Editing Line drawing algorithm (section)

== Antialiasing ==
The biggest issue of single color line drawing algorithms is that they lead to [[Jaggies|lines with a rough, jagged appearance]]. On devices capable of displaying multiple levels of brightness, this issue can be avoided through [[Spatial anti-aliasing| antialiasing]]. For this, lines are usually viewed in a two-dimensional form, generally as a rectangle with a desired thickness. To draw these lines, points lying near this rectangle have to be considered.

=== Gupta and Sproull algorithm ===
The [[Gupta-Sproull algorithm|Gupta-Sproull]] algorithm is based on [[Bresenham's line algorithm|Bresenham's]] line algorithm but adds [[Anti-aliasing|antialiasing]].

An optimized variant of the Gupta-Sproull algorithm can be written in pseudocode as follows:

 DrawLine(x1, x2, y1, y2) {
     x = x1;
     y = y1;
     dx = x2 − x1;
     dy = y2 − y1;
     d = 2 * dy − dx; // discriminator

     // Euclidean distance of point (x,y) from line (signed)
     D = 0; 

     // Euclidean distance between points (x1, y1) and (x2, y2)
     length = sqrt(dx * dx + dy * dy); 

     sin = dx / length;
     cos = dy / length;
     '''while''' (x <= x2) {
         IntensifyPixels(x, y − 1, D + cos);
         IntensifyPixels(x, y, D);
         IntensifyPixels(x, y + 1, D − cos);
         x = x + 1
         '''if''' (d <= 0) {
             D = D + sin;
             d = d + 2 * dy;
         } '''else''' {
             D = D + sin − cos;
             d = d + 2 * (dy − dx);
             y = y + 1;
         }
     }
 }

The IntensifyPixels(x,y,r) function takes a radial line transformation and sets the intensity of the pixel (x,y) with the value of a cubic polynomial that depends on the pixel's distance r from the line.