TRIANGULATION
Triangulation of 2D data


TRIANGULATION, a C library which computes a triangulation of a set of points in 2D, and carries out various other related operations on triangulations of order 3 or 6.

The mesh is the collection of triangles. Each triangle is termed an "element". The points used to define the shape of the triangle (the corners, and sometimes a few more points) are called the "nodes".

Routines are available to:

Since triangulations are often used to define a finite element mesh, which in turn defines a sparse matrix, there are routines available which can define the sparse compressed column arrays needed for a sparse matrix associated with a mesh of order 3 or 6. The special case of the Taylor-Hood mixed element is also handled, which is essentially an order 6 grid counted twice and an order 3 grid that only uses the vertices of the order 6 grid.

Licensing:

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

Languages:

TRIANGULATION is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version.

Related Programs:

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

triangulation_test

TRIANGULATION_NODE_TO_ELEMENT, a C program which reads files describing a set of nodes, their triangulation, and the value of one or more quantities at each node, and outputs a file that averages the quantities for each element. This operation in effect creates an "order1" finite element model of the data.

TRIANGULATION_SVG, a C program which creates a Scalable Vector Graphics (SVG) image of a triangulation, which can be displayed by a web browser.

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.

References:

  1. Franz Aurenhammer,
    Voronoi diagrams - a study of a fundamental geometric data structure,
    ACM Computing Surveys,
    Volume 23, Number 3, September 1991, pages 345-405.
  2. Paul Bratley, Bennett Fox, Linus Schrage,
    A Guide to Simulation,
    Second Edition,
    Springer, 1987,
    ISBN: 0387964673.
  3. Marc deBerg, Marc Krevald, Mark Overmars, Otfried Schwarzkopf,
    Computational Geometry,
    Springer, 2000,
    ISBN: 3-540-65620-0.
  4. Barry Joe,
    GEOMPACK - a software package for the generation of meshes using geometric algorithms,
    Advances in Engineering Software,
    Volume 13, 1991, pages 325-331.
  5. Albert Nijenhuis, Herbert Wilf,
    Combinatorial Algorithms for Computers and Calculators,
    Second Edition,
    Academic Press, 1978,
    ISBN: 0-12-519260-6,
    LC: QA164.N54.
  6. Atsuyuki Okabe, Barry Boots, Kokichi Sugihara, Sung Nok Chiu,
    Spatial Tessellations: Concepts and Applications of Voronoi Diagrams,
    Second Edition,
    Wiley, 2000,
    ISBN: 0-471-98635-6,
    LC: QA278.2.O36.
  7. Joseph ORourke,
    Computational Geometry,
    Second Edition,
    Cambridge, 1998,
    ISBN: 0521649765,
    LC: QA448.D38.

Source Code:


Last revised 23 August 2019