Clipping2
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The document discusses two algorithms for polygon clipping: 1. The Sutherland-Hodgeman algorithm clips polygons by processing vertices against window boundaries from left to right, bottom to top. It works for convex polygons but can produce extraneous lines with concave polygons. 2. The Weiler-Atherton algorithm modifies this by following either the polygon or window boundary depending on if the vertex pair is entering or exiting the clip region. This correctly handles concave polygons by producing separated clipped sections rather than extraneous lines.
Clipping2
- 1. Polygon Clipping When a closed polygon is clipped as a collection of lines, the original closed polygon becomes one or more open polygons or discrete lines . For polygon clipping we require an algorithm that will generate one or more closed areas. The output of a polygon clippers be a sequence of vertices that defines the clipped polygon boundary.
- 2. Sutherland Hodgeman Algorithm We can correctly clip a polygon by processing a polygon boundary as a whole against each window edge. This could be accomplished by processing all polygon vertices against each clip rectangle boundary. Beginning with the initial set of polygon vertices, we could first clip against the left rectangle boundary to procedure a new sequence of vertices.
- 3. Sutherland Hodgeman Algorithm The new set of vertices could than be successively passed to a right boundary clipper, a bottom boundary clipper, & a top boundary clipper. At each step a new sequence of output vertices is generated & passed to the next window boundary clipper. These are four possible cases when processing vertices in sequence around the perimeter of a polygon.
- 4. Sutherland Hodgeman Algorithm Left Clipper Right Clipper Bottom Clipper Top Clipper
- 5. Sutherland Hodgeman Algorithm As each pair of adjacent polygon vertices is passed to a window boundary clipper we make the following tests. * If the first vertex is outside the window boundary & the second vertex is inside, the intersection point of the polygon edge with the window boundary & the second vertex are added to the output vertex list. V1 V2 V1’ Out – In Save V1’, V2
- 6. Sutherland Hodgeman Algorithm * If both input vertices are inside the window boundary only the second vertex is added to the output vertex list. V1 V2 In – Out Save V2
- 7. Sutherland Hodgeman Algorithm * If the vertex is inside the window boundary & the second vertex is outside; only the edge intersection with the window boundary is added to the output vertex list V1 V2 In – Out Save V2’ V2’
- 8. Sutherland Hodgeman Algorithm * If both input vertices are outside the window boundary, nothing is added to the output list. V1 V2 Save None
- 9. Sutherland Hodgeman Algorithm Left Edge List a’bcdefghii’ Right Edge List bcdd’e’fghii’a’ Bottom Edge List cdd’e’ff’h’ii’a’b Top Edge List c’dd’e’ff’h’ii’a’bb’ a a’ b b’ c c’ d d’ e e’ f f’ g h h’ i i’
- 10. Sutherland Hodgeman Algorithm Convex polygon are correctly clipped by the Sutherland-Hodgeman algorithm but concave polygon may be displayed with extraneous lines. This is occur when the clipped polygon should have two or more separate section. Since there is only one output vertex list, the last vertex in the list is always joined to the first vertex list
- 11. Weiler-Atherlton Polygon Clipping In this method, vertex processing procedures for window boundaries are modified so that concave polygons are displayed correctly. This clipping procedure was developed as a method for identifying visible surfaces, & so it can be applied with arbitrary polygon clipping regions. The basic idea in this algorithm is that instead of always processing around the polygon edges as vertices are processed, we some times want to follow the window boundaries.
- 12. Weiler-Atherlton Polygon Clipping Which path we follow depends on the polygon processing directions (clockwise or counter clockwise) & whether the pair of polygon vertices currently being processed represented an outside to inside pair or an inside to outside pair. For an outside to inside pair of vertices, follow the polygon boundary. For an inside to outside pair of vertices, follow the window boundary in a clockwise direction.
- 13. Weiler-Atherlton Polygon Clipping Concave Polygon V1 V1’ V2 V3 V3’ V4 V4’ V5 V5’ V6
- 14. Weiler-Atherlton Polygon Clipping c1 c2 c3 c4 s1 s2 s3 s4 s5 s6 s7 I1 I2 I3 I4 I5 I6 I7 I8 Subject Polygon Clip Polygon
- 15. Weiler-Atherlton Polygon Clipping Subject Polygon List Clip Polygon List s1 c1 I2 I1 I3 I2 s2 c2 I4 I3 s3 I4 I5 c3 s4 I5 I6 I6 I7 c4 s5 I7 I8 I8 s6 c1 I1 s7 s1