Delaunay Triangulation of 2D Data

DELAUNAY_TREE_2D is a C++ program which reads a file of point coordinates in 2D and produces a PostScript file containing an image of the Delaunay triangulation of the points, by Olivier Devillers.

Warning: A limitation of the program is that it assumes that the user's input coordinates are "reasonable" PostScript coordinates! Reasonable results will be achieved then if both X and Y coordinates are positive and range from 0 to 1000 or so, say. On the other hand, a user whose data is in the unit square will get a PostScript file which actually plots the entire image in a near infinitesimal and useless box! A reasonable fix is to rescale data so that it lies between 0 and 612. (The PostScript coordinates, by default, are in units of 1/72 inch, so 8.5 inches wide = 612.)

It would not be hard to correct the code so that the user can input data with any scaling whatsoever, while the program would (simple) just rescale it, or (better) insert the appropriate PostScript scaling commands in the plot file.

In any case, the program is more interesting for being a fairly clean embodiment of a Delaunay triangulation algorithm, and the author himself suggests that a user might profitably and easily modify the code to write out the information defining the triangulation.


delaunay_tree_2d < data.txt >
reads the point coordinates from data.txt and writes a PostScript image of the Delaunay triangulation to


DELAUNAY_TREE_2D is available in a C++ version.

Related Data and Programs:

DELAUNAY_LMAP_2D, a FORTRAN90 program which reads in a pointset and a linear map and writes out the Delaunay triangulation for the linearly transformed data.

GEOMPACK, a C++ library which computes the Delaunay triangulation or Voronoi diagram.

STRIPACK, a FORTRAN90 library which can compute the Delaunay triangulation of a set of points on a sphere.

TABLE_DELAUNAY, a C++ program which reads a file of 2d point coordinates and computes the Delaunay triangulation.

TABLE_VORONOI, a C++ program which can compute information about the Voronoi diagram of a set of points stored in a file.

TRIANGULATION_DISPLAY_OPENGL, a C++ program which reads files defining a triangulation and displays an image using Open GL.

TRIPACK, a FORTRAN90 library which can compute the Delaunay triangulation of a set of points.


Olivier Devillers


  1. a software download site at INRIA.
  2. Franz Aurenhammer,
    Voronoi diagrams - a study of a fundamental geometric data structure,
    ACM Computing Surveys,
    Volume 23, Number 3, pages 345-405, September 1991.
  3. Jean-Daniel Boissonnat, Monique Teillaud,
    On the randomized construction of the Delaunay tree,
    Theoretetical Computer Science,
    Volume 112, pages 339-354, 1993.
  4. Olivier Devillers, Stefan Meiser, Monique Teillaud,
    Fully dynamic Delaunay triangulation in logarithmic expected time per operation,
    Computational Geometry: Theory and Applications,
    Volume 2, Number 2, pages 55-80, 1992.
  5. Olivier Devillers, Robust and efficient implementation of the Delaunay tree,
    INRIA Research Report 1619, 1992.

Source Code:

Examples and Tests:

DEVILLERS_02_01000 is a set of 1000 points.

DIAMOND_02_00009 is a set of 9 points. Unfortunately, the data is scaled to lie in the unit box, so TABLE_SCALE was called to rescale both X and Y to lie between 0 and 612:

List of Routines:

You can go up one level to the C++ source codes.

Last revised on 16 March 2006.