The centroidal Voronoi tessellation based Delaunay triangulation (CVDT) provides an optimal distribution of generating points with respect to a given density function and accordingly generates a high-quality mesh. In this paper, we discuss algorithms for the construction of the constrained CVDT from an initial Delaunay tetrahedral mesh of a three-dimensional domain. By establishing an appropriate relationship between the density function and the specified sizing field and applying the Lloyd's iteration, the constrained CVDT mesh is obtained as a natural global optimization of the initial mesh. Simple local operations such as edges/faces flippings are also used to further improve the CVDT mesh. Several complex meshing examples and their element quality statistics are presented to demonstrate the effectiveness and efficiency of the proposed mesh generation and optimization method. Copyright © 2003 John Wiley & Sons, Ltd.