Generalized barycentric coordinates (GBC) Ver. 1.0.2

Description

Implementation of some generalized barycentric coordinates in R2.

This package includes:

1. Pointwise coordinates:

A. Coordinates for polygons:

• Bilinear coordinates
• Wachspress coordinates
• Discrete harmonic coordinates
• Mean value coordinates
• Positive mean value coordinates
• Cubic mean value coordinates
• Three-point coordinates
• Metric coordinates
• Poisson coordinates
• Gordon-Wixom coordinates
• Positive Gordon-Wixom coordinates
• Maximum entropy coordinates

B. Coordinates for scattered points:

• Affine coordinates
• Sibson coordinates
• Laplace coordinates

2. Mesh-based coordinates:

A. Coordinates for polygons:

• Harmonic coordinates
• Local barycentric coordinates

I tried to keep the code as stand alone as possible, but many classes still have quite a few dependencies. However, all these dependencies are included in the package and do not require any special treatment like building or compiling. At the beginning of each file I also indicate which dependencies the corresponding class has.

NOTE: This code has been tested only on Mac OS!

Run the code

In order to run the code, do the following:

1. Install macports
2. Open main.cpp and edit the path to the folder with images on the line 142
3. Open terminal and type the following:

  sudo port install cmake

  cd path_to_your_folder_with_gbc_package/2d/

  mkdir bin

  cd bin

  cmake -DCMAKE_BUILD_TYPE=Debug ..

  make

  ./gbc

For the release version use instead:

cmake -DCMAKE_BUILD_TYPE=Release ..

NOTE: If the output result shows FAILED for some tests, it is ok. It happens because the corresponding coordinate functions do not satisfy some theoretical properties of generalized barycentric coordinates!

Simple example

// Polygon.
std::vector<VertexR2> poly(4);

poly[0] = VertexR2(0.1, 0.1);
poly[1] = VertexR2(1.0, 0.0);
poly[2] = VertexR2(0.9, 0.9);
poly[3] = VertexR2(0.2, 1.0);

// Evaluation point.
VertexR2 centre(0.5, 0.5);

// Storage for the computed barycentric coordinates.
std::vector<double> b;

// Compute mean value coordinates.
MeanValueR2 mvc(poly);
mvc.compute(centre, b);

// Output the resulting coordinates.
std::cout << "\nMean value coordinates: ";
for (size_t i = 0; i < b.size(); ++i) std::cout << b[i] << " ";
std::cout << "\n\n";

NOTE: For more examples see main.cpp!

Visual output

This package allows you to save the coordinate functions in the eps format, for example:

Wachspress coordinates

Mean value coordinates

Metric coordinates

Harmonic coordinates

Bugs

Please note that some parts of this code are not optimized and may bug. I only tested it for the specific cases that I used during the last years of my Ph.D. That is why, if you find any bugs, please report them to me, and I will try to fix them as soon as possible!