Design and data structure of fully adaptive, multigrid, finite-element software
ACM Transactions on Mathematical Software (TOMS)
A Delaunay refinement algorithm for quality 2-dimensional mesh generation
SODA '93 Selected papers from the fourth annual ACM SIAM symposium on Discrete algorithms
Quality local refinement of tetrahedral meshes based on bisection
SIAM Journal on Scientific Computing
Hierarchical triangulation for multiresolution surface description
ACM Transactions on Graphics (TOG)
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Adaptive refinement of unstructured finite-element meshes
Finite Elements in Analysis and Design
ROAMing terrain: real-time optimally adapting meshes
VIS '97 Proceedings of the 8th conference on Visualization '97
Smooth view-dependent level-of-detail control and its application to terrain rendering
Proceedings of the conference on Visualization '98
Geometry and topology for mesh generation
Geometry and topology for mesh generation
Introduction to Algorithms: A Creative Approach
Introduction to Algorithms: A Creative Approach
Visualization of large terrains made easy
Proceedings of the conference on Visualization '01
PARED: A Framework for the Adaptive Solution of PDEs
HPDC '99 Proceedings of the 8th IEEE International Symposium on High Performance Distributed Computing
Efficient Implementation of Real-Time View-Dependent Multiresolution Meshing
IEEE Transactions on Visualization and Computer Graphics
Parallel decoupled terminal-edge bisection method for 3D mesh generation
Engineering with Computers
Data Structures and Algorithm Analysis in C++ (3rd Edition)
Data Structures and Algorithm Analysis in C++ (3rd Edition)
A geometric diagram and hybrid scheme for triangle subdivision
Computer Aided Geometric Design
Complexity of the bisection method
Theoretical Computer Science
Journal of Computational Physics
On global and local mesh refinements by a generalized conforming bisection algorithm
Journal of Computational and Applied Mathematics
On a bisection algorithm that produces conforming locally refined simplicial meshes
LSSC'09 Proceedings of the 7th international conference on Large-Scale Scientific Computing
Multithread parallelization of Lepp-bisection algorithms
Applied Numerical Mathematics
Technical note: Longest-edge algorithms for size-optimal refinement of triangulations
Computer-Aided Design
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Longest edge (nested) algorithms for triangulation refinement in two dimensions are able to produce hierarchies of quality and nested irregular triangulations as needed both for adaptive finite element methods and for multigrid methods for PDEs. In addition, right-triangle bintree triangulations are multiresolution algorithms used for terrain modeling and real time visualization of terrain applications. These algorithms are based on the properties of the consecutive bisection of a triangle by the median of the longest edge, and can be formulated in terms of the longest edge propagation path (Lepp) and terminal edge concepts, which implies the use of very local refinement operations over fully conforming meshes (where the intersection of pairs of neighbor triangles is either a common edge or a common vertex). In this paper we review the Lepp-bisection algorithms, their properties and applications. To the end we use recent simpler and stronger results on the complexity aspects of the bisection method and its geometrical properties. We discuss and analyze the computational costs of the algorithms. The generalization of the algorithms to 3-dimensions is also discussed. Applications of these methods are presented: for serial and parallel view dependent level of detail terrain rendering, and for the parallel refinement of tetrahedral meshes.