but need not, separate the foreground and background pixels along the direction of color balancing.

Abstract: The invention relates to methods, systems, and programming for producing and displaying subpixel-optimized images and digital content including such images. Some embodiments access digital content represented by a mark-up language and display it with its images scaled down in a subpixel-optimized manner in a format dictated by the mark-up language. Some embodiments produce subpixel-optimized images by calculating the luminosity of a subpixel in such an image as a function of the length of a plurality of coverage lines within a window in a source image corresponding to the subpixel that is covered by source image pixels having the subpixel's color.

Abstract: The present invention is a method for determining the optimum angle for displaying a line on raster output devices. The preferred embodiment defines the possible adjustments of a line as it is being displayed at a raster resolution as a penalty which comprises of a weighted sum of a distance variable and an angular variable. The weight permits the user to decide between a trade-off between the fidelity to original angle and the quality of a line being displayed. To determine the optimum angle for displaying a line at a particular raster resolution, the present invention finds the angle with the smallest penalty. The optimum angle is further constrained by a plurality of variables set by the user. Once the user provides the constraints on the minimum penalty, the present invention automatically determines the optimum angle for displaying a line on a raster output devices.

Abstract: An arbitrary curve formulated as a quadratic B-spline with a plurality of second order Bezier curves is approximated. Applying a forward differencing to the parametric equation of the second degree Bezier curves, a second order difference coefficient is derived. By defining the error from approximating the curve with forward differencing as the distance between the approximated point on the curve and the midpoint between the end points of the curve, the second order differential coefficient is directly proportional to the error. Additionally, the error resulting from increasing the number of parametric intervals for the forward differencing is proportional to the original error. It follows from the relationship established for the second order differential coefficient, the number of parametric intervals, and the error threshold that the user specifies, the number of parametric intervals is determined.

Abstract: A method for manipulating the control points of a symbol image represented by an outline font to improve the appearance of the font on raster output devices which are under control of a computer. The method includes storing control points specifying the outlines of a symbol image, specifying the desired movement direction defined by a first unit vector in which the control point should move, and specifying a desired measurement direction defined by a second unit vector by which the movement of the control point should be measured. The desired measurement direction and the desired movement direction forming an angle of predetermined size. The method further includes moving the control points in the desired movement direction and measuring the control points against the predetermined angle with the desired measurement direction, this measurement producing a resulting movement direction and storing the results of the manipulation of the control points in a memory means.

Abstract: In a computer system with a raster output device, a method for manipulating the outlines of a symbol image at various sizes such that the outline defines a close representation of the symbol image. A plurality of control points which correspond to an outline of the symbol image are stored in a memory of the computer system. The size of the symbol image which is to be output on the raster device is determined. The computer system then determines, given the size of the symbol image, whether the control points of the outline of the symbol must be adjusted in order to provide a proper display of the symbol. If adjustment is warranted, at least one of the control points for the outline is selected. The selected control points are then displaced by a predetermined amount to form a new outline of the symbol image. This adjusted outline is then stored in the computer system's memory and may be output in the raster device.

Abstract: A method for manipulating the control points of a symbol image represented by an outline font to improve the appearance of the font on raster output devices which are under control of a computer. The method includes storing control points specifying the outlines of a symbol image, specifying the desired movement direction defined by a first unit vector in which the control point should move, and specifying a desired measurement direction defined by a second unit vector by which the movement of the control point should be measured. The desired measurement direction and the desired movement direction forming an angle of predetermined size. The method further includes moving the control points in the desired movement direction and measuring the control points against the predetermined angle with the desired measurement direction, this measurement producing a resulting movement direction and storing the results of the manipulation of the control points in a memory.