## Introduction

The boundary fill algorithm is a method used in computer graphics to fill a closed region with a specific color. It works by starting at a point inside the region and then recursively filling all connected points that have the same color as the boundary. This algorithm is commonly used in various graphics applications, such as digital painting programs and image editing software.

In this article, we'll learn about the boundary fill algorithm in detail, including its recursive nature, implementation, and the differences between 4-connected and 8-connected pixels. We'll also compare the boundary fill algorithm with the flood fill algorithm.

## Boundary Fill Algorithm is Recursive in Nature

The Boundary Fill Algorithm uses recursion, a programming technique where a function calls itself to solve smaller instances of the same problem. This makes the algorithm efficient for filling enclosed areas in graphics because it can repeatedly apply the same filling process to adjacent pixels until it reaches the boundary of the area.

Recursion starts at a point inside the region & colors it if it's not already part of the boundary or filled. Then, the algorithm recursively calls itself for neighboring pixels: north, south, east, & west. This step is repeated until all pixels within the boundary are filled, ensuring no spots are missed.

Using recursion allows the algorithm to navigate complex shapes easily since it can adapt to any irregular boundaries without needing complex loops or conditional statements. It simplifies the code but requires careful handling to avoid excessive memory use, which can lead to a stack overflow if the area to be filled is too large.

To manage this, developers must ensure that the recursion depth is not too deep by limiting the size of the area or optimizing the recursion steps. For example, the algorithm can be modified to check if a pixel is already filled before proceeding, which reduces unnecessary function calls.

Here's a basic example of how the Boundary Fill Algorithm can be implemented using recursion in Python:

```
def boundary_fill(x, y, fill_color, boundary_color, screen):
if screen[x][y] != boundary_color and screen[x][y] != fill_color:
screen[x][y] = fill_color
boundary_fill(x + 1, y, fill_color, boundary_color, screen)
boundary_fill(x - 1, y, fill_color, boundary_color, screen)
boundary_fill(x, y + 1, fill_color, boundary_color, screen)
boundary_fill(x, y - 1, fill_color, boundary_color, screen)
# Example to use the function assuming screen is a 2D pixel array
# screen dimensions and colors must be defined earlier
```

This code snippet shows how the algorithm works step-by-step. The function takes a position and the color to fill, then fills the pixel if it’s not the boundary color or already filled, and recurses into adjacent pixels.

This recursive nature allows for efficiently filling connected areas in graphics, making it ideal for various applications in computer graphics design and development.