retistruct (version 0.8.0)

sphere.tri.area: Area of triangles on a sphere

Description

This uses L'Hullier's theorem to compute the spherical excess and hence the area of the spherical triangle.

Usage

sphere.tri.area(P, Tr)

Value

Vectors of areas of triangles in units of steradians

Arguments

P

2-column matrix of vertices of triangles given in spherical polar coordinates. Columns need to be labelled phi (latitude) and lambda (longitude).

Tr

3-column matrix of indices of rows of P giving triangulation

Author

David Sterratt

Examples

## Something that should be an eighth of a sphere, i.e. pi/2
P <- cbind(phi=c(0, 0, pi/2), lambda=c(0, pi/2, pi/2))
Tr <- cbind(1, 2, 3)
## The result of this should be 0.5
print(sphere.tri.area(P, Tr)/pi)

## Now a small triangle
P1 <- cbind(phi=c(0, 0, 0.01), lambda=c(0, 0.01, 0.01))
Tr1 <- cbind(1, 2, 3)
## The result of this should approximately 0.01^2/2
print(sphere.tri.area(P, Tr)/(0.01^2/2))

## Now check that it works for both
P <- rbind(P, P1)
Tr <- rbind(1:3, 4:6)
## Should have two components
print(sphere.tri.area(P, Tr))