RiemCirc: A Generator of Nodes and Weights for Riemann Integration on the Circle

TL;DR

RiemCirc is a C++ tool that generates evenly distributed nodes and weights for numerical integration on the circle using Voronoi tessellation to define polygonal areas.

Contribution

It introduces a novel method for generating homogeneous node distributions and weights for circle integration based on Voronoi tessellation.

Findings

Produces homogeneous node distributions on the circle.

Calculates weights using polygonal Voronoi areas.

Facilitates accurate numerical quadrature on the circle.

Abstract

RiemCirc is a C++ program which allocates points inside the unit circle for numerical quadrature on the circle, aiming at homogeneous equidistant distribution. The weights of the quadrature rule are computed by the area of the tiles that surround these nodes. The shapes of the areas are polygonal, defined by Voronoi tessellation.