Volume computation and sampling


The volesti package provides R with functions for volume estimation and sampling. In particular, it provides an R interface for the C++ library volesti.

volesti computes approximations of volume of polytopes given as a set of points or linear inequalities or as a Minkowski sum of segments (zonotopes). There are two algorithms for volume approximation as well as algorithms for sampling, rounding and rotating polytopes.

Download and install



For more details, features, examples and references you can read the documentation.


Copyright (c) 2012-2019 Vissarion Fisikopoulos
Copyright (c) 2018-2019 Apostolos Chalkis

You may redistribute or modify the software under the GNU Lesser General Public License as published by Free Software Foundation, either version 3 of the License, or (at your option) any later version. It is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY.

Main development by Vissarion Fisikopoulos while he was affiliated with University of Athens (UoA, Greece) and University of Brussels (ULB, Belgium), and Chalkis Apostolos affiliated with University of Athens. Part of the development was done while A.Chalkis (as student) and V.Fisikopoulos (as mentor) were participating in Google Summer of Code 2018 program.


  1. I.Z. Emiris and V. Fisikopoulos, Efficient random-walk methods for approximating polytope volume, In Proc. ACM Symposium on Computational Geometry, Kyoto, Japan, p.318-325, 2014.
  2. I.Z. Emiris and V. Fisikopoulos, Practical polytope volume approximation, ACM Transactions on Mathematical Software, vol 44, issue 4, 2018.
  3. L. Cales, A. Chalkis, I.Z. Emiris, V. Fisikopoulos, Practical volume computation of structured convex bodies, and an application to modeling portfolio dependencies and financial crises, Proc. of Symposium on Computational Geometry, Budapest, Hungary, 2018.