Sutherland–Hodgman algorithm: Difference between revisions

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{{Short description|Algorithm for clipping polygons}}

The '''Sutherland-–Hodgman algorithm''' is an [[algorithm]] used for [[Clipping (computer graphics)|clipping]] [[polygon]]s. It works by extending each line of the [[convex polygon|convex]] ''clip polygon'' in turn and selecting only vertices from the ''subject polygon'' that are on the visible side.

==Description==

BeginThe algorithm begins with aan input [[List set(computing)|list]] of all vertices in the subject polygon. Assuming the clip polygon is a rectangleNext, start by extending the upperone side acrossof the wholeclip ofpolygon theis 2Dextended spaceinfinitely wein areboth considering. Nextdirections, starting fromand the first vertexpath of the subject polygon, followis thetraversed. pathVertices offrom the polygoninput tolist theare nextinserted vertexinto inan theoutput subjectlist polygon.if Createthey newlie vertices whereon the pathvisible crossesside of the extended clip polygon line., Repeatand thisnew until wevertices are backadded atto the firstoutput subjectlist polygonwhere vertex.the Nowsubject createpolygon apath new set of all vertices that are on or beneathcrosses the extended clip polygon line, including vertices from the clip polygon that are entirely within the subject polygon.

WeThis thenprocess needis torepeated repeat this processiteratively for each clip polygon side, by extendingusing the lineoutput andlist creatingfrom newone setsstage ofas verticesthe thatinput arelist onfor the visible sidenext. Once all sides of the processclip ispolygon completehave been processed, athe setfinal generated list of vertices will definedefines a new single polygon that is entirely visible. However,Note that if the subject polygon was [[concave polygon|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.

[[image:Sutherland-Hodgman_clipping_sampleHodgman clipping sample.svg|center|frame|All steps offor clipping concave polygon 'W' bywith a 5-sided convex polygon]]

The [[Weiler-–Atherton]] algorithm overcomes this by returning a set of divided polygons, but is more complex and computationally more expensive, so Sutherland-–Hodgman is used for many rendering applications. Sutherland-–Hodgman can also be extended into 3D space by clipping the polygon paths based on the boundaries of planes defined by the viewing space.

==Pseudo CodePseudocode==

Given a specificlist of edges in a clip planepolygon, and ana arraylist containing theof vertices ofin a singlesubject polygon, the following procedure clips the subject polygon against the planeclip polygon.

List outputList = subjectPolygon;

arrayLength = array.size

vertex S = array[ arrayLength - 1 ]

'''for''' (Edge clipEdge in clipPolygon) '''do'''

for( j = 0, j < arrayLength, j = j+1 )

List inputList = outputList;

{

outputList.clear();

vertex P = array[ j ]

if( P is inside clip_plane )

'''for''' (int i = 0; i < inputList.count; i += 1) '''do'''

{

if(Point Scurrent_point is= not inside clip_plane )inputList[i];

Point prev_point = inputList[(i − 1) % inputList.count];

{

Output( ComputeIntersection( S, P, clip_plane ) )

Point Intersecting_point = ComputeIntersection(prev_point, current_point, clipEdge)

}

Output( P )

'''if''' (current_point inside clipEdge) '''then'''

}

else '''if''' (prev_point S isnot inside clip_plane clipEdge) '''then'''

outputList.add(Intersecting_point);

{

Output( ComputeIntersection( P, S, clip_plane'''end ) )if'''

outputList.add(current_point);

}

S = P

'''else if''' (prev_point inside clipEdge) '''then'''

}

outputList.add(Intersecting_point);

{'''end if'''

'''done'''

'''done'''

The vertices of the clipped polygon are to be found in ''outputList'' when the algorithm terminates. Note that a point is defined as being ''inside'' an edge if it lies on the same side of the edge as the remainder of the polygon. If the vertices of the clip polygon are consistently listed in a counter-clockwise direction, then this is equivalent to testing whether the point lies to the left of the line (left means ''inside'', while right means ''outside''), and can be implemented simply by using a [[cross product]].

'''Output''' and '''ComputeIntersection''' are functions that have not been implemented here for ease of readability (and they are not very complex).

''ComputeIntersection'' is a function, omitted here for clarity, which returns the intersection of a line segment and an infinite edge. Note that the intersecting point is only added to the output list when the intersection is known to exist, therefore both lines can always be treated as being infinitely long.

'''Output''' is generally some function or code that adds vertices to an array.

==Implementations==

'''ComputeIntersection''' finds the intersection points of a line segment and a clip plane and returns that values (vertices) in order from S to P.

A Python implementation of the Sutherland-Hodgman can be found [https://github.com/mdabdk/sutherland-hodgman here].

==See also==

*[[Weiler-AthertonOther polygon clipping algorithm]]algorithms:

*[[Weiler&ndash;Atherton clipping algorithm]]

*[[Vatti clipping algorithm]]

On the subject of clipping:

*[[Category:Clipping (computer graphics)]]

*[[Rasterisation#Clipping|Clipping (in rasterisation)]]

*[[Line clipping|Line clipping algorithms]]

== References==

* Mel Slater, Anthony Steed, Yiorgos Chrysanthou: ''Computer Graphics and Virtual Environments: From Realism to Real-Time.'' Addison Wesley, 2002. {{ISBN|0-201-62420-6}}.

* [[Ivan Sutherland]], Gary W. Hodgman: ''Reentrant Polygon Clipping.'' [[Communications of the ACM]], vol. 17, pp.&nbsp;32–42, 1974

==External links==

* [http://www.cs.drexel.edu/~david/Classes/CS430/Lectures/L-05_Polygons.6.pdf Polygon clipping and filling] Describes the algorithm using images that are easy to understand.

* [https://rosettacode.org/wiki/Sutherland-Hodgman_polygon_clipping Rosetta Code example]

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[[de:Algorithmus von Sutherland-Hodgman]]

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