C++ Examples for Delaunay Triangulation – Getting Started (0)

Welcome to our guide to Delaunay triangulation with C++. In this article, we’ll introduce you to the Fade2D library and show you how to perform a basic Delaunay triangulation on four points. This article serves as both an overview of the library and a practical example to get you started.

Fade2D is a powerful library for Delaunay triangulation, and we’ve prepared a series of concise C++ examples to help you get started. The below example collections showcase the library’s practical applications for specific tasks:

• C++ Examples for 2D triangulations and Voronoi diagrams
• C++ Examples for 2.5D triangulations and meshing algorithms
• Examples from practice

All described example source codes are included in the download package.

Point Cloud Properties: 2D vs. 2.5D vs. 3D

Before we dive into the first example, let’s clarify the dimensions:

• 2D: The Fade2D SDK is designed for 2D Delaunay triangulation in the xy-plane. It offers features like constraint edges, zones, and boolean operations on zones.
• 2.5D: Similar to Fade2D, Fade2.5D performs Delaunay triangulation but for lifted points. It includes a z-coordinate and additional algorithms for land surveying tasks.
• 3D: For 3D point clouds, there are two libraries available – Fade3D, which produces tetrahedral meshes, and WOF, which generates 3D triangle meshes

The distinction between 2.5D and 3D is that in 2.5D, each (x, y) coordinate pair corresponds to a single z-coordinate, commonly employed for terrain and height data. In contrast, 3D encompasses surfaces with multiple z-coordinates per (x, y) pair, even for straightforward objects like spheres.

Example 0: HelloTriangulation

Get started quickly with this fundamental Delaunay triangulation example in C++. This code demonstrates the basics, equivalent to a “HelloWorld” program:

// An empty triangulation
Fade_2D dt;
// 4 points
Point2 p0(0.0,0.0);
Point2 p1(1.0,0.0);
Point2 p2(0.5,2.0);
Point2 p3(0.5,0.5);
// Insert the points
dt.insert(p0);
dt.insert(p1);
dt.insert(p2);
dt.insert(p3);
// Draw as postscript graphic
dt.show("example0.ps");

This concise code initializes a Fade_2D object, defines four points, inserts them into the triangulation, and generates a postscript graphic of the resulting triangulation. It’s the perfect starting point for your Delaunay triangulation journey.

If you plan to use Fade2.5D, you can jump right into those examples. Nevertheless, you’re welcome to return to the 2D examples at any time to solidify the fundamental concepts that also apply to Fade2.5D.

# Choose a matching distribution below:
# DISTRO :=../lib_centos6.4_${ARCHITECTURE}
# DISTRO :=../lib_ubuntu14.04_${ARCHITECTURE}
# DISTRO :=../lib_fedora24_${ARCHITECTURE}
DISTRO :=../lib_ubuntu22.04_${ARCHITECTURE}
# DISTRO :=../lib_APPLE
# DISTRO :=../lib_raspberry_armv6l
# DISTRO :=../lib_raspberry_armv7l

The next example benchmarks the performance of Fade on your computer.