Abstract: Simulating the generation of fragments of a bomb explosion is critical to show the visual effect and power of explosion．Conceptual models of concealed fragment，apparent fragment and stochastic half-edge data structure are formulated．Two fragment generation methods are discussed，namely the facet equivalence approach and patch enclosure approach．Three practical algorithms are realized： granulation of virtual body；facet equivalence transform； and patch enclosure compilation．Time complexity of the three algorithms is O （n） ．Two trial applications verify the algorithms，and produce fairly good results．