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 #include #include #include "map.h" int Xgilbert(struct place *p, double *x, double *y) { /* the interesting part - map the sphere onto a hemisphere */ struct place q; q.nlat.s = tan(0.5*(p->nlat.l)); if(q.nlat.s > 1) q.nlat.s = 1; if(q.nlat.s < -1) q.nlat.s = -1; q.nlat.c = sqrt(1 - q.nlat.s*q.nlat.s); q.wlon.l = p->wlon.l/2; sincos(&q.wlon); /* the dull part: present the hemisphere orthogrpahically */ *y = q.nlat.s; *x = -q.wlon.s*q.nlat.c; return(1); } proj gilbert(void) { return(Xgilbert); } /* derivation of the interesting part: map the sphere onto the plane by stereographic projection; map the plane onto a half plane by sqrt; map the half plane back to the sphere by stereographic projection n,w are original lat and lon r is stereographic radius primes are transformed versions r = cos(n)/(1+sin(n)) r' = sqrt(r) = cos(n')/(1+sin(n')) r'^2 = (1-sin(n')^2)/(1+sin(n')^2) = cos(n)/(1+sin(n)) this is a linear equation for sin n', with solution sin n' = (1+sin(n)-cos(n))/(1+sin(n)+cos(n)) use standard formula: tan x/2 = (1-cos x)/sin x = sin x/(1+cos x) to show that the right side of the last equation is tan(n/2) */