| Title: | Algorithm for Computation of the Intersection Areas of N Circles |
|---|---|
| Description: | Implementation of Librino, Levorato, and Zorzi (2014) <doi:10.1002/wcm.2305> algorithm for computation of the intersection areas of an arbitrary number of circles. |
| Authors: | Hugo Salinas [aut, cre] |
| Maintainer: | Hugo Salinas <[email protected]> |
| License: | MIT + file LICENSE |
| Version: | 1.1 |
| Built: | 2025-02-13 03:25:42 UTC |
| Source: | https://github.com/hugosal/circlesintersections |
'intersection_two_circles()' Function for the the area of intersection of two circles.
'intersection_three_circles()' Function for the area of intersection of three circles.
intersection_two_circles(centers_x, centers_y, radii) intersection_three_circles(centers_x, centers_y, radii)intersection_two_circles(centers_x, centers_y, radii) intersection_three_circles(centers_x, centers_y, radii)
centers_x, centers_y, radii
|
Numeric vectors of length N with the x, y coordinates of the center, and the radius of the circles. |
The area of intersection of the circles is computed.
This function computes the exclusive areas of intersection of N circles.
Librino_N(centers_x, centers_y, radii)Librino_N(centers_x, centers_y, radii)
centers_x, centers_y, radii
|
Numeric vectors of length N with the x, y coordinates of the center, and the radius of the circles. |
This is an implementation of Librino, Levorato, and Zorzi (2014) algorithm for computation of the intersection areas of an arbitrary number of circles.
A list of length N containing the areas of exclusive intersection. The position of each element in the list indicates the number of intersecting circles. The first element of the list corresponds to the area of non-overlap of every circle, the second element is the pairwise area of intersection. Up to the last element of the list which corresponds to the area of intersection of all circles. Each of the elements of the list is a named numeric vector corresponding to the area of intersection between a set of circles. The names of the vector indicate the number of the circles in the intersection.
Hugo Salinas [email protected].
Librino, F., Levorato, M., & Zorzi, M. (2014). An algorithmic solution for computing circle intersection areas and its applications to wireless communications. Wireless Communications and Mobile Computing, 14, 1672–1690.
# Example of intersection areas including a Reuleaux triangle x <- c(0, 1, 0.5) y <- c(0, 0, sqrt(1-0.5**2)) radii <- c(1, 1, 1) intersections <- Librino_N(centers_x = x, centers_y = y, radii = radii) intersections # Example with more circles x2 <- c(0, 4, 2, 4, 5) y2 <- c(1, 5, 4, 2, 1) radii2 <- c(1, 4 ,2, 2, 1) intersections2 <- Librino_N(centers_x = x2, centers_y = y2, radii = radii2) intersections2# Example of intersection areas including a Reuleaux triangle x <- c(0, 1, 0.5) y <- c(0, 0, sqrt(1-0.5**2)) radii <- c(1, 1, 1) intersections <- Librino_N(centers_x = x, centers_y = y, radii = radii) intersections # Example with more circles x2 <- c(0, 4, 2, 4, 5) y2 <- c(1, 5, 4, 2, 1) radii2 <- c(1, 4 ,2, 2, 1) intersections2 <- Librino_N(centers_x = x2, centers_y = y2, radii = radii2) intersections2
Checks if the sum of the areas of intersection of each circle adds to the total area of the circle, as it should.
validate_Librino(librino, radii)validate_Librino(librino, radii)
librino |
A named numeric vector with the from resulting from [Librino_N()] |
radii |
Numeric vectors of length N with the radius of each circle. |
TRUE if all the partitions of the circles add to their total area, else a numeric vector with the number of the circles that failed this test.
Hugo Salinas [email protected].
# Example of intersection areas including a Reuleaux triangle x <- c(0, 1, 0.5) y <-c(0, 0, sqrt(1-0.5**2)) radii <- c(1, 1, 1) intersections <- Librino_N(centers_x = x, centers_y = y, radii = radii) validate_Librino(librino = unlist(intersections, use.names = TRUE), radii = radii)# Example of intersection areas including a Reuleaux triangle x <- c(0, 1, 0.5) y <-c(0, 0, sqrt(1-0.5**2)) radii <- c(1, 1, 1) intersections <- Librino_N(centers_x = x, centers_y = y, radii = radii) validate_Librino(librino = unlist(intersections, use.names = TRUE), radii = radii)