C++ examples of Fade2D Fade2D contains a collection of small, self-contained C++ examples. Each example demonstrates step by step for a certain topic how to apply the library practically. For example, the goal of this very first example is to show you how to compile C++ source code with Fade2D and how to create and…

# Author: Bernhard Kornberger

Fade2D is a numerically robust C++ Delaunay triangulation library. But it is nevertheless extremely fast. Certainly you can verify it on your own hardware with the below Delaunay triangulation benchmark. Benchmark Code Step 1 in the above code calls Fade_2D::setNumCPU(int numCPU) to enable multithreading. Possible values for numCPU are: numCPU>1 specifies the number of cpu’s…

This article has two goals: First, it shows how you can access the elements of a triangulation. Second, it shows how you can draw them. Because development is much easier when you can visualize your work. Preparing a triangulation Let’s prepare and draw a simple triangulation for this demo: In Step 1 we fill the…

## Constraint Edges – Example3

When you triangulate just the vertices of a polygon, it is not guaranteed that its edges are edges of the Delaunay triagulation. But you can insert them as Constraint Edges as demonstrated for a 2D triangulation and one segment below. Similarly you can insert breaklines into 2.5D triangle meshes, see Breaklines, ISO Contours and the…

## Polygons and Zones – Example4

This is the right example if you want to triangulate polygons or perform polygon clipping. In Fade, a Zone2 object defines a specific area of triangulation. It allows you to combine shapes using the Boolean set operations union, difference, symmetric difference and intersection. The result is again a zone whose triangles, contour and area can…

Polygon Clipping, Boolean Set Operations Fade provides polygon clipping and functions to combine shapes through the boolean operations: Union (A OR B) Intersection (A AND B) Difference (A NOT B) Symmetric Difference (A XOR B) You can find the C++ source code for the polygon clipping demo in examples_2D/ex5_booleanOps.cpp in the Fade download. Creating two…

Boolean operations on Polygons with Holes can be difficult to implement. Thus the present example examples_2D/ex6_booleanOps2.cpp consists of ready-made C++ source code that handles arbitrary shapes (convex or non-convex, with or without holes). So feel free to use it in your project. You might also want to check the previous Example5. For example, it demonstrates…

The term Delaunay meshing does not mean simply creating a Delaunay mesh on points, but it is about Quality Meshing i.e., creating a Delaunay mesh with triangles that have a very specific quality. This is generally achieved by adding points, that is, by refining an existing triangulation. As always you can find the below source…

A frequently asked question is how to export a triangulation as a list of points and indices. Up to now this could be done with the help of custom indices and it still works. But since Fade v1.84 there is an explicit solution for this task, which is also memory efficient, because it releases the…

When coding geometry, numerical errors and unexpected geometric settings occur frequently. Thus automated software testing with random geometric data is essential. But for example creating random polygons without self-intersection is not trivial at all. Therefore the module testDataGenerators is provided to create repeatable sequences of random geometric objects for software testing and debugging. These are…

Fade is fast and most of the time you will not need progress updates at all. But for very large triangulations you may still want to connect your own progress bar to Fade2D’s update mechanism. Your own Progress Receiver Class Create some custom class that derives from MsgBase so that it can receive messages from…

Manually saving and loading a triangulation is difficult. This is especially true when there are millions of elements and it must be fast. For this reason, there are functions in Fade to support you in saving and loading a triangulation, it’s zones and constraint edges. The contained file “examples_2D/ex11_save_and_load.cpp” provides simple demo source code for…

The Voronoi diagram (Wikipedia) of a point set is the dual graph of its Delaunay triangulation. It divides the plane into convex regions, so that each region is closest to one point of the set. There is an incredible number of applications for the Voronoi diagram so many scientists and engineers are familiar with this…

2.5D Delaunay triangulations (TIN – Triangulated Irregular Networks) are like a 2D Delaunay triangulation, but with elevated points. This article describes the optional simplification of point clouds from LiDAR scans and surface metrology data using adaptive and grid-based clustering methods. Further it shows how to triangulate point clouds in a memory-efficient way and how to…

In this example, we will flip edges in an unnatural looking triangulation to better match its valleys and ridges. Further we will use Fade’s Weighted Laplacian smoothing technique to improve the quality of a noisy triangle mesh. And finally we address an annoying problem, namely bad shaped triangles at the boundary of a triangulation. We…

In the field of land surveying constraint edges are maybe better known as “breaklines”. Similarly to the 2D case you can insert them into the triangle mesh, forcing segment subdivision or not. In addition you can insert a segment with its original height or you can adjust its height to the triangulation. This results in…

The Segment Checker computes intersections of 2D or 2.5D line segments. But in contrast to 3D two line segments are considered to intersect when their 2D projections in the xy-plane intersect. In other words, even if the involved segments are at different heights. The Segment Checker is fast and robust against degenerate and glancing intersections.…

## Cut and Fill Volumes in C++

Cut And Fill (Wikipedia) Earthwork volume computations for C++. The library module Cut-And-Fill takes two overlapping surfaces and computes the volume between. The result is a set of volumes where soil must be filled or where material must be digged off to turn one surface into the other one. Example Source Code – Basic Usage…