Step by Step solution about How to resolve the algorithm Bitmap/Bresenham's line algorithm step by step in the C programming language

The provided C code implements the Bresenham's line drawing algorithm, which is a technique used to draw lines between two points on a 2D grid. Here's a detailed explanation of how the code works:

1. Initialization:

   • x0, y0: Starting coordinates of the line.
   • x1, y1: Ending coordinates of the line.
   • dx, dy: Absolute differences in x and y coordinates, respectively.
   • sx, sy: Sign of the differences in x and y coordinates, respectively (used to determine the direction of the line).
   • err: Initial error value used in the Bresenham's algorithm.

2. Loop:

   • The code enters an infinite loop that continues until x0 and y0 reach the ending coordinates x1 and y1.
   • Inside the loop, it sets the pixel at (x0, y0) to the desired color using the setPixel() function.
   • It then calculates a new error value (e2) based on the current error value (err).
   • If e2 is greater than -dx, then the error value is decremented by dy, and x0 is incremented by sx. This means the line is drawn in the x-direction.
   • If e2 is less than dy, then the error value is incremented by dx, and y0 is incremented by sy. This means the line is drawn in the y-direction.
   • The loop continues until the ending coordinates are reached.

In summary, this code implements the Bresenham's algorithm, which efficiently draws a line between two given points on a 2D grid by determining the direction and incrementing the coordinates based on the error value. The setPixel() function is responsible for setting the pixel at the current coordinates to the desired color.

void line(int x0, int y0, int x1, int y1) {

  int dx = abs(x1-x0), sx = x0<x1 ? 1 : -1;
  int dy = abs(y1-y0), sy = y0<y1 ? 1 : -1; 
  int err = (dx>dy ? dx : -dy)/2, e2;

  for(;;){
    setPixel(x0,y0);
    if (x0==x1 && y0==y1) break;
    e2 = err;
    if (e2 >-dx) { err -= dy; x0 += sx; }
    if (e2 < dy) { err += dx; y0 += sy; }
  }
}