Convert Cartesian coordinates to spherical coordinates — cartesian_to

This function converts Cartesian coordinates to spherical coordinates.

Usage

cartesian_to_spherical(x, byrow = TRUE)

Arguments

x: A matrix where each row represents a point in Cartesian coordinates.
byrow: logical. If TRUE (the default) the matrix is filled by rows, otherwise the matrix is filled by columns.

Value

A matrix where each row represents a point in spherical coordinates.

Details

The Cartesian coordinates (x, y, z) are converted to spherical coordinates (theta, phi). Theta represents the inclination angle (0 to pi), and phi represents the azimuth angle (0 to 2*pi).

Examples

#example1
cartesian_points1 <- matrix(c(1/sqrt(3), 1/sqrt(3), 1/sqrt(3),-1/sqrt(3), 1/sqrt(3), -1/sqrt(3)),
  ncol = 3, byrow = TRUE)
cartesian_to_spherical(cartesian_points1)
#>          theta       phi
#> [1,] 0.9553166 0.7853982
#> [2,] 2.1862760 2.3561945
#example2
cartesian_points2 <- matrix(c(1, 0, 0, 0, 1, 0, 0, 0, 1),ncol = 3, byrow = TRUE)
cartesian_to_spherical(cartesian_points2)
#>         theta      phi
#> [1,] 1.570796 0.000000
#> [2,] 1.570796 1.570796
#> [3,] 0.000000 0.000000