A Characterization of Ten Hidden-Surface Algorithms
ACM Computing Surveys (CSUR)
Communications of the ACM
Hidden surface removal using polygon area sorting
SIGGRAPH '77 Proceedings of the 4th annual conference on Computer graphics and interactive techniques
Winged edge polyhedron representation.
Winged edge polyhedron representation.
Boundary evaluation of non-convex primitives to produce parametric trimmed surfaces
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Partitioning Polyhedral Objects into Nonintersecting Parts
IEEE Computer Graphics and Applications
Near real-time shadow generation using BSP trees
SIGGRAPH '89 Proceedings of the 16th annual conference on Computer graphics and interactive techniques
Towards image realism with interactive update rates in complex virtual building environments
I3D '90 Proceedings of the 1990 symposium on Interactive 3D graphics
Domain composition methods for associating geometric modeling with finite element modeling
SMA '91 Proceedings of the first ACM symposium on Solid modeling foundations and CAD/CAM applications
Shape transformation for polyhedral objects
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Efficient clipping of arbitrary polygons
ACM Transactions on Graphics (TOG)
SCG '85 Proceedings of the first annual symposium on Computational geometry
The Brush-Trajectory Approach to Figure Specification: Some Algebraic Solutions
ACM Transactions on Graphics (TOG)
An analysis and algorithm for polygon clipping
Communications of the ACM
An Editable Nonmanifold Boundary Representation
IEEE Computer Graphics and Applications
A new algorithm for computing Boolean operations on polygons
Computers & Geosciences
Technical section: A new algorithm for Boolean operations on general polygons
Computers and Graphics
Industrial strength polygon clipping: A novel algorithm with applications in VLSI CAD
Computer-Aided Design
An efficient algorithm for clipping operation based on trapezoidal meshes and sweep-line technique
Advances in Engineering Software
Diagrams'12 Proceedings of the 7th international conference on Diagrammatic Representation and Inference
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All of the information necessary to perform the polygon set operations (union, intersection, and difference) and therefore polygon clipping can be generated by a single application of a process called polygon comparison. This process accepts two or more input polygons and generates one or more polygons as output. These output polygons contain unique homogenous areas, each falling within the domain of one or more input polygons. Each output polygon is classified by the list of input polygons in which its area may be found. The union contour of all input is also generated, completing all of the information necessary to perform the polygon set operations. This paper introduces a polygon comparison algorithm which features reduced complexity due to its use of a graph data representation. The paper briefly introduces some of the possible approaches to the general problem of polygon comparison including the polygon set and clipping problems. The new algorithm is then introduced and explained in detail. The algorithm is sufficiently general to compare sets of concave polygons with holes. More than two polygons can be compared at one time; all information for future comparisons of subsets of the original input polygon sets is available from the results of the initial application of the process. The algorithm represents polygons using a graph of the boundaries of the polygons. These graphs are imbedded in a two dimensional geometric space. The use of the graph representation simplifies the comparison process considerably by eliminating many special cases from explicit consideration. Polygon operations like the ones described above are useful in a variety of application areas, especially those which deal with problems involving two dimensional or projected two dimensional geometric areas. Examples include VLSI circuit design, cartographic and demographic applications, and polygon clipping for graphic applications such as viewport clipping, hidden surface and line removal, detailing, and shadowing.