Anti-aliasing method for polynomial curves using integer arithmetics
First Claim
Patent Images
1. A computer graphics rendering process for displaying on a raster scan computer display having a limited resolution of H×
- V pixels an analytical curve that passes between centers of a pair of adjacent pixels in display space without intersecting the center of either pixel, the analytical curve to be displayed in a first shade or color on a background field displayed in one or more other shades or colors, comprising the steps of;
selecting a plurality of equidistant points along a line segment joining said adjacent pixels, said plurality of equidistant points including end points, defined by said adjacent pixels, of said line segment;
evaluating an analytic expression, defining said analytic curve, at a plurality of said equidistant points;
identifying, from among N ordinal pairs of adjacent ones of said plurality of equidistant points, an Mth pair between which said analytic curve passes;
assigning to each of said adjacent pixels, in accordance with the ratio M/N+1, a display shade or color that is a ratiometric combination of said first shade or color and another shade or color and that is different from both said first shade or color and said another shade or color;
displaying said adjacent pixels in their respective assigned shades or colors; and
repeating the foregoing steps for multiple such pairs of adjacent pixels.
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Abstract
A method of performing anti-aliasing on polynomial curves using only integer arithmetic. The anti-aliasing method includes the steps of: defining an polynomial equation of a curve, dividing grid units into an finite number of sub-intervals, associating a mix ratio to each of the sub-intervals, determining which sub-interval the curve bisects, assigning a mix ratio to each picture element bordering the grid unit according to the mix ratio associated with the sub-interval determined to be bisected by the curve.
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4 Claims
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1. A computer graphics rendering process for displaying on a raster scan computer display having a limited resolution of H×
- V pixels an analytical curve that passes between centers of a pair of adjacent pixels in display space without intersecting the center of either pixel, the analytical curve to be displayed in a first shade or color on a background field displayed in one or more other shades or colors, comprising the steps of;
selecting a plurality of equidistant points along a line segment joining said adjacent pixels, said plurality of equidistant points including end points, defined by said adjacent pixels, of said line segment; evaluating an analytic expression, defining said analytic curve, at a plurality of said equidistant points; identifying, from among N ordinal pairs of adjacent ones of said plurality of equidistant points, an Mth pair between which said analytic curve passes; assigning to each of said adjacent pixels, in accordance with the ratio M/N+1, a display shade or color that is a ratiometric combination of said first shade or color and another shade or color and that is different from both said first shade or color and said another shade or color; displaying said adjacent pixels in their respective assigned shades or colors; and repeating the foregoing steps for multiple such pairs of adjacent pixels. - View Dependent Claims (2, 3, 4)
- V pixels an analytical curve that passes between centers of a pair of adjacent pixels in display space without intersecting the center of either pixel, the analytical curve to be displayed in a first shade or color on a background field displayed in one or more other shades or colors, comprising the steps of;
Specification