Sutherland–Hodgman algorithm

The algorithm begins with an input list of all vertices in the subject polygon. Next, one side of the clip polygon is extended infinitely in both directions, and the path of the subject polygon is traversed. Vertices from the input list are inserted into an output list if they lie on the visible side of the extended clip polygon line, and new vertices are added to the output list where the subject polygon path crosses the extended clip polygon line.

This process is repeated iteratively for each clip polygon side, using the output list from one stage as the input list for the next. Once all sides of the clip polygon have been processed, the final generated list of vertices defines a new single polygon that is entirely visible. Note that if the subject polygon was concave at vertices outside the clipping polygon, the new polygon may have coincident (i.e. overlapping) edges – this is acceptable for rendering, but not for other applications such as computing shadows.

PSEUDO CODE:-

List outputList = subjectPolygon;
  for (Edge clipEdge in clipPolygon) do
     List inputList = outputList;
     outputList.clear();
     Point S = inputList.last;
     for (Point E in inputList) do
        if (E inside clipEdge) then
           if (S not inside clipEdge) then
              outputList.add(ComputeIntersection(S,E,clipEdge));
           end if
           outputList.add(E);
        else if (S inside clipEdge) then
           outputList.add(ComputeIntersection(S,E,clipEdge));
        end if
        S = E;
     done
  done

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CLIPPING PLANE

Clipping planes can be used in addition of those used created for the viewing volume. OpenGL define 6 clipping plane GL_CLIP_PLANEi (i goes from 0 to 5).
A clipping plane is a plane that separate the space in two regions. One region is included from the viewing volume, the other is excluded.

In mathematics, a plane is defined by this equation :
    a*x+b*y+c*z+d = 0
(x, y, z) are the coordinates of the points in the 3D space. All points that verify this equation are on the plane.
The inequality (< or > instead of =) define the region in each side of the plane.

In OpenGL, a clipping plane is the region defined by this equation :
    a*x+b*y+c*z+d >= 0
A clipping plane is creates with the 4 values a, b, c & d likethis :
    double[] eq = {a, b, c, d}
    gl.glClipPlane(GL_CLIP_PLANEi, eq)    

All points draw , the other are excluded (will not be rendered on the screen).

Like for lights, clipping planes have to be enable to be active :
    gl.glEnable(GL_CLIP_PLANEi) 

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ORTHOGRAPHIC PROJECTION

The Viewing Volume shape in this case is a parallelepiped. The 6 clipping planes delimiting the space can be created with the aid of :
    gl.glOrtho(left, right, bottom, top, near, far)

VIEW VOLUME LOOKS LIKE:-

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