Abstract: A constrained triangulation method under the situation of arbitary bounded space domain and scattered sample is presented in this paper.First, by the boundary recursive triangulation the boundary surface of the domain can be approximated by a new domain D consisted of the triangle group.Then through a new concept space loop table,the boundary recursive triangulation method is generalized to work on three dimension space and a triangulation of D is gained.At last some additional tetrahedrons are designed specially to fill up the whole bounded space domain with the triangulation of D together.Applications indicate that,the method is simple and effective.