Given a set of latitude and longitude coordinates representing a closed curve, output a gridded binary mask.
mask_dh = Curve2Mask (n, profile, np, [nprofile, sampling, centralmeridian])
dh_mask : integer, dimension (n, n*sampling)
: A Driscoll and Healy (1994) sampled grid describing the concentration region R. All elements on output will either be 1 (for inside the concentration region) or 0 (for outside R).
n : integer
: The number of latitudinal samples in dh_mask. The effective spherical harmonic bandwidth of this grid is L=n/2-1.
profile : float, dimension (nprofilein, 2)
: List of latitude [:,0] and longitude [:,1] coordinates in degrees specifying a single closed curve.
np : integer
: The value of the returned mask at the North pole (90N, 0E). If the North pole is outside of the concentration region, set this to 0; if it is inside the concentration region, set this to 1.
nprofile : optional, integer, default = nprofilein
: The number of coordinates in the curve profile.
sampling : optional, integer, default = 1
: For 1, dh_mask has n x n samples. For 2, dh_mask has n x 2n samples.
centralmeridian : optional, integer, default = 0
: If 1, the curve is assumed to pass through the central meridian: passing from < 360 degrees to > 0 degrees. The curve makes a complete circle about the planet in longitude.
Curve2Mask will take a list of latitude and longitude coordinates that represent a single closed curve, and output a mask mask_dh that contains 1s and 0s where the grid nodes are inside and outside of the curve, respectively. mask_dh must be sampled according to the Driscoll and Healy (1994) sampling theorem with n samples in latitude, and either possess n samples in longitude (sampling=1) or 2n samples in longitude (sampling=2). It is necessary to specify a single point as being inside or outside of the curve, and for this the value at the North pole (90N, 0E) must be specified as either 0 or 1.
This routine saves the three-term recursion factors and square roots of the integers the first time being called. If subsequent calls possess the same value of lmax, these will not be recomputed. If you wish to deallocate this memory, which is an array of length (lmax+1)*(lmax+2), recall this routine with lmax=-1.
Driscoll, J.R. and D.M. Healy, Computing Fourier transforms and convolutions on the 2-sphere, Adv. Appl. Math., 15, 202-250, 1994.