Scan Converting a Line

You know that a line in computer graphics typically refers to a line segment, which is a portion of a straight line that extends indefinitely in opposite directions. You can define a line by its two end points and by the line equation y = mx + c, where m is called the slope and c the y intercept of the line. Let the two end points of a line be P1(x1, y1) and P2(x2, y2). The line equation describes the coordinates of all the points that lie between the two endpoints.

 A simple approach to scan convert a line is to first scan convert P1 and P2 to pixel coordinates (x1’, y1’) and (x2’, y2’) respectively. Then let us set m = (y2’- y1’)/(x2’- x1’) and b = y1’-mx1’. Find |m| and if |m| ? 1, then for every integer value of x between and excluding x1’ and x2’, calculate the corresponding value of y using the equation and scan convert (x, y). If |m| >1, then for every integer value of y between and excluding y1’ and y2’, calculate the corresponding value of x using the equation and scan convert (x, y).

Design criteria of straight lines

From geometry we know that a line, or line segment, can be uniquely specified by two points. From algebra we also know that a line can be specified by a slope, usually given the name m and a y-axis intercept called b. Generally in computer graphics, a line will be specified by two endpoints. But the slope and y-intercept are often calculated as intermediate results for use by most line-drawing algorithms.

The goal of any line drawing algorithm is to construct the best possible approximation of an ideal line given the inherent limitations of a raster display. Before discussing specific line drawing algorithms, it is useful to consider general requirements for such algorithms. Let us see what are the desirable characteristics needed for these lines.

The primary design criteria are as follows

• Straight lines appear as straight lines
• Straight lines start and end accurately
• Displayed lines should have constant brightness along their length, independent of the line length and orientation.
• Lines should be drawn rapidly