Skip to content

Delaunay and Constrained Delaunay Triangulations in Java, providing high-performance utilities for modeling surfaces with support for Lidar LAS files, Digital Elevation Models (DEM), finite element analysis, path planning, natural neighbor interpolation, and other applications of Triangulated Irregular Networks (TIN)

Switch branches/tags

Latest commit


Git stats


Failed to load latest commit information.
Latest commit message
Commit time


High-Performance 2D Delaunay Triangulation and Related Utilities Written in Java


The Tinfour compiled binary files (Jar files) are available at Sonatype's Maven Central Repository or the Maven Central Repository

We are migrating some of our documentation to a separate project. Visit TinfourDocs to check it out.

Delaunay Triangulation

The Delaunay Triangulation defines an optimal form for organizing unstructured or semi-random sample points into a triangular mesh. That optimality makes the Delaunay Triangulation a useful tool for interpolation, grid construction, and surface analysis.

Surface Models using TINs


Tinfour is a software library written in Java that provides tools for constructing and applying Triangulated Irregular Networks (TINs) that conform to the Delaunay criterion. Because it is intended to process large data sets, the implementation gives a great deal of attention to performance and memory use. On a conventional laptop, Tinfour is capable of processing sample points at a rate of better than one million points per second.

The Tinfour source code includes extensive documentation. This project also includes an informal paper that describes the uses, algorithms, and implementation of the software with enough detail to support potential developers who may wish to contribute code or employ Tinfour in their own work. For more details, see Data Elements and Algorithms for the Tinfour Libary. If you would like to discuss the Tinfour project or tell us about your own work, feel free to visit The Tinfour Discussion Page.

The Tinfour Viewer

When someone first sees a project like Tinfour, they might reasonably ask that most thorny of questions "What is it good for?" To answer that question, this library includes a simple demonstration application called Tinfour Viewer that allows the user to exercise the major functions of the Tinfour library. Using Tinfour Viewer, the user can explore data sets ranging in size from just a few points up to the millions.

Here's a screenshot from the Tinfour Viewer showing a collection of Lidar elevation data collected over a section of Interstate highway in the U.S. Northeast.

Lidar over Guilford, CT

The Tinfour Viewer application is intended to show how the Tinfour library could be integrated into a full-featured GIS application or other analysis tool. It's a simple implementation with a minimum of features. Instructions for setting up and running the Tinfour Viewer application are provided at the wiki page Tinfour Execution from the Command Line. Our wiki page attempts to simplify the process of running Tinfour demostration applications as much as possible. It also explains some of the nuances of the launch procedures and provides the details you will need to set up a command window and run the command-line variations for all the various Tinfour applications.

To run the Tinfour software, you must have Java installed on your system. If you do not have Java installed on your computer, you may download an installer for free from Oracle Corporation, Java Downloads.

Sources of Data

Lidar is a system for collecting surface elevation using laser measuring devices mounted on low flying aircraft. It's pretty amazing technology. There are excellent sources of Lidar data to be had for free, you might start at Free LiDAR Data Sources or the USGS 3D Elevation Program. The Commonwealth of Pennsylvania was one of the first states to collect and post a comprehensive survey of lidar data, and they did the job right... Their site includes not just lidar data, but the supporting breakline files (Shapefiles), multi-spectral imagery, and project metadata (including Dewberry reports). Visit this excellent resource at PAMAP Lidar Elevation Data.

If you just want to download a single Lidar file and view it, we recommend PAMAP Tile 4100133PAS which can be found at At 36.7 megabytes, the PAMAP file isn't dainty. But it does contain interesting land features and sufficient detail to exercise the major functions of the viewer.

A short demo

Recently, we found an earlier Delaunay triangulation project by "The Mad Creator" (Bill Dwyer) that provided a four-line demo. It was such a elegant way of introducing the package, that we decided to include one of our own.

public static void main(String []args) throws Exception {
    IncrementalTin tin = new IncrementalTin(1.0);
    List<Vertex>vertexList = TestVertices.makeRandomVertices(100, 0);
    tin.add(vertexList, null);
    TinRenderingUtility.drawTin(tin, 500, 500, new File("tin.png"));

Does Tinfour require external project dependencies?

The core Tinfour module has no external dependencies. All it requires is the standard Java API. Thus, you can integrate the core classes into your own applications without adding unnecessary object code to your software.

The associated, extended-functionality modules do depend on object code from external projects. These include modules that can read data from Geographic Information System (GIS) sources (Shapefiles and airborne Lidar LAS files) and those that perform advanced mathematical and statistical analysis. These modules and dependencies are described in the Tinfour wiki page Tinfour Builds and Dependencies.

What version of Java is required for Tinfour?

Tinfour is compiled under Java 8.

Configuring Tinfour in an IDE

In terms of its software and package organization, Tinfour has a relatively simple structure, so opening it in an Integrated Development Environment (IDE) is straight forward. The major Java IDEs (Netbeans, Eclipse, and IntelliJ) all support direct access to Maven projects. If you have one of these IDE's you can simply load the Tinfour project and run with it. All work fine. More hints and background information on configuring Tinfour for use in an IDE are included in the Tinfour wiki page Tinfour Builds and Dependencies.

Current Work

Development work on the Constrained Conforming Delaunay Triangulation is now complete.

Development work for the next release of Tinfour will focus on the introduction of Delaunay Refinement. Delaunay Refinement is a technique for improving the quality of the triangles formed by a Delaunay Triangulation through the introduction of synthetic vertices at well-chosen positions. Refinement techniques are particularly useful in areas near the boundaries of constraints or near the permimeter of a triangulation. These areas are often prone to the formation of "skinny" triangles (triangles with two small angles and one very large angle).

Currently, we are investigating the use of Ruppert's Algorithm as a refinement technique, though other refinement techniques do exist (such as Chew's Second Delaunay Refinement Algorithm).

For more detail about the Tinfour project development plans, see the Tinfour Project Status and Roadmap page.

Our Companion Project

Visit the Gridfour Software Project to learn more about our companion software project dedicated to creating open-source software tools for raster (grid) data sets.


Finally, the whole point of working on a project like Tinfour is to see it employed to do something useful. To that end, I welcome ideas, requests, and recommendations for analysis tools and applications that would benefit the open source and scientific communities. Got something to say? You can contact the Tinfour project at


Delaunay and Constrained Delaunay Triangulations in Java, providing high-performance utilities for modeling surfaces with support for Lidar LAS files, Digital Elevation Models (DEM), finite element analysis, path planning, natural neighbor interpolation, and other applications of Triangulated Irregular Networks (TIN)








No packages published