A simple algorithm for Boolean operations on polygons

Abstract

In this paper a simple and efficient algorithm for computing Boolean operations on polygons is presented. The algorithm works with almost any kind of input polygons: concave polygons, polygons with holes, several contours and self-intersecting edges. Important topological information, as the holes of the result polygon, is computed.

References

1. [1] Andreev, R.D., Algorithm for clipping arbitrary polygons. Comput Graph Forum. v8 i3. 183-191.
2. [2] Sutherland, I.E. and Hodgman, G.W., . Commun ACM. v17 i1. 32-42.
3. [3] Liang, Y.D. and Barsky, B.A., An analysis and algorithm for polygon clipping. Commun ACM. v26 i11. 868-877.
4. [4] Greiner, G. and Hormann, K., Efficient clipping of arbitrary polygons. ACM Trans Graph. v17 i2. 71-83.
5. [5] Kim, D. and Kim, M., An extension of polygon clipping to resolve degenerate cases. Comput-Aid Des Appl. v3. 447-456.
6. [6] Kui Liu, Y., Qiang Wang, X., Zhe Bao, S., Gomboši, M. and ¿alik, B., An algorithm for polygon clipping, and for determining polygon intersections and unions. Comput Geosci. v33 i5. 589-598.
7. [7] Rivero, M. and Feito, F.R., Boolean operations on general planar polygons. Comput Graph. v24 i6. 881-896.
8. [8] Peng, Y., Yong, J.-H., Dong, W.-M., Zhang, H. and Sun, J.-G., A new algorithm for boolean operations on general polygons. Comput Graph. v29 i1. 57-70.
9. [9] Feito, F.R. and Rivero, M., Geometric modelling based on simplicial chains. Comput Graph. v22 i5. 611-619.
10. [10] Nievergelt, J. and Preparata, F.P., Plane-sweep algorithms for intersecting geometric figures. Commun ACM. v25 i10. 739-747.
11. [11] de Berg, M., Cheong, O., van Kreveld, M. and Overmars, M., Computational geometry: algorithms and applications. 2008. 3rd ed. Springer, Berlin.
12. [12] Bentley, J. and Ottmann, T., Algorithms for reporting and counting geometric intersections. IEEE Trans Comput. v28 i9. 643-647.
13. [13] Vatti, B.R., A generic solution to polygon clipping. Commun ACM. v35 i7. 56-63.
14. [14] Wang, J., Cui, C. and Gao, J., An efficient algorithm for clipping operation based on trapezoidal meshes and sweep-line technique. Adv Eng Softw. v47 i1. 72-79.
15. [15] Martínez, F., Rueda, A.J. and Feito, F.R., A new algorithm for computing boolean operations on polygons. Comput Geosci. v35 i6. 1177-1185.

Index Terms

• Computing methodologies

  • Computer graphics

    • Shape modeling

• Theory of computation

  • Randomness, geometry and discrete structures

    • Computational geometry