Determine Adjacent Neighbors in Triangulation

TRIG_TO_NEIB, a C program which reads files defining the nodes and elements of a triangulation, and computes a list of the node neighbors, and, optionally, information about the Voronoi decomposition of the region, by Lili Ju.

The input files are a pair of "NODE" and "ELE" files that use a format specified by the triangle() program.

For each node N1, its set of "neighbors" includes every node N2 which occurs in some element that also includes node N1.

The output node neighbor file lists, for each node, the number of node neighbors, followed by the neighbors in counter clockwise order.

An image of the triangulation can be made using the showme program, or the triangle_display program.


trig_to_neib nodes.txt elements.txt neib.txt voro.txt


The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.


TRIG_TO_NEIB is available in a C version.

Related Data and Programs:

SHOWME, a C program which uses the X Window library to display triangulatons, by Jonathan Shewchuk.

TRIANGLE, a C program which computes a triangulation of a geometric region, by Jonathan Shewchuk.

TRIANGLE_FILES, a data directory of examples of files used by the triangle and showme programs.

TRIANGULATION, a C library which performs various operations on order 3 (linear) or order 6 (quadratic) triangulations.

TRIANGULATION_TRIANGLE_NEIGHBORS, a C program which reads data defining a triangulation, determines the neighboring triangles of each triangle, and writes that information to a file.



Lili Ju


  1. Lili Ju,
    Conforming centroidal Voronoi Delaunay triangulation for quality mesh generation,
    International Journal of Numerical Analysis and Modeling,
    Volume 4, Number 3-4, 2007, pages 531-547.
  2. Robert Renka,
    Algorithm 751: TRIPACK, A Constrained Two-Dimensional Delaunay Triangulation Package,
    ACM Transactions on Mathematical Software,
    Volume 22, Number 1, March 1996, pages 1-8.
  3. Jonathan Shewchuk,
    Triangle: Engineering a 2D Quality Mesh Generator and Delaunay Triangulator,
    in Applied Computational Geometry: Towards Geometric Engineering,
    edited by Ming Lin, Dinesh Manocha,
    Lecture Notes in Computer Science, Volume 1148,
    Springer, 1996,
    ISBN: 354061785X,
    LC: QA448.D38.A635.

Source Code:

Last revised on 23 August 2019.