| Type: | Package |
| Title: | Algorithm for Computation of the Intersection Areas of N Circles |
| Version: | 1.1 |
| 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. |
| License: | MIT + file LICENSE |
| Encoding: | UTF-8 |
| BugReports: | https://github.com/hugosal/CirclesIntersections/issues |
| URL: | https://github.com/hugosal/CirclesIntersections |
| RoxygenNote: | 7.2.0 |
| NeedsCompilation: | no |
| Packaged: | 2023-02-23 08:58:42 UTC; hmatus |
| Author: | Hugo Salinas 
[aut, cre] |
| Maintainer: | Hugo Salinas <hugosal@comunidad.unam.mx> |
| Repository: | CRAN |
| Date/Publication: | 2023-02-23 11:00:02 UTC |
Implementation of Librino's algorithm for computing circle intersection areas
Description
This function computes the exclusive areas of intersection of N circles.
Usage
Librino_N(centers_x, centers_y, radii)
Arguments
centers_x, centers_y, radii |
Numeric vectors of length N with the x, y coordinates of the center, and the radius of the circles. |
Details
This is an implementation of Librino, Levorato, and Zorzi (2014) algorithm for computation of the intersection areas of an arbitrary number of circles.
Value
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.
Author(s)
Hugo Salinas hugosal@comunidad.unam.mx.
References
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.
Examples
# 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
Auxiliary functions for computing circle intersection areas
Description
'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.
Usage
intersection_two_circles(centers_x, centers_y, radii)
intersection_three_circles(centers_x, centers_y, radii)
Arguments
centers_x, centers_y, radii |
Numeric vectors of length N with the x, y coordinates of the center, and the radius of the circles. |
Value
The area of intersection of the circles is computed.
Simple validation test of the output of Librino_N()
Description
Checks if the sum of the areas of intersection of each circle adds to the total area of the circle, as it should.
Usage
validate_Librino(librino, radii)
Arguments
librino |
A named numeric vector with the from resulting from [Librino_N()] |
radii |
Numeric vectors of length N with the radius of each circle. |
Value
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.
Author(s)
Hugo Salinas hugosal@comunidad.unam.mx.
Examples
# 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)