Nicholl-Lee-Nicholl (NLN) clipping algorithm

The NLN clipping algorithm works by intersecting the line segment with each edge of the polygon and then selecting the intersecting portion of the line segment that lies inside the polygon. The algorithm works as follows:

1. Initialize two variables, `t1` and `t2`, to 0 and 1, respectively.

2. For each edge of the polygon, calculate the normal vector `n` to the edge and the distance `d` from the origin to the edge.

3. Calculate the dot product of the line segment's direction vector and the edge's normal vector.

4. If the dot product is zero, the line segment is parallel to the edge and either lies completely inside or outside the polygon. If the dot product is positive, the line segment lies outside the polygon and can be discarded. If the dot product is negative, the line segment intersects the edge and the algorithm proceeds to the next step.

5. Calculate the distance `t` from the line segment's start point to the intersection point with the edge, using the dot product of the edge's normal vector and the line segment's start point plus the edge's distance from the origin, divided by the dot product of the line segment's direction vector and the edge's normal vector.

6. If the dot product of the edge's normal vector and the line segment's direction vector is negative, update `t1` to the maximum of `t1` and `t`. Otherwise, update `t2` to the minimum of `t2` and `t`.

7. If `t1` is greater than or equal to `t2`, the line segment lies completely outside the polygon and can be discarded.

8. If all edges of the polygon have been checked, select the portion of the line segment that lies between the start point plus `t1` times the direction vector and the start point plus `t2` times the direction vector.

The NLN clipping algorithm can handle convex polygons with any number of sides, and it can clip line segments that intersect multiple edges of the polygon. However, it can be computationally expensive for complex polygons or large numbers of line segments.