Derivation of an Algorithm for Calculation of the Intersection Area of a Circle with a Grid with Finite Fill Factor

TL;DR

This paper presents an exact algorithm for calculating the intersection area between a circle and a grid with finite fill factor, improving precision over common approximation methods in applications like imaging sensors and tiled surfaces.

Contribution

It introduces a novel geometric algorithm for precise intersection area calculation, surpassing typical approximation techniques used in related fields.

Findings

Algorithm provides exact intersection areas

Applicable to real-world grid structures like CCDs and tiles

Enhances accuracy in geometric computations

Abstract

The problem deals with an exact calculation of the intersection area of a circle arbitrary placed on a grid of square shaped elements with gaps between them (finite fill factor). Usually an approximation is used for the calculation of the intersection area of the circle and the squares of the grid. We analyze the geometry of the problem and derive an algorithm for the exact computation of the intersection areas. The results of the analysis are summarized in the tally sheet. In a real world example this might be a CCD or CMOS chip, or the tile structure of a floor.