Sutherland-Hodgman Polygon Clipping Algorithm

Clips a polygon against a convex polygon. The clipped polygon may fracture into other polygons.

The convexity of the clipper is because you are iterating over each cutting edge. For the cutting edges to be independent you need a convex cutting shape.

This simplifies the algorithm somewhat. All I have to do is describe the cutting of the polygon by one of the cutting edges and since its independent of the others the algorithm is repeated for them.

Cutting a polygon in 2D is done by a line. Either the point being tested is inside the clipping region or outside.

Algorithm

Have a vector v of points which describe the polygon.
Push back the first point of v as another point terminating the polygon vector v. For algorithm iteration purposes.
Let the point have an bool inside attribute.
Select any cutting edge ce. Iterate over v initializing inside relative to ce.

This sets up the data structure so that a linear transversal generates the new polygon vector. Here is an example.

Let v2 be the new polygon vector having been clipped by ce.
Have a routine to find the intersection across the cutting line. eg   point intersection(point p1, point p2) .

There are 4 cases to consider as each line is a set of points and a point has 2 possibilities (inside or out). 2 by 2 is 4 possibilities. For convenience I have used a 2 bit binary number in the algorithm where the first is v[i-1].inside and the second is v[i].inside.

for ( i=1; i<v.size(); ++i )
  10 - v2.push_back( intersection(v[i],v[i-1]) )
  01 - v2.push_back( intersection(v[i],v[i-1]) ), v2.push_back(v[i]).
  11 - v2.push_back(v[i])
  00 - do nothing.