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Polygon clipping
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Polygon clipping

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  • 1. Polygon ClippingCollection of connected lines is considered asPolygon. A polygon clipper takes as input thevertices of a polygon and returns one(or more)polygons. A closed Polygon when clipped Cthen we may get one or more open c d polygon or Dlines. a A b B
  • 2. When we want clipping of a solid polygonarea(closed polygon), then after clipping theresulting polygon should be closed. It requiresthat lines ab & cd be added to make it closedpolygon. Hence it is difficult to find out whichpieces of sections should be joined to makethe clipped polygon closed.
  • 3. A polygon is called convex if the line joining any two interior points of the polygon lies completely inside the polygon. A non- convex polygon is said to be concave. B B A A
  • 4. Another problem occurs when clipping aclosed polygon into several distinct smallerpolygons as shown: Clipping Window Concave Polygon
  • 5. By convention, a polygon with vertices p1..pnis said to be positively oriented if it producesa anticlockwise direction. And if producesclockwise it will be negative oriented. C D D C L R E L R E B B A A
  • 6. SUTHERLAND-HODGMAN ALGORITHM Each edge of the polygon must be testedagainst each edge of the clip rectangle; newedges must be added, and existing edges mustbe discarded, retained, or divided. Multiplepolygons may result from clipping a singlepolygon. We need an organized way to dealwith all these cases.
  • 7. Steps of Sutherland-Hodgmans polygonclipping algorithm Polygons can be clipped against each edge of the window one at a time.
  • 8.  Vertices which are kept after clipping against one window edge are saved for clipping against the remaining edges. Note that the number of vertices usually changes and will often increases. The original polygon and the clip rectangle.
  • 9. After clipped by theright clip boundary.After clipped by the right and bottomclip boundaries.
  • 10. After clipped by theright, bottom, andleft clip boundaries.After clipped byall fourboundaries.
  • 11. Four Cases of polygon clipping against oneEdge:The clip boundary determines a visible andInvisible region. The edges from vertex can beone of four types: Case 1 : Wholly inside visible region - save endpoint Case 2 : Exit visible region - save the intersection
  • 12.  Case 3 : Wholly outside visible region - save nothing Case 4 : Enter visible region - save intersection and endpoint V1 V2 V1 V1’ V2 Out  in in  in Save V1’,V2 Save V2
  • 13. V2 V1V2 V1’ V1 in  out out  out Save V1’ Save none