VILTRUM: Varied Integration Layouts for arbiTRary integrals in a Unified Manner - A C++17 header-only library that provides a set of numerical integration routines.

viltrum is a header-only library and has no external dependencies, so installation is rather simple (it does not require any compilation process). You just need to download the library in a specific folder:

folder> git clone https://github.com/adolfomunoz/viltrum.git

Then make sure folder is within the included directories (-Ifolder parameter in g++, include_directories("folder") in CMake) and include it from C++.

#include <viltrum/viltrum.h>

That would be enough to use all the features of the library. There are other alternatives that might be more comfortable for you, see them here. There is a CMake-based building system for several example and test executable files that automatically downloads external dependencies and compiles all executables but it is not needed for the libray's usage.

Integrating a function in a specific n-dimensional range is rather simple. You need the following information:

• An integrator, a numerical integration method, for which there are several to choose from.
• An integrand, a function to be integrated. It's only parameter has to be a std::array<F,N>, where F is a floating point number and N is the number of dimensions. There are several ways in which such integrand can be defined.
• A range, the integration domain, that is composed on two std::array<F,N> marking the limits of the potentially multidimensional integration domain, which can be defined in different ways.

Example:

float sphere(const std::array<float,3>& x) {
    return (x[0]*x[0]+x[1]*x[1]+x[2]*x[2])<=1.0f?1.0f:0.0f;
}
int main() {
    unsigned long samples = 1024;
    auto method = viltrum::integrator_monte_carlo_uniform(samples);
    auto range = viltrum::range(std::array<float,3>{-1.0f,-1.0f,-1.0f},std::array<float,3>{1.0f,1.0f,1.0f});
    std::cout<<"Sphere volume = "<<method.integrate(sphere,range)<<"\n";
}

This code is released under the GPL v3. Additionally, if you are using this code in academic research, we would be grateful if you cited our paper, for which we generated with this source code:

@article{crespo21primary,
	title = {Primary-Space Adaptive Control Variates using Piecewise-Polynomial Approximations.},
	year = {2021},
	journal = {ACM Transactions on Graphics},
	author = {Crespo, Miguel and Jarabo, Adrian and Mu\~{n}oz, Adolfo},
    volume = {40},
    number = {3},
    issn = {0730-0301},
    url = {https://doi.org/10.1145/3450627},
    doi = {10.1145/3450627},
    issue_date = {July 2021},
    month = jul,
    articleno = {25},
    numpages = {15},
    keywords = {adaptive quadrature, numerical integration, control variates, rendering, piecewise polynomial}
}