The Delaunay triangulation is commonly used to generate triangulated irregular network (TIN) models for a best description of the surface morphology in a variety of applications in geographic information systems (GIS). This paper discusses the definitions and basic properties of the standard and constrained Delaunay triangulations. Several existing Delaunay algorithms are reviewed and classified into three categories according to their procedures: (1) divide-and-conquer methods, (2) incremental insertion methods, and (3) triangulation growth methods. Furthermore, a linear-time Convex Hull Insertion algorithm is presented to construct TINs for a set of points as well as specific features such as constraint breaklines and exclusion boundaries. Empirical results over various sets of up to 50000 points on personal computers show that the proposed algorithm efficiently expedites the construction of TIN models in approximately O(N) for N randomly distributed points.

Delaunay triangulations in TIN creation: an overview and a linear-time algorithm

Hierarchical triangulation using cartographic coherence

This paper is a review of the application of terrain modelling to surveying and civil engineering. The first section considers the theoretical background to the subject and two distinct approaches are identified based on the use of either grid or randomly located height data. The relative merits of each are discussed and the most frequently used algorithms for interpolation and contouring are examined. This is followed by a review of the characteristics of a selected number of terrain modelling and contouring packages. Five distinct groups of packages are identified. Finally, a review of applications is presented together with some views on the future trends in this field.

Terrain Modelling in Surveying and Civil Engineering

BMSweep is a new algorithm to determine the location of interior nodes while generating hexahedral meshes using the volume sweeping method. Volume sweeping is performed on two and one half-dimensional volumes by identifying a ‘source’ surface which is meshed with quadrilaterals. These quadrilaterals are then swept through the volume towards a ‘target’ surface generating layers of hexahedra along the way. BMSweep uses background mesh interpolation to locate interior nodes during sweeping. The interpolation method provides for quality element creation, while allowing the volume boundary to vary. The cross-section of the volume can vary along the length of the sweep, the sweep path need not be linear, and the source and target areas need not be flat. Three dimensional volumes can be swept using BMSweep after being decomposed into two and one half-dimensional subvolumes.

BMSweep: Locating Interior Nodes During Sweeping

This paper first introduces the key features of big data in different processing modes and their typical application scenarios, as well as corresponding representative processing systems. It then summarizes three development trends of big data processing systems. Next, the paper gives a brief survey on system supported analytic technologies and applications (including deep learning, knowledge computing, social computing, and visualization), and summarizes the key roles of individual technologies in big data analysis and understanding. Finally, the paper lays out three grand challenges of big data processing and analysis, i.e., data complexity, computation complexity, and system complexity. Potential ways for dealing with each complexity are also discussed.

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Survey on Big Data System and Analytic Technology

For some applications, triangulated irregular networks are superior to rectangular grids in modeling complex surfaces. The radial sweep algorithm is an improvement of TIN techniques.

MiranteA.

Papers

The Radial Sweep Algorithm for Constructing Triangulated Irregular Networks