Polygon clipping
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Polygon clipping involves taking a polygon and clipping it against another shape to produce one or more smaller polygons. The Sutherland-Hodgman algorithm handles polygon clipping by testing each edge of the clipping polygon against each edge of the clip shape. There are four cases for how an edge can be clipped - wholly inside, exit, wholly outside, enter - and the algorithm saves or discards vertices based on these cases. Repeatedly clipping against each edge of the clip shape handles all cases and produces the final clipped polygon(s).
Polygon clipping
- 1. Polygon Clipping Collection of connected lines is considered as Polygon. A polygon clipper takes as input the vertices of a polygon and returns one(or more) polygons. A closed Polygon when clipped C then we may get one or more open c d polygon or D lines. a A b B
- 2. When we want clipping of a solid polygon area(closed polygon), then after clipping the resulting polygon should be closed. It requires that lines ab & cd be added to make it closed polygon. Hence it is difficult to find out which pieces of sections should be joined to make the 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 a closed polygon into several distinct smaller polygons as shown: Clipping Window Concave Polygon
- 5. By convention, a polygon with vertices p1..pn is said to be positively oriented if it produces a anticlockwise direction. And if produces clockwise 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 tested against each edge of the clip rectangle; new edges must be added, and existing edges must be discarded, retained, or divided. Multiple polygons may result from clipping a single polygon. We need an organized way to deal with all these cases.
- 7. Steps of Sutherland-Hodgman's polygon clipping 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 the right clip boundary. After clipped by the right and bottom clip boundaries.
- 10. After clipped by the right, bottom, and left clip boundaries. After clipped by all four boundaries.
- 11. Four Cases of polygon clipping against one Edge: The clip boundary determines a visible and Invisible region. The edges from vertex can be one 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 V1 V2 V1’ V1 in out out out Save V1’ Save none