Drawing Anti--aliased Straight Line Based on Double--Step Approach

• Main Authors: ZHENG--HAO CHIN, 秦正浩
• Other Authors: KUO--LIANG CHUNG
• Format: Others
• Language: en_US
• Published: 1999
• Online Access: http://ndltd.ncl.edu.tw/handle/67747961657346879512

碩士 === 國立臺灣科技大學 === 資訊工程研究所 === 87 === Since Bresenham proposed a line drawing algorithm, which determines one pixel at a time using only integer operations, many improved line drawing algorithms have been developed. But All of them did not take the jagged problem into consideration. In this paper, we used Rokne and Rao’s double-step incremental linear interpolation algorithm and supersampling technique to draw anti-aliasing straight line. The purpose of linear interpolation algorithm is to find the set of n+1 equidistant points on an interval [a,b] . We claim that n, a and b, as well as the points produced by the interpolation are integers and n>0. Let xi be the interpolation points, where 0<=i<=m. Then the value of xi is as follow: xi=a+[(b-a)/n]i=a+ki, where k=(b-a)/n. The double-step algorithm determines the best integer approximation to xi. Drawing straight line is a special case of linear interpolation. A straight line can be regarded as a line consisting of horizontal segments when the slope of the line is less than 1 and greater than 0. Using double-step algorithm, we can decide the positions of two end points of a segment fastly. Our method inherit the computational advantage of double-step algorithm. Moreover, we use supersampling technique at each starting pixel of segment for anti-aliasing. That is, we first find the portion of the starting pixel belong to the segment. Then two gray levels of the starting pixel and the pixel below the starting pixel are determined according to the portion for anti-aliasing. This algorithm involves only integer operation.