cohen sutherland line clipping algorithm

Cohen-Sutherland line clipping algorithm is a widely used line clipping algorithm in computer graphics. It is a method to clip a line segment against a rectangular clip region. The algorithm divides the clip region into nine regions and checks whether a line segment lies completely inside or outside the clip region.

The nine regions are defined as follows:

```

| 1001 | 1000 | 1010 |

|------|------|------|

| 0001 | 0000 | 0010 |

|------|------|------|

| 0101 | 0100 | 0110 |

```

Each region is represented by a four-bit binary code where the leftmost bit represents the top region, the second bit represents the bottom region, the third bit represents the right region, and the fourth bit represents the left region. For example, the region with code `1000` represents the top region, while the region with code `0100` represents the left region.

The algorithm works as follows:

1. Calculate the region codes for the endpoints of the line segment.

2. If both endpoints have a region code of `0000`, the line segment is completely inside the clip region and can be drawn.

3. If both endpoints have a region code that shares a common bit, the line segment is completely outside the clip region and can be discarded.

4. If the line segment is partially inside the clip region, calculate the intersection points of the line segment with the clip region.

5. Update the endpoints of the line segment with the intersection points and repeat steps 1-4 until the line segment is either completely inside or completely outside the clip region.

The Cohen-Sutherland algorithm is simple, efficient, and easy to implement. It can handle both horizontal and vertical lines and can be extended to handle more complex clip regions.