Technical section: A new algorithm for Boolean operations on general polygons

Authors:
Yu Peng;Jun-Hai Yong;Wei-Ming Dong;Hui Zhang;Jia-Guang Sun
Affiliations:
Department of Computer Science and Technology, Tsinghua University, Beijing 100084, PR China;School of Software, Tsinghua University, Beijing 100084, PR China;Department of Computer Science and Technology, Tsinghua University, Beijing 100084, PR China;School of Software, Tsinghua University, Beijing 100084, PR China;Department of Computer Science and Technology, Tsinghua University, Beijing 100084, PR China and School of Software, Tsinghua University, Beijing 100084, PR China
Venue:
Computers and Graphics
Year:
2005

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Abstract

A new algorithm for Boolean operations on general planar polygons is presented. It is available for general planar polygons (manifold or non-manifold, with or without holes). Edges of the two general polygons are subdivided at the intersection points and touching points. Thus, the boundary of the Boolean operation resultant polygon is made of some whole edges of the polygons after the subdivision process. We use the simplex theory to build the basic mathematical model of the new algorithm. The subordination problem between an edge and a polygon is reduced to a problem of determining whether a point is on some edges of some simplices or inside the simplices, and the associated simplicial chain of the resultant polygon is just an assembly of some simplices and their coefficients of the two polygons after the subdivision process. Examples show that the running time required by the new algorithm is less than one-third of that by the Rivero and Feito algorithm.