Point scanning: (x,y) -> (round(x), round(y)),

round(w) = int(w + 0.5), closest integer to the real number

Continuous image	Discrete image

General equation:  y = mx + b, m is the slope of the line.
Horizontal lines:    y=b    (m = 0)
Vertical lines:        x = c    (m = oo)
Diagonal:

x = y + b    (m = 1)
x = y + b    (m = -1)

m = (y2 - y1) / (x2 - x1)
b = y1 - m x1

• y = mx + b
• Lines passing through O have b=0.
• Lines bellow 45^o have m<1. Lines above 45o have m>1.
• Parallel lines have the same slope.
• y=mx+b and y=nx+c are orthogonal if mn=-1.
• For any point (x₁, y₁), if m x₁ + b > y₁ then the point is bellow the line. If m x₁ + b < y₁, the point is above the line.

if m < 1 : horizontal
if m > 1 : vertical

compute m = (y2 - y1) / (x2 - x1)
for each x, x1 <= x <= x2
compute y = round (m x + b)
draw pixel (x,y)

For the case x1 < x2, 0 < m < 1.

x = x1; y = y1;
dx = x2 - x1; dy = y2 - y1;
dT = 2 (dy - dx); dS = 2dy;
d = 2dy - dx;
setPixel(x, y);
while (x<x2) {
  x++;
  if (d < 0)
    d = d + dS;
  else {
    y++;
    d = d + dT;
  }
  setPixel(x, y);
}

Region: an area enclosed by a boundary in which all of the pixels are connected.
Connectivity modes: 4-connected or 8-connected.

An algorithm for a 4-connected area.

FloodFill (x0, y0, fill_color, original_color)
{
  int color, x, y;
  x = x0; y = y0;
  getPixel(x, y, color);
  if (color == original_color) {
    while (color == original_color) {
      setPixel(x, y, fill_color);
      FloodFill(x, y+1, fill_color, original_color);
      FloodFill(x, y-1, fill_color, original_color);
      x = x - 1;
      getPixel(x, y, color);
    }
    x = x0 + 1; y = y0;
    getPixel(x, y, color);
    while (color == original_color) {
      setPixel(x, y, fill_color);
      FloodFill(x, y+1, fill_color, original_color);
      FloodFill(x, y-1, fill_color, original_color);
      x = x + 1;
      getPixel(x, y, color);
    }
  }
}

Original color c0      New color    c1      0.67*c0+0.33*c1      0.67*c1+0.33*c0

Flood-fill with anti-aliasing:

replace the check for

color == original_color

with

abs(color - original_color) < 0.33

do not use anti-aliasing for setPixel while flood-filling a region.