## Who created Delaunay triangulation?

Boris Delaunay

The triangulation was invented by Boris Delaunay in 1934. Based on Delaunay’s definition, the circumcircle of a triangle formed by three points from the original point set is empty if it does not contain vertices other than the three that define it (other points are permitted only on the very perimeter, not inside).

**How fast is Delaunay triangulation?**

This paper describes a simple scheme which may be used to compute Delaunay triangulations for both small and large sets of points. Analysis of the algorithm indicates that its run time is 0(N s/4) for points that are distributed randomly within a square domain.

**What is an advantage of the tin over the DEM?**

An advantage of using a TIN over a DEM in mapping and analysis is that the points of a TIN are distributed variably based on an algorithm that determines which points are most necessary to an accurate representation of the terrain. Also, because TINs are linear, many edges will appear jagged, distorting the image.

### What is the principle of Trilateration?

trilateration, method of surveying in which the lengths of the sides of a triangle are measured, usually by electronic means, and, from this information, angles are computed.

**What is triangulation in research?**

Triangulation refers to the use of multiple methods or data sources in qualitative research to develop a comprehensive understanding of phenomena (Patton, 1999). Triangulation also has been viewed as a qualitative research strategy to test validity through the convergence of information from different sources.

**What is the relationship among distance map Voronoi diagram and Delaunay triangulation?**

There is a one-to-one relation between the Voronoi cells and the cells of the Delaunay triangulation. A vertex of the Voronoi diagram is a point where at least three sites (points of P) are equally distant. They are centrepoints for circumcenters in the Delaunay triangulation.

## What is TIN used for in GIS?

Triangular irregular networks (TIN) have been used by the GIS community for many years and are a digital means to represent surface morphology. TINs are a form of vector-based digital geographic data and are constructed by triangulating a set of vertices (points).

**What is the difference between a DEM and a TIN?**

A DEM represents a regular array of elevation points. It can be converted to an elevation raster by placing each elevation point at the center of a cell. A TIN approximates the land surface with a series of nonoverlapping triangles.