The concept of optimal Delaunay triangulation (ODT) and the corresponding error-based quality metric are first introduced. Then one kind of mesh smoothing algorithm for tetrahedral mesh based on the concept of ODT is ...The concept of optimal Delaunay triangulation (ODT) and the corresponding error-based quality metric are first introduced. Then one kind of mesh smoothing algorithm for tetrahedral mesh based on the concept of ODT is examined. With regard to its problem of possible producing illegal elements, this paper proposes a modified smoothing scheme with a constrained optimization model for tetrahedral mesh quality improvement. The constrained optimization model is converted to an unconstrained one and then solved by integrating chaos search and BFGS (Broyden-Fletcher-Goldfarb-Shanno) algorithm efficiently. Quality improvement for tetrahedral mesh is finally achieved by alternately applying the presented smoothing scheme and re-triangulation. Some testing examples are given to demonstrate the effectiveness of the proposed approach.展开更多
对文献(Dwyer R A.Higher-dimensional Voronoi diagrams in linear expected time.Discrete&ComputationalGeometry,1991,6(4):342-367)给出的对d≥2维空间站点集合构造Delaunay超三角形算法做了改进,提高了其计算效率,并把站点的...对文献(Dwyer R A.Higher-dimensional Voronoi diagrams in linear expected time.Discrete&ComputationalGeometry,1991,6(4):342-367)给出的对d≥2维空间站点集合构造Delaunay超三角形算法做了改进,提高了其计算效率,并把站点的分布从限于单位球体扩展成d≥2维空间中任意凸的超多面体.证明了如果站点是独立地从一致分布在凸的超多面体的点集中取出,在线性期望时间内可对站点集实现Delaunay三角化.该证明方法比较直观.虽然这类算法对输入点集有一致分布的要求,但在很多实际应用情况下这种要求常是被满足的,此时使用这类算法便可体现文中算法快速和易于实现的优点.展开更多
文摘The concept of optimal Delaunay triangulation (ODT) and the corresponding error-based quality metric are first introduced. Then one kind of mesh smoothing algorithm for tetrahedral mesh based on the concept of ODT is examined. With regard to its problem of possible producing illegal elements, this paper proposes a modified smoothing scheme with a constrained optimization model for tetrahedral mesh quality improvement. The constrained optimization model is converted to an unconstrained one and then solved by integrating chaos search and BFGS (Broyden-Fletcher-Goldfarb-Shanno) algorithm efficiently. Quality improvement for tetrahedral mesh is finally achieved by alternately applying the presented smoothing scheme and re-triangulation. Some testing examples are given to demonstrate the effectiveness of the proposed approach.
文摘对文献(Dwyer R A.Higher-dimensional Voronoi diagrams in linear expected time.Discrete&ComputationalGeometry,1991,6(4):342-367)给出的对d≥2维空间站点集合构造Delaunay超三角形算法做了改进,提高了其计算效率,并把站点的分布从限于单位球体扩展成d≥2维空间中任意凸的超多面体.证明了如果站点是独立地从一致分布在凸的超多面体的点集中取出,在线性期望时间内可对站点集实现Delaunay三角化.该证明方法比较直观.虽然这类算法对输入点集有一致分布的要求,但在很多实际应用情况下这种要求常是被满足的,此时使用这类算法便可体现文中算法快速和易于实现的优点.
