great_circle_line {tigers}

Great Circle Line

Description

This function calculates the coordinates of the line on the surface of a sphere between two points. All coordinates are in decimal degrees.

gcl is simply an alias.

Usage

great_circle_line(x0, y0, x1, y1, linear = FALSE, npoints = 100)
gcl(x0, y0, x1, y1, linear = FALSE, npoints = 100)

Arguments

x0, y0, x1, y1

the coordinates of the two points similar to segments.

linear

a logical value.

npoints

an integer giving the number of points where the coordinates are calculated (should be at least two).

Details

The interval between x0 and x1 is split into regular segments, then the latitudes are computed, by default, using a great circle formula (Chamberlain and Duquette, 2007).

If linear = TRUE, the coordinates are treated as linear (i.e., Euclidean).

Value

a numeric matrix with two columns and colnames 'x' and 'y'.

Author(s)

Emmanuel Paradis

References

Chamberlain, R. G. and Duquette, W. H. (2007) Some algorithms for polygons on a sphere. JPL Open Repository. <doi:2014/41271>

See Also

geod

Examples

X1 <- 3; Y1 <- 49 # Paris
X2 <- 101; Y2 <- 13 # Bangkok
## if (require(maps))  map() else
plot(c(-180, 180), c(-90, 90), "n")
text(X1, Y1, "Paris")
text(X2, Y2, "Bangkok")
lines(gcl(X1, Y1, X2, Y2), col = "blue", lwd = 2)
lines(gcl(X1, Y1, X2, Y2, linear = TRUE), col = "red", lwd = 2)

## assess the error implied by using linear interpolation for the
## diagonal of a 1 degree by 1 degree square near the equator:
xya <- gcl(0, 0, 1, 1)
xyb <- gcl(0, 0, 1, 1, TRUE)
## the error in degrees:
error <- xya[, "y"] - xyb[, "y"]
plot(xya[, "x"], error * 3600, "o",
     xlab = "Longitude (degrees)", ylab = "Error (arc-seconds)")

## max (vertical) distance between these 2 curves:
geod(c(0.5, 0.5), c(0.5, 0.5 + max(error))) # ~6.5 m
## NOTE: the actual shortest (orthogonal) distance
## between these two curves is ~4.6 m
## (assuming the vertical distance helps to define a rectangular
## triangle, we have: 0.5 * sqrt(6.5^2 * 2)) ~ 4.6)

## NOTE2: dividing the coordinates by 10 results in dividing
## these deviations by 1000