spherepc (version 0.1.2)

PrincipalCircle: Principal circle on sphere

Description

This function fits a principal circle on sphere via gradient descent algorithm.

Usage

PrincipalCircle(data, step.size = 1e-3, thres = 1e-5, maxit = 10000)

Arguments

data

matrix or data frame consisting of spatial locations with two columns. Each row represents longitude and latitude.

step.size

step size of gradient descent algorithm. For convergence of the algorithm, step.size is recommended to be below 0.01.

thres

threshold of the stopping condition.

maxit

maximum number of iterations.

Value

three-dimensional vector.

Details

This function fits a principal circle on sphere via gradient descent algorithm. The function returns three-dimensional vectors whose components represent longitude and latitude of the center and the radius of the circle in regular order.

References

Jang-Hyun Kim, Jongmin Lee, Hee-Seok Oh (2020), Spherical principal curves <arXiv:2003.02578>.

See Also

GenerateCircle

Examples

# NOT RUN {
library(rgl)
library(sphereplot)
library(geosphere)
#### example 1: half-great circle data
circle <- GenerateCircle(c(150, 60), radius = pi/2)
half.great.circle <- circle[circle[, 1] < 0, , drop = FALSE]
sigma <- 2
half.great.circle <- half.great.circle + sigma * rnorm(nrow(half.great.circle))
## find a principal circle
# }
# NOT RUN {
PC <- PrincipalCircle(half.great.circle)
result <- GenerateCircle(PC[1:2], PC[3])
## plot
rgl.sphgrid()
rgl.sphpoints(half.great.circle, radius = 1, col = "blue", size = 12)
rgl.sphpoints(result, radius = 1, col = "red", size = 6)
# }
# NOT RUN {
#### example 2: circular data
n <- 700                            
x <- seq(-180, 180, length.out = n)
sigma <- 5                          
y <- 45 + sigma * rnorm(n)
simul.circle <- cbind(x, y)
## find a principal circle
PC <- PrincipalCircle(simul.circle)
result <- GenerateCircle(PC[1:2], PC[3])
## plot
rgl.sphgrid()
rgl.sphpoints(simul.circle, radius = 1, col = "blue", size = 12)
rgl.sphpoints(result, radius = 1, col = "red", size = 6)

#### example 3: earthquake data
data(Earthquake)
names(Earthquake)
earthquake <- cbind(Earthquake$longitude, Earthquake$latitude)   
# }
# NOT RUN {
PC <- PrincipalCircle(earthquake)
# }
# NOT RUN {
result <- GenerateCircle(PC[1:2], PC[3])
## plot
rgl.sphgrid(col.long = "black", col.lat = "black")
rgl.sphpoints(earthquake, radius = 1, col = "blue", size = 12)
rgl.sphpoints(result, radius = 1, col = "red", size = 6)
# }