Lines and bodies are two important spatial objects in 3D space. Research on topological relations between lines and bodies have great value in many application fields such as mining

military and transportation. In order to analyze the topological relations between 3D lines and bodies especially complicated lines and bodies correctly and efficiently

a group of sample spatial objects are defined. Then nine-intersection model is used to describe the topological relations between spatial objects. Using nine negative conditions between lines and bodies

eleven types of topological relations between sample lines and bodies are deduced. Then the composed reasoning method is used to deduce the topological relations between compound lines and bodies and there are altogether nineteen types. Finally the algorithm to analyze the topological relations between complicated lines and bodies is deduced. After detailed analysis and discussion

the completeness of topological relations between lines and bodies is proved. Therefore

the algorithm can guaranteed the correctness and greatly simplify the analysis of the topological relations between complicated lines and bodies.