http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
Geometric modeling studies how to construct and represent shapes of objects. The shape of a physical object can be measured and represented as a geometric model on the computer. The shape of a non-existing object can be designed and represented as a geometric model on the computer. Algorithms for Boolean operations construct complex models from simpler models. This research presents a simple, robust, and fast algorithm for Boolean operations on polygon meshes. The proposed algorithm systematically classifies the relationship of two intersecting polygons into four types and subdivides intersecting polygons by using one of three methods. Singular intersections are defined and a method which locally classifies polygons in singular intersections is documented. As well as 2-manifold objects, certain types of non-2-manifold objects are acceptable as input. The robustness of the algorithm is graphically illustrated by resulting objects constructed by an implementation of the algorithm. The binary index list subdivision methods (BILS methods) presented here for geometric search are simple but powerful: the methods allow the Boolean operation algorithm to have computational time which is linear in the size of the input. The BILS search methods are described and experimental evidence is presented to show that the complexity of the algorithm is linear in the size of the input.