## What is Delaunay triangulation used for?

Delaunay triangulations maximize the minimum angle of all the angles of the triangles in the triangulation; they tend to avoid skinny triangles. The triangulation was invented by Boris Delaunay in 1934.

### Is Delaunay triangulation always possible?

Delaunay triangulation: Mainly centred on demonstrating in a practical way that it is always possible the tranformation between 2 triangulations of any points only using interchanges of edges.

#### What is the principle of Delaunay triangulation for tin model?

Delaunay triangulation (Kidner and Smith, 1993) has been most commonly used in the geosciences because it meets three basic requirements for TIN formation (Li et al., 2005): (1) the resulting TIN from any set of points should be identical if the same algorithm is used, regardless of the starting point of the algorithm; …

How does a Delaunay triangulation relate to a Voronoi diagram?

The red vertices and edges are the Voronoi diagram. The black points and edges are the Delaunay triangulation. The Delaunay triangulation only involves edges between existing points, while the Voronoi diagram creates new vertices and needs a way to represent edges going infinitely in one direction.

Is the Delaunay triangulation unique?

For four or more points on the same circle (e.g., the vertices of a rectangle) the Delaunay triangulation is not unique: each of the two possible triangulations that split the quadrangle into two triangles satisfies the “Delaunay condition”, i.e., the requirement that the circumcircles of all triangles have empty …

## What is the principle of Delaunay triangulation for TIN model?

### What is the difference between DEM and 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.

#### What is triangulation algorithm?

Introduction. Computing the triangulation of a polygon is a fundamental algorithm in computational geometry. In computer graphics, polygon triangulation algorithms are widely used for tessellating curved geometries, as are described by splines [Kumar and Manocha 1994].

Why is TIN better than DEM?

TIN is a result of interpolation between measured elevation values. Unlike DEM, composed of regular grid, TIN facets have different sizes depending on data density. Therefore, TIN can describe terrain surface better.